Category: Timeline Stories

The French Jesuit mathematician Claude François Milliet Dechales (1621–1678) was best remembered for his book Cursus seu mundus mathematicus, a complete course of mathematics, published in Lyon in 1674. Dechales published also several other books, and in one of them, devoted to the principles of navigation—L’ art de naviger demontré par principes & confirmé par plusieurs observations tirées de l’experience, published in Paris in 1677, he described a small counting device with a ratchet wheel as input and analog display indicators.

The counting device of Dechales is described in a section for the calculation of distances, on pages 191, 192, and 193 (see page 192 below). Its purpose is to measure the force of the wind.

The horizontal wheel, one or two feet in diameter (marked with C on the upper drawing), composed of small cone-shaped wings, rotates according to the force of the wind. The motion from wheel C is transferred to the inner counting wheels D, G, K, etc., connected to display indicators N, O, P.

Biography of Claude Dechales

Claude François Milliet Dechales (aka Milliet de Challes, or Deschales), was born in 1621 in Chambéry, Savoy. He was the youngest son (of three) of Hector Milliet, Baron de Challes and d’Arvillars (1568-1642), and his second wife Madeleine de Montchenu (1586-1651).

Claude’s grandfather, Louis Milliet (1527-1599) was a jurisconsult, first president of the Senate of Savoy, Grand Chancellor, and ambassador. He obtained the title of Baron in 1569, buying the seigneuries of Faverges, then of Challes.

Claude’s father, Hector Milliet, became Baron de Challes in 1618, then he acquired the lordship of Arvillars in 1628, and took the name Milliet d’Arvillars. He was the first president of the Chamber of Accounts of Savoy, then the first president of the Sovereign Senate of Savoy and ambassador.

Claude’s elder brothers Jean Louis (1613-1675) and Sylvestre (1616-1685) inherited from his father noble titles Marquis de Challes and Marquis d’Arvillars, but Claude choose a religious and scholarly career. At the age of 15 (21 September 1636), he entered the Jesuit Order. By the time Dechales entered the Order, it contained over 16000 men. The main task of the Jesuits was education, but the next most important task was missionary work throughout the world.

After spending some 10 years in education (as a full Jesuit he would have had both the equivalent of a B.A. within the order, and a doctorate in theology), in the middle 1640s Dechales was sent as a Jesuit missionary to the Ottoman Empire, where he taught letters in the schools of his order for nine years. After his return to France around 1656, Dechales lectured at Jesuit colleges, first in Paris where for four years he taught at the Collège de Clermont. Then he taught philosophy, mathematics, and theology at College de la Trinite de Lyon and was a rector at Chambéry. From Chambéry he went to Marseilles, where King Louis XIV appointed him Royal Professor of Hydrography. In Marseilles he taught navigation, military engineering, and other applications of mathematics. From Marseilles, he moved to the College of Turin, in Piedmont, where he was appointed professor of mathematics.

Claude Dechales was known for his friendliness and pedagogical competence in the teaching of mathematics and for his ability to teach and write clear explanations of complex technical topics, not for his research ability, advanced mathematical imagination, or originality of his work. His correspondence with Hevelius, Huygens, and Cardinal Bona, among others, survives.

Claude François Milliet Dechales died on 28 March 1678 in Turin, Italy, where he taught mathematics at the local college.

In Leonardo’s manuscript Codex Madrid I, compiled by the genius in 1493, when he served at the Castle of Milan under Duke Ludovico il Moro, there is a sketch, picturing a mechanism, which is very likely to be designed for calculating purposes.

Leonardo da Vinci is probably the most diversely talented person ever to have lived. He was a remarkable painter, engineer, anatomist, architect, sculptor, musician, etc. During his life, Leonardo produced thousands of pages of perfectly illustrated notes, sketches, and designs. A part of these pages (only half of almost 13000 original pages), as impressive and innovative, as his artistic work, managed to survive to our time. They are collected now in 20 notebooks (so-called codices), comprising some 6000 pages. These codices decorate expositions of many museums (the only codex, that is in private hands is the Codex Leicester, a small volume of only 36 pages, which was purchased in 1994 by Bill Gates for $30.8 million).

Some of the manuscripts were so thoroughly lost, that they weren’t found again until the last few decades! In February 1965, an amazing discovery was made by Dr. Julius Piccus, Professor of Romance Languages ​​in Boston, working in the Biblioteca Nacional de España (National Library of Spain) in Madrid, who was searching for medieval Spanish ballads and troubadours. Instead of ballads, searching in some cabinets, he stumbled upon two unknown collections of Leonardo’s manuscripts, bound in red Moroccan leather, which were known by the Spanish librarians, but were not described yet (the public officials stated that the manuscripts “weren’t lost, but just misplaced”, because of an error in the catalog).

These manuscripts were in the collection of the 16th-century Italian sculptor Pompeo Leoni (1533-1608) and were taken by him to Spain, to be offered to the Spanish King Felipe II in the 1590s. For some reason, Leoni kept the collection in his house, and after his death, it was divided into several parts, which went to England, France, and Italy, but few remained in Spain and in 1642 were donated to King Felipe IV, to become later part of the Royal Library (later Biblioteca Nacional) in Madrid. These manuscripts (almost 700 pages, on subjects such as architecture, geometry, music, mechanics, navigation, and maps) are now referred to as Madrid Manuscripts or Codex Madrid I and Codex Madrid II.

Codex Madrid I (composed of 192 pages with a size of 21/15 cm) is an engineer’s delight treatise on mechanics, full of perfectly drawn and laid out gadgets, gears, and inventions. Interestingly, this codex was not put together after Leonardo’s death (which is for example what happened with the miscellaneous contents of the Codex Atlanticus, the largest collection of Leonardo’s manuscripts), but it was in fact Leonardo himself who put it together and it has survived almost intact, except for 16 pages, which have been torn out and seem to have been lost. Codex Madrid I can be called the first and most complete treatise in the history of Renaissance mechanics, and in it, there is a sketch, picturing a mechanism, which is very likely to be designed for calculating purposes.

The gear wheels in the figure are numerated as follows: the small wheels are numerated with 1, while the bigger wheels are numerated with 10 (take into account, that in this case Leonardo, as in many of his writings, writes laterally inverted from right to left!).

The text bellow the figure is written using the strange 15th century Italian language of Leonardo, again inverted, and it is not very informative – Questo modo è ssimile a cquello delle lieve che qui è a risscontro in pari numero di asste. E non ci fo altro divario sennonchè quessto, per essere fatto con rote dentate colle sue rochette, esso ha continuatione nel suo moto, della qual cosa lo sstrumento delle lieve senplici n’è privato.

The language of Leonardo is never easy to understand because it is indeed quite cryptic and his writings are more private notes, than a clear explanation for readers. A rough translation of the text below the figure is: This manner is similar to that of the levers, although different, because, being this made of gears with their pinions, it can move continuously, while the levers cannot.

The Italian engineer, Dr. Roberto Ambrogio Guatelli (born 4 Sep. 1909 in Binago, near Milan-died Sep. 1993), a science and engineering graduate from the University of Milan, was a world-renowned expert of Leonardo da Vinci, who specialized in building working replicas of Leonardo’s machines since the early 1930s. When in the late 1930s his collection (some 200 models) went on exhibit, Italian dictator Mussolini was so pleased with this great example of Italy’s engineering heritage, that he decided to fund a traveling exhibition to impress the whole world.

In 1940 Guatelli, emerging as one of the leading model makers, traveled to New York for an exhibition at the Museum of Science and Industry in the Rockefeller Center. When World War II broke out, Guatelli was forced to flee to Japan with his models, but there he was interned, and the models blew to bits in a bombing of a warehouse, in which they were stored. After his return to Italy, he was invited to show again his models in the USA, so he began rebuilding his models and created about 60 new devices.

In 1947 Guatelli had an exhibition at the Ford Museum in Dearborn, Michigan. Eleanor Roosevelt, who was visiting the museum introduced Guatelli to Thomas Watson Sr. who was also visiting. Watson recognized Guatelli’s genius and hired him in 1951 to rebuild more of his models for IBM which then toured them as a corporate-sponsored exhibition. IBM placed a workshop at Guatelli’s disposal and organized traveling tours of his replicas (see the upper image of Guatelli, demonstrating one of his models), which were displayed at museums, schools, offices, labs, galleries, etc.

In 1967, shortly after the discovery of the Madrid Manuscripts, Guatelli went to the library of the Massachusetts Institute of Technology (MIT), to examine its copy of the manuscripts. When seeing the page with the above-mentioned sketch, he remembered seeing a similar drawing in Codex Atlanticus. In fact, Codex Atlanticus contains a lot of gear-wheel transmissions, see for example the lower sketch.

The left and the middle drawings are of hodometers, devices for measuring distance, known for many centuries (it seems the first odometer was described by Heron of Alexandria, who used an analogue train of gear wheels (linked so that each time one wheel completes a revolution the next wheel turns one-tenth of a revolution, thus recording a carry), while the right drawing is of a ratio mechanism. Leonardo certainly was not the inventor of gear-wheels and the hodometer, and he knew very well at least the fundamental treatise of Vitruvius—De architectura, written about 15 BC. In Book X, Chapter IX of this treatise describes one hodometer with gear wheels and a carry mechanism.

Using the two above-mentioned drawings, in 1968 Dr. Guatelli built a hypothetical replica of Leonardo’s calculating device (see the lower photo). It was displayed in the IBM exhibition, as the text beside the replica was:
Device for Calculation: An early version of today’s complicated calculator, Leonardo’s mechanism maintains a constant ratio of ten to one in each of its 13-digit-registering wheels. For each complete revolution of the first handle, the unit wheel is turned slightly to register a new digit ranging from zero to nine. Consistent with the ten-to-one ratio, the tenth revolution of the first handle causes the unit wheel to complete its first revolution and register zero, which in turn drives the decimal wheel from zero to one. Each additional wheel marking hundreds, thousands, etc., operates on the same ratio. Slight refinements were made on Leonardo’s original sketch to give the viewer a clearer picture of how each of the 13 wheels can be independently operated and yet maintain the ten-to-one ratio. Leonardo’s sketch shows weights to demonstrate the equability of the machine.

After a year the controversy regarding the replica had grown and an interesting Academic trial was then held at the Massachusetts Technological University, in order to ascertain the reliability of the replica.

Amongst others were present I. Bernard Cohen (1914-2003), professor of the history of science at Harvard University—consultant for the IBM collection, and Dr. Bern Dibner (1897-1988)—an engineer, industrialist, and historian of science and technology.

The objectors claimed that Leonardo’s drawing was not of a calculator but actually represented a ratio machine. One revolution of the first shaft would give rise to 10 revolutions of the second shaft, and 10 to the power of 13 at the last shaft. And what is more, such a machine could not be built, due to the enormous amount of friction that would result. Dr. Guatelli managed to build a replica, but the technology in the 15th century was so primitive, compared to ours, that a working machine could not be built.

It was stated that Dr. Guatelli had used his own intuition and imagination to go beyond the statements of Leonardo. The vote was a tie, but nonetheless, IBM decided to remove the controversial replica from its display.

Sadly, it seems the objectors were right because such mechanisms were quite popular several centuries ago. There is another picture on the same Codex Madrid I (f. 51v), which describes a similar mechanism (see the nearby image). Leonardo’s text below the picture says: Quando la rota d dà una volta intera, la rota c ne dà 10 e lla rota b ne dà 100, e così la rota a ne dà 1000. Onde, per l’oposito, si scanbia la forza, come detto nella 2^a del sesto di sopra, che dov’è magiore il moto, lì è magiore forza. (When wheel d makes one full turn, wheel c makes 10 turns and wheel b makes 100, and so wheel a makes 1000. Thus, the force changes the other way round, as said in the 2^nd paragraph above, that where higher is the movement, higher is the force. [This statement seems wrong, but what Leonardo means is possibly that the same torque applied to a is ten times more efficient (in raising the right-end weight) than when applied to b].

Moreover, a similar mechanism can be seen (see the lower image) in the famous encyclopedia Theatrum Machinarium of Jacob Leupold.

My correspondent Mr. Silvio Hénin from Milan (the author of historic investigations of the machines of other Italian inventors, like Luigi Torchi and Tito Gonnella), also thinks that Guatelli was almost certainly wrong. Mr. Hénin was so kind to give his expert opinion regarding this matter:
Leonardo was possibly studying the properties of gear trains in comparison with systems of levers; both can multiply forces (torques), but only gears can produce a continuous movement. In the other direction, the gear train can multiply rotation speed. On the same page, in fact, a compound pulley system is shown, which has the same force-multiplying properties as a gear train, a demonstration of what Leonardo was examining.
I can only add some points:
1. Leonardo’s drawing does not show any numbering on the gear wheels (mandatory for a calculator).
2. No way to set the operands is shown (which is mandatory).
3. No way (e.g. ratchet) to stop the wheels in precise discrete positions (which is mandatory) is shown.
4. Two weights are shown at the two ends (useless in a calculator).
5. The use of 13 decimal figures for calculations in the XV century is quite nonsense.

Guatelli worked for IBM until 1961 when he left and opened a workshop in New York. Interestingly, Guatelli built models not only of Leonardo da Vinci’s calculating device, but also of numerous other calculators; for example, the Pascaline by Blaise Pascal, the Stepped Reckoner by Gottfried Leibniz, the Differential Engine of Charles Babbage, the adding machine of Giovanni Poleni, the tabulating machine of Herman Hollerith, and the Millionaire direct multiplier of Steiger and Egli.

In 1673 the Parisian mechanic and watchmaker of King Louis XIV, René Grillet de Roven, published the small (49 pages) book Curiositez mathematiques de l’invention du Sr Grillet horlogeur a Paris. The book (see its title page nearby) describes several different inventions, but most of it is devoted to his Nouvelle machine d’arithmétique. However, the first edition of Grillet’s book (it was an edition of Jean-Baptiste Coignart, printer-bookseller of the King, and was reprinted in 1678) had a miserable fate, as it was seized by the Intendant of Police in Paris, because in his book Grillet described also a mercury barometer, for which he was accused of plagiarism from another Parisian instrument-maker, Hubin.

Five years later, in 1678, the earliest scientific journal published in Europe—the French Le Journal des Sçavans, published a short description (3 pages text and 1-page sketch) of the arithmetical machine of Grillet (see the image below).

Grillet obviously was so obsessed with keeping his design of the machine a secret, that he does very little to enlighten its mode of operation. After telling his readers that the idea for the machine originated from the rulers of Napier, mentioning that Pascal had invented an admirable machine for doing arithmetic and that Petit had given us a cylindre artihmetique (the French physicist Pierre Petit created in the early 1650s a kind of Napier’s bones engraved on a cylinder), Grillet stated that his device combines the wheels of Pascal with the cylinder of Petit, in order to provide a wonderful machine, which would perform all the arithmetic operations.

The sketch in the book depicts a box with 24 sets of wheels (3 rows by 8 wheels) on the lid. Each wheel consists of several concentric circles, while the bottom of the box contains a set of Napier’s bones, engraved on cylinders, reminiscent of those, described more than 20 years ago by Gaspard Shot. The construction of the machine is rather simple, with no connection between the group of wheels on the lid, which means, that tens carry cannot be performed automatically.

To perform an addition or subtraction on the lid dials, the operator would set up the first number on the upper line of wheels, the second number on the middle line of wheels, and then to perform the operation mentally, setting down the digits of the answer on the lower line of wheels. The wheels would have found their main use in adding up the partial products, generated by the set of the cylindrical Napier’s bones, located in the lower part of the machine.

Perhaps the most advanced aspect of Grillet’s machine was its size, as it was small enough to be carried in a (quite big) pocket (however, it was bigger, than the adding machine of Morland). Its dimensions are 14.5×32.5×5 cm, weight is 990 g. Materials used are wood, cardboard, paper, brass, and glass.

The reason for Grillet’s striving to keep the mode of operation and internal structure of his device a secret can be understood by the fact that he tried to make money from his machine, exposing it for a fee at fairs, and charging a silver coin to see it operate. It is known, that in 1673 the machine was exposed in Paris, at the Cloistre S. Jean de Latran and Quai de l’Horloge, №49. In 1681 the machine was exposed in Amsterdam, Netherlands. It seems Grillet tried to produce his machine in series and to sell it, but obviously without great market success :-), as only three examples of the device survived to the present day, two in the collection of Musée des Arts et Métiers in Paris, and one in private hands (on the image below you can see the 32.5cm x 14.5cm walnut cased mechanical calculator of Grillet, sold by Christie’s in 2013 for 119000 USD).

Biography of René Grillet de Roven

Not much is known about Grillet’s personal life. As it is clear from his name (spelled also René Grilliet), he originates from the town of Roven (Rouen), in northwestern France, the capital city of Normandy, the same town, where in the early 1640s Blaise Pascal created the famous Pascaline.

René Grillet’s parents were perhaps Jean Grillet (1605-1675) and Marie-Rosse Grillet. Jean Grillet was a king’s enameler (émailleur ordinaire de la Reyne), known as an author of a book—La Beauté des plus belles dames de la cour, les actions héroyques des plus vaillans hommes dece temps… et plusieurs autres pièces sur divers sujets gaillards et sérieux (Paris, 1648). Jean Grillet was interested in glassware, clocks, instrument making (he invented a thermometer, which was donated to his patron Monseigneur le comte de Montéclair) and all these sorts of curiosities, so obviously René inherited all these interests.

René Grillet became a well-known at the time french mechanic, instrument maker, and watchmaker, and he used to work for His Royal Highness King Louis XIV. Besides the calculating machine, which is of particular interest to us, he is known as a maker of several other devices—a hygrometer (anemometer); graphometers; drawing instrument set; protractor, sector, and square; set square, with plumb-bob, etc.

Let’s examine the curious history of one of Grillet’s inventions, the double mercury barometer. In early 1673 Hubin (he was an English enameller, who was established in Paris in the early 1670s as Emailleur ordinaire du Roy, and made thermometers, hygrometers, hydraulic, and air machines), published a pamphlet, in which he accused Grillet of fraud for using the principle of his mercury thermometer, already demonstrated to the French Academy and displayed it on his shop’s window sill. This accusation probably explains why Grillet’s 1673 book Curiositez mathematiques de l’invention du Sr Grillet horlogeur a Paris was seized by the Intendant of Police in Paris. That’s not the whole story, however. When sometime later the famous Dutch mathematician, astronomer, physicist, and horologist Christiaan Huygens presented his newly invented barometer, Grillet complained contra Huygens, stating that he had invented the double barometer two years before Huygens and that the latter stole the idea from him. Grillet even stressed he had demonstrated his invention during a meeting of the French Academy, which member was Huygens. Huygens however stated that Grillet had in fact shown a barometer to the Academy, but it had nothing particular to it. It seems Hubin was the only honest man in all this confusing story because he mentioned that the idea of putting serpentine tubes on his instrument he borrowed from a professor of Chartres, Laurent Cassegrain, while Grillet and Huygens didn’t give the proper credit to their precursors, trying to get all the glory.

In 1681 Grillet traveled to Amsterdam, Netherlands, where he exposed his calculating machine and instruments. It seems he stayed in the Netherlands for several years, working not only as an instrument-maker but also probably perfecting his printing art there under the care of the skilled Dutch master printers.

Later in the 1680s Grillet probably tried to establish a calico-printing workshop in France, but after the decree of 1686 prohibiting calico-printing in France, he went to try his fortune in England.

In 1690 René Grillet is mentioned to live already in England, where he took a patent for painting and printing calicos, and a factory for this purpose was opened in the Old Deer Park at Richmond, near London. It was the first calico-printing factory in England, but Grillet made the mistake to employ mostly Frenchmen and Roman Catholics, which led him into trouble with the local society and English authorities.

The English polymath Samuel Morland invented in the early 1660s a total of three calculating machines: one for multiplication and division, one for trigonometry, and one for addition and subtraction. Morland’s calculating machines were simple but became rather popular and London instrument-makers were still selling Morland’s calculators as late as 1710.

Samuel Morland entered government service in 1653 when he was chosen to accompany a British diplomatic mission to the court of Sweden’s Queen Christina. Christina of Sweden was a noted patron of the sciences, and it was most likely at her court that Morland first became acquainted with the calculating machine of Blaise Pascal, who in 1652 placed at Queen’s disposal an example. This is probably the most important reason, why Morland became interested in the construction of calculating devices.

In his book, The description and use of two arithmetick instruments (published in 1673 in London), Morland described two invented by him calculating devices, which are working without charging the memory, disturbing the mind, or exposing the operations to any uncertainty. This is the first book on a calculator, written in English, and the first separate work on the subject after Napier’s Rabdologiae. The book may also be considered the first comprehensive book in computer literature, as Blaise Pascal published nothing about his own machine, except one 18-page pamphlet in 1644.

The Machina Nova Cyclologica Pro Multiplicatione of Morland

It seems the first calculating machine of Morland, devised probably in 1664, was so so-called multiplication machine, based on the principle of Napier’s bones. The device was described in the above-mentioned book of Morland under the name Machina Nova Cyclologica Pro Multiplicatione (A New Multiplying Instrument).

Morland ordered manufacturing of the device to the famous English mechanics Henri Sutton (London instrument-maker, active mainly between 1650 and 1661) and Samuel Knibb (1625-1674), and the particular machine, shown here, was donated by Morland himself to Grand Duke Cosimo III de’ Medici in 1679. The dedication to the Grand Duke contains an obvious error: it gives 1666 as the year of invention and 1664 as the year of manufacturing. Let’s examine the construction of the multiplication machine.

In fact, the multiplication machine of Morland simplifies only the intermediate products, using the principle of Napier’s rods. There is no automatic or mechanical carry mechanism provided.

The device is made of silver, gilt, and silvered brass, wood, and crystal. The dimensions are 18 x 55.5 cm.

The digits from the ten Napier’s rods are inscribed across the periphery of 10 thin metal disks in such a manner, that units and tens of the rods are placed on the opposite ends of the circle (see the lower images for a closer view of the mechanism). There are two rows of axes in the device, the upper axes are fixed, while the lower can be rotated. In the row of windows, placed between the two axes can be set numbers, thus it serves as a mechanical memory. To perform a multiplication, the appropriate disk must be removed from the upper fixed axis and to be mounted to the lower working axis. Each of the lower axes is attached to a small pinion in the body of the machine, and this pinion is engaged with a toothed strip. This strip can be moved in the horizontal direction by means of the key, which can be seen in the lower right part of the lower figure, and its movement is marked by an arrow, which can be moved across a scale.

When the appropriate disks are set (according to the digits of the multiplicand), the lower part of the machine is covered by a lid, which has windows. The key must be rotated by the operator until the arrow comes to the digit of the multiplier on the scale, and during this rotation, the toothed strip will move and rotate the pinions, engaged with it. Thus in the lower row of windows can be seen the product. If the factors are multi-digital, then these actions must be repeated until all digits will be used.

For example, to multiply 23 by 7, the user would first take the discs for 2 and 3, place them on the central posts and close the door so that in the window the number 23 appears (3 in the left-most window and 2 in the left side of the second pair of windows). Then the user would turn the key until the pin on the slider scale pointed to 7. Each time the key is turned the discs are rotated once, which advances the display of the multiplication table for the selected numbers (2 and 3) by one. The windows are constructed so that a number on the leftmost edge of one disc appears next to the number on the rightmost edge of the next disc. The final answer must be obtained by adding the adjacent numbers in the windows, either with pen and paper or, as the inventor suggested, with the help of his instrument for addition. So, to finish the example, after discs 2 and 3 have been rotated 7 times, the numbers in the display window would read: 1 4 2 1. The final result is found by adding the adjacent digits to give 161.

The Machina Cyclologica Trigonometrica of Morland

Most probably in 1664, Samuel Morland invented a device, that can be used for trigonometric calculations, which he called the Machina Cyclologica Trigonometrica. The device was built in 1670 by John Marke (Maker of mathematical and astronomical instruments active in London between 1665 and 1679. Marke worked with Henry Sutton and succeeded him in 1665.) Materials used: silvered brass and silver, dimensions: 330×275 mm. The instrument is housed in an ebony case with a lid and engraved plate.

The trigonometric calculator of Morland allowed the operator to perform trigonometry by drawing out a problem and measuring the solution as with drawing instruments but without the need for pen and paper. It was a set of three rulers set into a divided circle that could be moved about using dials to form a triangle of any shape.

The device was used for determining the value of a trigonometric function (sine and cosine) of a known angle or, vice versa, for finding the value of an angle when its function is known. The instrument consists of a rectangular box holding a disk with a toothed circumference. At the center of the disk are mounted compasses with a fixed arm and a mobile arm rotating with the disk itself. Below are two smaller disks. The left-hand one shows the angle values. Its index is connected to the toothed circumference of the large disk and completes one revolution for every 30° traveled by the mobile compass arm. The right-hand disk shows the linear sine values. Its index is connected to the mobile horizontal rod on the upper half of the box and completes one revolution for every 25 units traveled by the rod on the side channels. The numbering of the horizontal rod and vertical channels basically represents the sine grid or reduction quadrant.

The machine for addition and subtraction of Samuel Morland

The adding machine of Samuel Morland (presented in the book as A new and most useful instrument for addition and subtraction of pounds, shillings, pence, and farthings…) was devised probably in 1665-1666, as four examples of the device survive to our time. The largest models can add up to one million, in either decimals or pounds, shillings, and pence.

The device (materials used are silver and brass), presented a true pocket calculator, measuring only 4 by 3 inches and less than a quarter of an inch thick (122 x 71 x 8 mm), weight 230 g. On page 12 of the book, Morland advertises that the instruments may be ordered from Humphry Adamson, living at Jonas Moore’s house in the Tower (Sir Jonas Moore was an English mathematician, surveyor, ordnance officer, and patron of astronomy, who warmly recommended the machines of Morland). Humphr(e)y Adamson was a very skillful English clock- and instrument-maker.

On the lid of the device are mounted 8 pairs of graduated dials. The scales of the dials are inscribed on the ring around them. The lower three scales are divided into 4, 12, and 20 parts and are inscribed and used for calculations in the English currency units of the 17th century—guinea (which was equal to 20 shillings), shilling (which was equal to 12 pennies), and penny (which was equal to 4 farthings). The upper five big dials have decimal scales and are inscribed with words unit, tens, hundreds, thousands, tenth.

Across the periphery of each big dial are made openings, according to the scale of the dial—4, 10, 12, or 20. In these openings can be put a stylus, and the dial can be rotated. During this rotation, in a little window in the upper part of each scale can be seen the appropriate number. Below each window is mounted a stop-pin, which is used for limiting the rotation during the adding operation. Over each big dial is mounted a smaller one, which serves as a counter to the revolutions of the big dial. For that purpose is used one-toothed gearing—the lower dial has one tooth, while the upper dial has ten teeth, so making a full revolution of the lower dial has as a result 1/10 revolution of the upper one.

The adding operation is performed by rotating the appropriate dials in the clockwise direction, pushing the stylus into the opening against the appropriate number, and turning the dial until the stylus will be stopped by the stop-pin. The subtraction can be done by rotating dials in the counter-clockwise direction, pushing the stylus in the opening below the window, and rotating the dial until it moves below the appropriate number.

The machine doesn’t have a tens carry mechanism, and this made it useless for practical needs. On 16 April 1668 Morland first printed short descriptions of his two adding devices in the London Gazette—As would now be expected, the adding instrument made its way into the pockets of modern young gentlemen (at a price of £3 10s).

Despite the excellent workmanship of the arithmetic devices of Morland, they were not very useful for practical needs, moreover, some of his contemporaries were not so fascinated by their usefulness also. Samuel Pepys (formerly Morland’s tutee at Cambridge from 1650, who did not think much of Morland) wrote in his 1667-8 years diary, that the machine of Morland is very pretty, but not very useful, while the famous scientist Robert Hooke, wrote in his diary for 31 January 1673: Saw Sir S. Morland’s Arithmetic engine Very Silly. The machines of Morland were, however, appreciated by King Charles II and Cosimo III de’ Medici, Grand Duke of Tuscany, which was more important for Morland as a typical courtier–inventor.

Biography of Samuel Morland

Samuel Morland was born in 1625 at Sulhamstead Bannister, near Reading in Berkshire, England. He was the son of Rev. Thomas Morland, a rector of the local parish church.

Morland entered Winchester School in Hampshire in 1638, and in May 1644, as a sizar (i.e. paying no fees but instead doing basic menial labor for the college between his studies) at Magdalene College, Cambridge. In 1649 he was elected a fellow of the society, and stayed there until 1653, but took no degree. While in College, Morland devoted much time to the study of mathematics, but he also became an accomplished Latinist and was proficient in Greek, Hebrew, and French (then the language of culture and diplomacy).

For the latter half of his time at university, Morland was a noted supporter of the Parliamentarian Party, and, from 1647 onward, he took part in student politics. In November 1653, he was included in the retinue of the English lawyer, writer, and parliamentarian Bulstrode Whitelocke, on an embassy to the Queen of Sweden for the purpose of concluding a military alliance. Whitelocke describes him as a very civil man and an excellent scholar; modest and respectful; perfect in the Latin tongue; an ingenious mechanist.

Upon his return from Sweden in July 1654, Morland was appointed as an assistant to John Thurloe, the secretary of the Lord Protector Oliver Cromwell. Later Cromwell appointed him as “commissioner extraordinary for the distribution of the collected moneys” and one of the clerks of the signet. In May 1655, Morland was sent by Cromwell to the King of France and to the Duke of Savoy to remonstrate with him on cruelties inflicted by him upon the sect of Waldenses or Vaudois, which had strongly excited the English public. Morland remained, for some time, in Geneva as an English resident, and his actions were highly appreciated after his return to England in December 1655.

Upon his return to England, Morland became intimately associated with the Government of the Commonwealth and he became a witness to several not-so-legitimate actions of his magnates, e.g. of Dr. Hewitt’s being “trepanned to death” in June 1658 by Thurloe and his agents. The most remarkable intrigue, however, which came to his knowledge was the so-called Sir Richard Willis’s Plot from the beginning of 1659. Its object was to induce King Charles II and his brother to effect a landing on the Sussex Coast, under the pretense of meeting their adherents and putting them both to death the moment they disembarked. This plot is said to have formed the subject of a conference between Cromwell, Thurloe, and Willis at Thurloe’s office, and the conversation was overheard by Morland, who pretended to be asleep at his desk. From this time, Morland endeavored to promote the Restoration and warned the King about the plot. In justifying to himself the abandonment of his former principles and associates, he observes that avarice could not be his object, as he was, at this time, living in greater plenty than he ever did after the Restoration, having a house well furnished, an establishment of servants, a coach, & co, and £1,000 a year to support all this, with several hundred pounds of ready money, and a beautiful young woman to his wife for a companion (in 1657, Morland married Susanne, daughter of Daniel de Milleville, Baron of Boissay in Normandy).

Morland officially joined the King’s party in May 1660, when in departed to Breda, bringing with him letters and notes of importance. The King welcomed him graciously and publicly acknowledged the services he had rendered for some years past, making him liberal promises of “future preferment” but these were, for the most part, unfulfilled. On 18 July 1660, Morland was made a baronet, being described as of Sulhamstead Bannister, although it does not appear very clear whether he was in possession of any considerable property in the parish. He was also made a Gentleman of the Privy Chamber; but this appointment, he says, was rather expensive than profitable, as he was obliged to spend £450 in two days on attending the ceremonies accompanying the coronation. He, indeed, obtained a pension of £500 from the post office, but his embarrassments obliged him to sell it, and, returning to his mathematical studies, he endeavored, by various experiments and the construction of machines, to earn a livelihood. But the King’s gratitude went no further. Morland was extravagant, sold his pension, wasted the proceeds in France, and ended as a beggar.

In 1666, Morland obtained, in conjunction with Richard Wigmore, Robert Lindsey, and Thomas Culpeper, a probably remunerative patent “for making metal fire-hearths”. From correspondence between Morland and Dr. Pell, it appears that about this same time (1666), the former had intended to publish a work “On the Quadrature of Curvilinear Spaces” and had actually proceeded to print part of it, but was happily persuaded, by Pell, to lay it aside. In carrying out his experiments in hydrostatics and hydraulics, Morland encountered many difficulties as a consequence of their expense. In December 1672, the King granted to him the sum of £260 to defray the charges of about five hundred looking-glasses “to be by him provided and set up in Olive wood frames for our special use and service,” as well as an annuity of £300 “in consideration of his keeping and maintaining in constant repair a certain private printing press… which by our Especial Order and Appointment he hath lately erected and set up”.

In 1681, Morland was appointed “magister mechanicorum” to the King, who, in recognition of his ingenuity, presented him with a medallion portrait of himself, set in diamonds, together with a medal as “an honorable badge of his signal loyalty”. In October 1684, the King advanced him £200 and, a year later, Morland received a similar sum by way of “bounty”.  According to his own account, his mechanical experiments pleased the King’s fancy; but when he had spent £500 or £1,000 upon them, he received sometimes only half, and sometimes only a third, of the cost.

In 1682, Charles II sent him to France “about the King’s waterworks,” but there also he seems to have lost more than he gained. On his return, King James II restored to him his pensions, which had been, for some reason, withdrawn and, likewise, granted him part of the arrears, but Morland was never repaid the expenses of the engine which he had constructed for bringing water from Blackmore Park, near Winkfield, to the top of Windsor Castle. In 1686, Morland was corresponding with Pepys about the new naval gun-carriages. In 1687, his pension was paid down to Lady Day 1689.

In 1689, Morland addressed a long letter to Archbishop Tenison, giving an account of his life, and concluding with a declaration that his only wish was to retire and spend his life “in Christian solitude”; and he begs the primate’s “helping hand to have his condition truly represented to his Majesty.” Tenison probably did something for him, as there is a letter of thanks for “favours and acts of charity,” dated 5 March 1695. The errors of his life were probably considerable, as he speaks of having been, at one time, excommunicated; but some of his writings show that he was a sincere penitent, particularly ‘The Urim of Conscience’ (1695), written, as the title says, “in blindness and retirement.”

Morland married four times but was definitely not happy in his family life. In 1657 he married the Huguenot Susanne de Milleville, the beautiful daughter of Daniel de Milleville, seigneur de Boissay, Commissaire du roi au syndic provincial de Normandie, and Catherine de la Wespierre, his wife. They had three children (one son, Samuel), but Susanne died in 1668, when she returned with the children to France, mortally ill with dropsy (In his Sep. 1667 diary Samuel Pepys mentioned that they went to King’s Play House and …Here we saw Madam Morland, who is grown mighty fat but is very comely.)

Morland married secondly, on 26 October 1670, in Westminster Abbey, Carola Harsnett (1651-1674), daughter of Sir Roger Harsnett, knight. They had two children, but Carola died on 10 October 1674, aged 22. Morland married thirdly, on 10 November 1676, in Westminster Abbey, Anne Fielding (1661-1680), third daughter of George Fielding of Solihull, Warwickshire, by Mary, second daughter of Sir Thomas Shirley, knight, of Wiston, Sussex (Anne died on 20 February 1680, aged 19, leaving no issue). Lastly, Morland married, at the Knightsbridge Chapel, Middlesex, on 1 February 1687, Mary Ayliffe, a woman of low origin and infamous character, from whom he obtained a divorce for adultery on 16 July the following year.

Morland lost his sight about three years before his death. He died on 30 December 1695 and was buried in the Hammersmith Chapel on 6 January 1696. He must have been in an extremely weak condition, as he was unable to sign his will. By it, he disinherited his only son, Samuel (died Nov. 1716), who was the second and last baronet of the family, as the reason for this appears from a passage in a letter “I have been, in my youthful days, very undutiful to my parents, for which God has given me a son, altogether void of filial respect or natural affection”.

In 1667, Sir Charles Cotterell, an English courtier and translator, suggested a calculating instrument, called Arithmetical Compendium (Instrument for Arithmetick). It was a combination of Napier’s Bones with a bead-type abacus, used to avoid writing down the partial products of multiplication using the rods. In fact, Cotterell’s idea was popularized several years later, circa 1670, when Robert Jole (Jole was a scientific instrument maker, brother in the Clockmakers’ Company, who was active in London between 1664 and 1704), produced his version of the device.

Cotterell most probably knew and was influenced by Samuel Morland, who devised in the 1660s a total of three calculating machines, which were presented to King Charles II and the general audience.

The calculating instrument of Cotterell has a boxwood case (size: 184 mm x 59 mm x 19 mm, weight: 0.13 kg), and was made of brass (binding pieces), glass, iron, engraved paper, and vellum. There is a separate silvered brass tool, for pushing beads and lifting out rods.

The user of Cotterell’s device would slide a window up and down to expose different parts of the times table, reading off the multiplicand on the edge of the instrument frame.

The box is inscribed with the text The Index of ye Quotient The Index of ye Multiplier Divisor Multiplic and The Fore Rule. The separate brass tool is inscribed with the text Robert Jole att ye Crowne Nere ye new Exchainge fecit.

Biography of Charles Cotterell

Charles Cotterell (or Cottrell) was born on 7 April 1615 in Wilsford, Lincolnshire, England, and was baptized there two days later. He was the only son (there were four daughters) of Sir Clement Cotterell (1585–1631) and Anne Alleyne (d. 1660, an heiress and daughter of Henry Alleyne of Wilsford), who married in 1606.

Sir Clement Cotterell was appointed as muster-master of Buckinghamshire in 1616 and groom-porter to King James I in 1619, and was knighted in 1620. He was a Vice-Admiral of Lincolnshire from 1620 to 1631. In 1621, he was elected Member of Parliament for Grantham. In 1624 he was elected Member of Parliament again.

Charles Cotterell attended Queens’ College, Cambridge, from 1629 until 1632, but did not take any degree. In June 1632 he began touring Europe with aristocratic friends. Shortly after returning to England in 1634 he was engaged to take the Earl of Pembroke’s sons Charles and Philip Herbert on their travels. Though the tour was marred by the death of Charles, Cotterell entered Pembroke’s service on his return in 1636. Cotterell served the Earl of Pembroke under courtly and military service in the Cavalier army until knighted in Oxford in 1645.

In the early 1640s Cotterell served in the privy chamber troop against the Scots, and his real opportunity for advancement came with the death in July 1641 of the King’s master of the ceremonies, Sir John Finet. Sir Balthasar Gerbier had the reversion to Finet’s place and Cotterell replaced him as assistant master on 30 July. In December 1643 he was promoted to the rank of major and, having fought at Edgehill, at both battles of Newbury, and at Alresford, was knighted in Oxford on 21 March 1645.

In Oxford, Cotterell collaborated with William Aylesbury in translating Davila’s Storia delle guerre civile (published in 1647) from Italian. at the request of the king. In March 1649, after the king’s execution, Cotterell (along with his wife and elder daughter Frances (or Frank), born in 1646, as their infant daughter, Anne, born in 1648, remained in England), accompanied Aylesbury and the Duke of Buckingham into exile in Antwerp.

By 1652 Cotterell had moved to The Hague as steward to Elizabeth Stuart, Queen of Bohemia, while completing a translation of La Calprenède’s Cassandre. After resigning his stewardship in September 1655, Cotterell was appointed an adviser to the Duke of Gloucester, under whom he fought in three campaigns in Flanders.

In the summer of 1642, Charles Cotterell married Frances West (1621–1657), daughter of Edward West of Marsworth, Buckinghamshire, and half-sister of the architect Roger Pratt. They had three daughters and two sons: Frances (Frank), their eldest daughter, born in 1846, died on 31 December 1653; Anne Dormer (Cottrell) (1648-1695); Clement (1650-1672), their eldest son, was killed in a naval engagement against the Dutch at the Battle of Southwold Bay, in May 1672; Elizabeth Trumbull (Cottrell) (1652-1704); Charles Lodowick (1654–1710), followed his father as Master of the Ceremonies.

On 29 May 1660, Cotterell returned with the royal party to London, with his children but without his wife Frances, who died around 1657, and was sworn Master of the Ceremonies on 5 June. The pursuit of a young widow, Anne Owen, led Cotterell to form a friendship with Katherine Phillips, whose husband was the Member of Parliament for Cardigan. Phillips was a young poet known in her salon as Orinda. Cotterell became a major figure in Orinda’s literary circle, and later took Phillips’s seat in Parliament from 1663 until 1678.

Sir Charles Cotterell resigned his seat as Master of the Ceremonies on 27 December 1686, in favor of his son Charles Lodowick. In 1693 he published a translation The Spiritual Year, a Spanish devotional tract.

Cotterell seems to have been well regarded by those who knew him. For example, the diarist and naval administrator Samuel Pepys described him as “ingenious”. The Italian historian and satirist Gregorio Leti lavished praise on him, believing he represented everything that any court in the world could seek in a master of ceremonies, describing him as “of kind disposition, soft and gentle, assiduous in his visits, of wise counsel, exemplary lifestyle, and the best conversation”.

After a sickness of some ten days, Charles Cotterell died at 6 p.m. on 7 June 1701 at his home in St Martin’s Lane, Westminster.

Jean Salomon de Caus was a French Huguenot engineer and scientist, who spent all his life moving across Europe. He worked as a hydraulic engineer and architect under Louis XIII from 1623 till his death in Paris in 1626. de Caus also was in service of the Prince of Wales and designed gardens in England, that of Somerset House among them. Salomon de Caus also designed the Hortus Palatinus, or Garden of the Palatinate, in Heidelberg, Germany (from 1614 till 1620 he was an engineer to the Elector Palatine, Frederick, at Heidelberg).

In 1615, de Caus published the book Les Raisons des Forces Mouvantes avec diverses machines tant utiles que plaisantes (The reasons for moving forces with various machines as useful as pleasant). It was an engineering treatise, which incorporated mechanical fountains, musical instruments, and other automata. His interest in these mechanical devices may have been influenced by the recovery of ancient texts by Heron of Alexandria around this time.

In his book, de Caus described an organ (see the upper image) in which a pegged cylinder, turned by a water wheel, activated levers that triggered bellows to force air through pipes.

A notable piece of work of de Caus was an automaton that had singing birds (see the picture below), directly influenced by a design by Heron. The birds flutter and chirp while an owl turns slowly toward them. When the intimidating owl faces the birds, they fall silent, but as he turns away, they resume their ruckus.

De Caus’s treatise also contains meticulous accounts of the mechanisms of hydraulic grottoes (small caves or caverns). In one (see the image below), Galatea rides astride a big seashell drawn by two dolphins. Behind her, Cyclops has put his club aside to play on a flageolet, while sheep gambol about. The mechanism is made entirely of wood, driven by two waterwheels, that are put in motion by jets of water from two pipes that emerge from a common reservoir. The pipes have valves that open and close alternately by means of a system of counterpoises so that the wheelwork turns one way and then the other as Galatea and her dolphins move back and forth across the scene. A third water wheel, through a train of gear wheels, drives a pinned barrel that is in turn connected with the keys of the flageolet.

Biography of Salomon de Caus

Jean Salomon de Caus was born in 1576 in Dieppe, Normandy, into a Protestant family. The whole family moved to England, where Salomon obtained his education, studying painting, ancient languages, and mathematics. He was interested in engineering and architecture and studied ancient curiosities, such as the statue of Memnon and the Archite pigeons.

From 1595 till 1598 de Caus visited Italy, where he observed the garden of Bernardo Buontalenti in Pratolino in Florence with the mechanical arts and the Villa d’Este at Tivoli, near Rome. Inspired by Buontalenti he designed several gardens and related structures fountains, grottos, and machinery.

From 1600 till 1608 de Caus was an engineer (from 1605 “ingéniaire à la fontaine artificielle et en toutes autres choses que luy seront commandées”) at the court of the Austrian Archduke Albert VII of Habsburg, governor of the Netherlands, and his wife Isabella in Brussels.

During 1608 and 1609 de Caus was in London to teach drawing to Prince Henry, Prince of Wales, and to Princess Elizabeth, then continued his service at the court of King Charles I. Together with the architect Constantino de’ Servi he built water features and a picture gallery in Richmond Palace. De Caus built also gardens in Greenwich Park, Wilton House near Salisbury in Wiltshire, Hatfield House in Salisbury, and Somerset House (London), as well as some work in Richmond park, Gorhamburry, Camden House in Kensington.

In 1614, through the intervention of Princess Elizabeth Stuart, who had married Prince Elector Palatine, he answered the call to Heidelberg, to serve as the architect and engineer of Elector Friedrich V. De Caus was the architect of the part built under Frederick V at the Castle of Heidelberg. He was also the architect of Elisabethentors and the designer of Hortus Palatinus. This work occupied De Caus for some years and was not completed when, but he published in 1620 his complete designs in a work entitled Hortus Palatinus a Friderico Rege Boemiæ Electore Palatino Heidelbergæ exstructus.

He left Heidelberg for Rouen, then to Paris, in 1620, because of the war, to start in the service of Louis XIII, who employed him as “Engineer et architecte du Roy” (engineer and architect to the king) and was among others responsible for the sanitation and fountains.

Salomon’s brother, Isaac de Caus (1590–1648), also an engineer and landscape architect, is the creator of Hortus Penbrochianus (Wilton House) in 1615. Isaac also created several automata, similar to these of his brother, such as the water-powered machinery that counterfeited singing birds in Dieppe in 1617. In 1644 Isaac de Caus published a book, Nouvelle invention de level l’eau plus hault que sa source avec quelques machines mouvantes par le moyen de l’eau, et un discours de la conduite d’icelle, with print designs, which seem to have been taken directly from Salomon.

On 16 April 1606, Salomon de Caus married Esther Picart. On 24 February 1607, was born their son Guillaume.

Salomon de Caus died on 28 February 1626, in Paris, and was buried in cimetière de la Trinité.

A simple calculating device with the fancy name Arithmetical Jewell was designed by William Pratt in the middle 1610s, and described in the book of the same name (The Arithmeticall Jewell: or the use of a small Table Whereby is speedily wrought, as well all Arithmetical workes in whole Numbers, as all fractional operations, without fraction or reduction. Invented by William Pratt. Published by his Maiesties privilege, granted to the inventor, under the Great Seale of England), published in 1617 in London.

William Pratt, in association with John Harpur and Jeremy Drury, received a patent (privilege) on 27 March 1616, for the sole making of a table for casting accounts. The patent was for making a device “by which all questions arithmetical may be resolved without the use of pen or compters [counters]”. On 4 April 1616, the three men obtained a privilege for printing a book explaining an “instrument or table for cyfering and casting of accomptes”. Soon thereafter, the partners fell out, and published competing manuals of instruction: Harpur entered his in the Stationers’ Register on 8 March 1617, and Pratt on 21 June 1617.

The Arithmetical Jewell of Pratt is an instrument with a flat grid of semi-circular, rotating brass wedges, devised to facilitate addition, subtraction, multiplication, division, and the extraction of roots.

William Pratt was a mathematical practitioner and a member of the active circle of London’s mathematical teachers, close to the famous Gresham College, where the logarithms of Napier were popularized at that time.

Pratt’s device was nothing more than a rudimentary mechanical reconfiguration of the conventional reckoning technique: a portable, fancier, and gentlemanly adaptation of the century-old techniques of calculation like plume (manual calculations) and jetons of the abacus. With the exception here that you did not need paper to inscribe, for instance, the carry-over numbers of an addition; one could instead, using a small metallic stylus, “inscribe” them on the instrument’s appropriate sectors of brass. The reckoning method, nonetheless, was precisely the same as the plume and jetons.

The Arithmetical Jewell comprises two ivory-faced wooden tablets, with dimensions 122 mm x 65 mm x 5 mm each, put in tooled leather binding, 5″ x 3″, with a brass stylus 5 inches long. The weight of the device is only 0.14 kg. One tablet (below in the picture) has 14 columns, each with small brass parallel sectors, made from brass (copper, zinc alloy). The other has seven pairs of columns for laying out astronomical fractions to the base 60. Numbers are put in by moving the flags to reveal dots. Sums are then worked out with a pen and paper.

There is a later account for Arithmetical Jewell by the English antiquary, natural philosopher, and writer John Aubrey (1626–1697):
Dr Pell told me, that one Jeremiah Grinken [a mathematical instrument maker] frequented Mr Gunters Lectures at Gresham College: He used an Instrument called a Mathematicall Jewell, by which he did speedily performe all Operations in Arithmeticke, without writing any figures, by little sectors of brasse [or some semi-circles] that did turn every one of them upon a Center. The Doctor has the booke… he told me, he thought his name is [William] Pratt.

In 1939 the famous Argentine writer and librarian Jorge Luis Borges published in Buenos Aires an essay entitled La bibliotheca total (The Total Library), describing his fantasy of an all-encompassing archive or universal library.

A universal library is supposed to contain all existing information, all books, all works (regardless of format), or even all possible works. The Great Library of Alexandria is generally regarded as the first library approaching universality, in the classical sense, i.e containing all existing at the moment knowledge. It is estimated that at one time, this library contained between 30 and 70 percent of all works in existence. Universal libraries are often assumed to have a complete set of useful features (such as finding aids, translation tools, alternative formats, etc.)

As a phrase, the “universal library” can be traced back to 1545, when the Swiss scientist Conrad Gessner (1515-1565) published his Bibliotheca universalis. At the end of the 19th century, with the development of technologies, machines, and human imagination, appeared the idea of the device of a library which is universal in the sense that it not only contains all existing written works, but all possible written works. This idea appeared in Kurd Lasswitz’s 1901 story “The Universal Library” (Die Universalbibliothek), and was later developed by Borges.

In 1941, Borges enhanced his idea in the short story “The Library of Babel” (La biblioteca de Babel), conceiving of a universe in the form of a vast library containing all possible 410-page books of a certain format and character set.

Borges’ story of a universe in the form of a library, or an imaginary universal library, has been viewed as a fictional or philosophical predictor of characteristics and criticisms of the Internet.

The narrator of “The Library of Babel” describes how his universe consists of an endless expanse of interlocking hexagonal rooms, each of which contains the bare necessities for human survival—and four walls of bookshelves. Though the order and content of the books are random and apparently completely meaningless, the inhabitants believe that the books contain every possible ordering of just a few basic characters (letters, spaces and punctuation marks). Though the majority of the books in this universe are pure gibberish, the library also must contain, somewhere, every coherent book ever written, or that might ever be written, and every possible permutation or slightly erroneous version of every one of those books. The narrator notes that the library must contain all useful information, including predictions of the future, biographies of any person, and translations of every book in all languages. Conversely, for many of the texts some language could be devised that would make it readable with any of a vast number of different contents.

Despite — indeed, because of — this glut of information, all books are totally useless to the reader, leaving the librarians in a state of suicidal despair. However, Borges speculates on the existence of the Crimson Hexagon, containing a book that contains the log of all the other books; the librarian who reads it is akin to God.

Now, it seems we have already the device, which can create the Universal Library, and this is the computer. We still have not provided this device with the tools (intellect in the form of software, and some hardware resources) needed for the creation of this library, but sometime or another, this will happen.

On 12 April 1859, a certain mysterious person, named C. Winter, of Piqua, from the county of Miami and the State of Ohio, received the 3-page US patent №23637 for Improved Adding-Machine, which was the fourth in the USA keyboard adder, after the machines of Parmelee, Castle and Nutz, and seventh in the world, after the machines of White, Torchi, and Schwilgué.

What makes this simple adding machine (in fact, a single column adding device. i.e. suitable for adding columns of numbers) a remarkable one is the fact, that (according to my personal investigation) its constructor is a woman, thus this machine is the first and the only mechanical calculator, devised by a woman. This remarkable lady was Caroline Winter from Piqua, a small town on the Great Miami River in southwest Ohio, developed along with the Miami and Erie Canal construction between 1825 and 1845.

Almost nothing is known about the inventor of this machine—Caroline Winter. She was mentioned in the business directories for Piqua in 1859-60 and 1860-61 as the owner of a general store in the town. There is a tombstone in the Piqua’s Cedar Hill Cemetery of Caroline Winters, born in 1816, died on 8 Jan 1899 in Lima, Allen County, Ohio, at the home of her daughter—Amelia (Winters) Stein (1848-1932).

No doubt, Caroline Winter devised this machine to facilitate the tedious calculations in her store and trade business, as it is specified in the patent “It will be perceived that by the use of this machine figures may be added rapidly and always with perfect correctness.” Interestingly, the witnesses of her patent—Augustin Thoma and John B. Larger probably also significantly contributed to the creation of her machine. Note: Both of them were emigrants from Germany, as it was a large part of Piqua’s population in the middle of the 19th century. Caroline Winter was most probably also an emigrant from Germany because, in the United States Index to Passenger Arrivals, we can find two records (from 1833 and 1835) for women named Caroline Winter arriving in the USA from Germany.

John B. (Baptiste) Larger was a wealthy Piqua merchant (b. 1828 in Fellering, Departement du Haut-Rhin, Alsace, France), who unfortunately got killed young, when in early 1862 volunteered 32^nd Regiment of Ohio Infantry to take part in Civil War, and was shot by a sniper in May 1862, while in camp.

Augustin (August, Augustus) Thoma (b. 3 Aug 1819 in Kappel (Lenzkirch), Baden, Germany, d. 30 Dec 1899 in Piqua, OH) was the founder of a successful jeweler’s business in Piqua (est. 1838), which was conducted by his descendants and survived up to 2010. He landed in New York at the age of 13 in 1832, served as an apprentice to a watchmaker, learned the trade, and in 1838 moved to Piqua to found his own jewelry business. Admittedly, Thoma was not only a good jeweler and merchant, but also a skillful instrument maker, and civic leader. He is a holder of three US patents—for a Jewelers Tool (pat. №67462 from 1867-08-06), for a Watch Jeweling Tool (№70049 from 1867-10-22), and for a Watch Maker Tool (№120618 from 1871-11-07), so we could easily imagine, that he was somehow involved in the construction of the Winter’s machine. Interestingly, Thoma had a daughter, named Caroline.

In contrast to the first US keyboard calculating machines (these of Parmelee and Castle), the machine of Caroline Winter survived to the present, in the form of the Original U.S. Patent Model (up to 1880, the Patent Office required inventors to submit a model with their patent application). At the beginning of our century, the device was a property of Auction Team Breker, Koeln, Germany (see the photos below) and was restored and sold in an auction in 2009 for $46480 to Arithmeum Museum in Bonn, Germany (I guess Auction Team Breker could eventually get a much better price if they knew my assumption that this is the first (and only) mechanical calculator, devised by a woman 🙂 Arithmeum recently uploaded a 3D animated video made by a student of Computer Science, showing the functionality of the machine in detail and also giving an impression of its operation and aesthetics (see Arithmeum video on Winter’s machine).

The size of the machine is 27 x 22 x 25 cm. The box is made from oak, with ivory key taps and two dial faces on the plate on top of the registers. The base part of the internal calculating mechanism is the big ratchet wheel (marked with K on the patent drawing), which is provided with 100 teeth, a smaller ratchet wheel (n, for counting hundreds), bevel-wheels j and i, pawls s and z, cord o, and pulley P. The dial plate on top of the box has two dials: a big dial B, divided into 100 divisions, and a smaller dial for counting hundreds C, which is within the big dial, and is divided into 6 divisions, thus the calculating capacity of the machine is up to 699.

The device has a resetting mechanism, presented by the lever (marked with c), which has its fulcrum at c’, slotted to embrace the shaft h, having a groove around it at the point of contact with the lever. d represents a spring secured to lever c, which serves to raise it again after being depressed.

The adding device of Caroline Winter doesn’t have a tens carry mechanism, and in fact, it doesn’t need it, because the smaller ratchet wheel (counting hundreds), rotates simultaneously with (and proportionally to) the bigger ratchet wheel (counting 1-99). However, when adding multidigit numbers, tens carry operations must be done manually, as described in the patent application.

Winter machine’s use of an elementary switching latch mechanism is characteristic since this mechanism had only been used in very few calculating machines before, for example, those made by Jean-Baptiste Schwilgué.

The Roulette ou Roue Paschaline (celebrated as Pascaline in France and abroad) of the great French scientist Blaise Pascal was for more than three centuries considered the first mechanical calculator in the world, as the Rechenuhr of Wilhelm Schickard was not widely known until the late 1950s. Pascal most probably didn’t know anything about Schickard’s machine. It is more likely Pascal to have read the Annus Positionum Mathematicarum, or Problemata (courses covering geometry, arithmetic, and optics) of Dutch Jesuit mathematician Jan Ciermans (1602-1648), who mentioned in his courses, that there is a method with rotuli (normally rolls of parchment for writing upon, but could also intend the more modern diminutive for rota i.e. little wheels) with pointers, which enables multiplication and division to be done with a little twist, so the calculation is shown without error.

In 1639 Étienne Pascal, the father of Blaise Pascal was appointed by the Cardinal de Richelieu as Commissaire député par sa Majesté en la Haute Normandie (financial assistant to the intendant Claude de Paris) in Rouen, capital of the Normandy province. Étienne Pascal arrived in the city of Rouen in January 1640. He was a meticulous, forthright, and honest man, and spent a considerable amount of his time completing arithmetic calculations for taxes. The task of calculating enormous amounts of numbers in millions of deniers, sols, and livres necessitated ultimately the help of his son Blaise and one of his cousins’ sons, Florin Perrier (1605-1672), who would soon marry Blaise’s sister Gilberte.

Étienne was buried with work and he and his helpers were often up until two or three o’clock in the morning, figuring and refiguring the ever-rising tax levies. They used initially only manual calculations and an abacus (counting boards), but in 1642 the Blaise started to design a calculating machine. The first variant of the machine was ready the next year, and the young genius continued his work on improving his calculating machine.

In his later pamphlet (Advis necessaire) Pascal asserted: …For the rest, if at any time you have thought of the invention of machines, I can readily persuade you that the form of the instrument, in the state in which it is at present, is not the first attempt that I have made on that subject. I began my project with a machine very different from this both in material and in form, which (although it would have pleased many) did not give me entire satisfaction. The result was that in altering it gradually I unknowingly made a second type, in which I still found inconveniences to which I would not agree. In order to find a remedy, I have devised a third, which works by springs and which is very simple in construction. It is that one which, as I have just said, I have operated many times, at the request of many persons, and which is still in perfect condition. Nevertheless, in constantly perfecting it, I have found reasons to change it, and finally recognizing in all these reasons, whether of difficulty of operation, or in the roughness of its movements, or in the disposition to get out of order too easily by weather or by transportation, I have had the patience to make as many as fifty models, wholly different, some of wood, some of ivory and ebony, and others of copper, before having arrived at the accomplishment of this machine which I now make known. Although it is composed of many different small parts, as you can see, at the same time it is so solid that, after the experience of which I have spoken before, I assure you that all the jarring that it receives in transportation, however far, will not disarrange it.

The first several copies (certainly made by a local clockmaker in Rouen, it was a time when clocks and clockwork were celebrated, with even the Universe being considered, at least metaphorically, as being a form of clockwork) of the machine didn’t satisfy the inventor. Meanwhile, in 1643, it happened an event, which almost managed to give up Pascal from the machine. A clockmaker from Rouen dared, (according to the words of the offended inventor, who named no name—whether he knew it is unknown), to make a beautiful, but absolutely useless work copy of the machine. Let’s look again at how describes this event Pascal himself in his pamphlet (Advis necessaire):
…Dear reader, I have good reason to give you this last advice, after having seen with my own eyes a wrong production of my idea by a workman of the city of Rouen, a clockmaker by profession, who, from a simple description which had been given him of my first model, which I had made some months previously, had the presumption, to undertake to make another; and what is more, by another type of movement. Since the good man has no other talent than that of handling his tools skillfully and has no knowledge of geometry and mechanics (although he is very skillful in his art and also very industrious in many things that are not related to it), he made only a useless piece, apparently true, polished and well filed on the outside, but so wholly imperfect on the inside that it was of no use. Because of its novelty alone, it was not without value to those who did not understand about it; and, notwithstanding all these essential defects which trial shows, it found in the same city a place in a collector’s cabinet which is filled with many other rare and curious pieces. The appearance of that small abortion displeased me to the last degree and so cooled the ardor with which I had worked to the accomplishment of my model, that I at once discharged all my workmen, resolved to give up entirely my enterprise because of the just apprehension that many others would feel a similar boldness and that the false copies which they would produce of this new idea would only ruin its value at its beginning and its usefulness to the public. But, some time afterward, Monseigneur le Chancelier, having deigned to examine my first model and to give testimony of the regard which he held for that invention, commanded me to perfect it. In order to eliminate the fear which held me back for some time, it pleased him to check the evil at its root and to prevent the course it could take in prejudicing my reputation and inconveniencing the public. This was shown in the kindness that he did in granting me an unusual privilege, and which stamped out with their birth all those illegitimate abortions which might be produced by others than by the legitimate alliance of the theory with art.

Later on, however, friends of Pascal presented to the Chancellor of France, Pierre Seguier (1588–1672), a prototype of the calculating machine. Seguier admired the invention and encouraged Pascal to resume the development. In 1645 Pascal wrote a dedicatory letter at the beginning of his pamphlet (the above-mentioned Advis necessaire) describing the machine (actually advertising the machine, as almost nothing is mentioned about its construction and operation) (see the letter and the pamphlet of Pascal), and donated a copy of the machine to the Chancellor (still preserved in CNAM, Paris). The text concluded that the machine could be seen in operation and purchased at the residence of Prof. Gilles de Roberval (Roberval was a friend of Étienne Pascal). This is the only preserved description of the device from the inventor.
The Chancellor Seguier continued to support Pascal and on 22 May 1649, by royal decree, signed by Louis XIV of France, Pascal received a patent (or privilege as it then was called) on the arithmetical machine, according to which the main invention and movement are this, that every wheel and axis, moving to the 10 digits, will force the next to move to 1 digit and it is prohibited to make copies not only of the machine of Pascal, but also of any other calculating machine, without permission of Pascal. It is prohibited for foreigners to sell such machines in France, even if they are manufactured abroad. The violators of the privilege will have to pay a penalty of 3 thousand livres (see the Privilege of Pascal).
The privilege again (as the Advise) mentions that Pascal has already produced fifty somewhat different prototypes. Moreover, the patent was awarded gratis and did not specify an expiration time, which was rather an unusual affair. It seems Pascal was an authentic favorite of the French crown 🙂

It seems later Pascal wanted to manufacture his machines as a full-scale business enterprise, but it proved too costly, and he didn’t manage to make money from this privilege. It’s not known how many machines were sold but the total was probably no more than ten or fifteen. Price may have been the main issue here, though accounts vary significantly, from the Jesuit mathematician François’s 100 livres to Tallemant de Réaux’s 400 livres and Balthasar Gerbier’s 500 livres (let’s mention, that 100 livres were enough to keep a seventeenth-century Frenchman in modest comfort for a year).

Pascal continued to experiment, constructing a lot of variants of the machine (later on called the Pascaline or Pascalene). He worked so hard on this machine, it is said, that his mind was disturbed (avoir latête démontée) for the next three years. According to his sister Gilberte, the young inventor’s exhaustion did not come from the labor he put into designing the machine, but rather in trying to make the Rouen artisans understand what it was all about.

Pascal decided to test the reliability of the machine, sending a copy on a long journey with carriage (from Rouen to Clermont and back, some one thousand kilometers) and the machine returned in perfect condition. Later he wrote: “Although [the Pascaline] is composed of many different small parts, as you can see, at the same time it is so solid that, after the experience of which I have spoken before of [‘carrying the instrument over more than two hundred and fifty leagues of road, without its showing any damage’], I assure that the jarring that it receives in transportation, however far, will not disarrange it.

Actually, the mechanism for tens carry is not very reliable and the machine has to be in a position, near to horizontal, in order to work reliably, and sometimes, a hit to the box can cause unwanted carry to be performed.

The Pascaline soon become well-known in France and abroad. The first public description was in 1652, in the newspaper Muse Historique. The machine was demonstrated to the public in Paris. Pierre de Ferval, a family friend and a mathematics professor at the Royal College of France, agreed to demonstrate the device to prospective customers in his apartment at the College Maitre Gervais every Saturday morning and afternoon. Pascal went to work writing advertising flyers for the invention and asked a friend, the poet Charles Vion Dalibray, to compose a publicity sonnet. The Polish queen Marie Louise de Gonzague, a high-ranking and keen patron of sciences, asked to buy two copies (her secretary Pierre Des Noyers already had a copy, and Polish monarchs were so fascinated by the device, that they wanted to buy two more). Another fan of science, Swedish queen Christina desired a copy to be granted to her. Pascal satisfied their desire (the device for Queen Christina was sent together with a short manual), but soon after this lost his interest and abandoned his occasions with the calculation machine until the end of his short life.

Of some 50 constructed Pascalines, only 8-9 survived to the present day and can be seen in private or museum collections (4 in CNAM, Paris, 2 in a museum in Clermont, and several in private collections, e.g. in IBM).

The first copies of the machine were with five digital positions. Later on, Pascal manufactured machines with 6, 8, and even 10 digital positions. Some of the machines are entirely decimal (i.e. the scales are divided into 10 parts), and others are destined for monetary calculations and have scales with 12 and 20 parts (according to French monetary units: 1 sol = 12 deniers, 1 livre = 20 sols).

The dimensions of the brass box of the machine (for 8 digital positions variant) are 35.1/12.8/8.8 cm. The input wheels are divided by 10, 12, or 20 spokes, depending on the scale. The spokes are used for rotating the wheels by means of a pin or stylus. The stylus rotates the wheel until it gets to an unmovable stop, fixed to the lower part of the lid. The result can be seen in the row of windows in the upper part, where is placed a plate, which can be moved upwards and downwards, allowing to be seen the upper or lower row of digits, used for addition or subtraction.

Let’s examine the principle of action of the mechanism, using the lower sketch.

The input wheels (used for entering numbers) are smooth wheels, across which periphery are made openings. Counter-wheels are crown-wheels, i.e. they have openings with attached pins across the periphery.

The movement is transferred from the input wheel (marked with N in the sketch), which can be rotated by the operator by means of a stylus, over the counter, which consists of four crown-wheels (marked with B1, B2, B3, and B4), pinion-wheel (K), and mechanism for tens carry (C), to the digital drum (I), which digits can be seen in the windows of the lid.

The tens carry mechanism (called by Pascal sautoir), works in this way:
On the counter-wheel of the junior digital positions (B1) are mounted two pins (C1), which during the rotating of the wheel around its axis (A1) will engage the teeth of the fork (M), placed on the edge of the 2-legs rod (D1). This rod can be rotated around the axis (A2) of the senior digital position, and the fork has a tongue (E) with a spring. When during the rotating of the axis (A1) the wheel (B1) reaches the position, according to the digit 6, then pins (C1) will engage with the teeth of the fork, and at the moment, when the wheel moves from 9 to 0, then the fork will slide off from the engagement and will drop down, pushing the tongue. It will push the counter wheel (B2) of the senior position one step forward (i.e. will rotate it together with the axis (A2) to the appropriate angle. The rod (L), which has a special tooth, will serve as a stop and will prevent the rotating of the wheel (B1) during the raising of the fork. The tens carry mechanism of Pascal has an advantage, compared e.g. to this of Schickard’s Calculating Clock, because it is needed only a small force for transferring the motion between adjacent wheels. This advantage, however, is paid for by some shortcomings—during the carrying is produced a noise, and if the box is hit, may occur unwanted carrying.

The wheels of the calculating mechanism are rotating only in one direction and there are no intermediate wheels provided (designated to reverse the direction of the rotation). This means, that the machine can work only as an adding device, and subtraction must be done by means of an arithmetical operation, known as a complement to 9. This inconvenience could have been avoided by adding additional intermediate gear-wheels in the mechanism, but Pascal, as well as all the next inventors of calculating machines (Leibniz, Lepine, Leupold, etc.), didn’t want to complicate the mechanism and didn’t provide such a possibility.

The rotating of the wheels is transferred via the mechanism to the digital cylinders, which can be seen in the windows (see the photo below).

On the surface of cylinders are inscribed 2 rows of digits in this way, that the pairs are complemented to 9, for example, if the upper digit is 1, the lower is 8. On the lid is mounted a plate (marked with 2 in the lower sketch), which can be moved upwards and downwards, and by means of this plate, the upper row of digits must be shown during the subtraction, while the lower one—is during the addition. If we rotate the wheels, we will notice that the digits of the lower row are changing in ascending order (from 0 to 9), while the digits of the upper row are changing in descending order (from 9 to 0).

Zeroing of the mechanism can be done by rotating the wheels by means of the stylus in such a way, that between the two starting spokes (marked on the wheel) to be seen 9 (see the lower sketch). At this moment the digits of the lower row will be 0, while the upper digits will be 9 (or 12 or 20, for sols and deniers) (see the lower sketch). The manuscript Usage de la machine (this is the earliest known manuscript for Pascaline, from the 18th century. The first part of this document is a manual for an accountant and describes how to perform addition, subtraction, multiplication, and division.) gives the following method:
“Before starting a calculus, you shift the sliding cover that lays over the display windows toward the edge of the machine. Then you have to set the marked spokes in order to read “0” on all the drums. This is done by setting the stylus in between the spokes that are marked with white paper and by turning the wheel until the needle stops it. This brings for each wheel the highest digit the drum can have, that is to say, “9” for all the wheels devoted to the “Livres”, “19” on the “sols” wheel, and “11” on the “deniers” wheel. Then you turn the last wheel on the right of only one position […] afterward all the drums will display “0”.”

An instruction for work with the machine from Pascal didn’t survive to the present day, so different sources described different ways of manipulation. I will describe a way, which is optimal as a number of operations, needed for performing calculations. To use this way, however, the operator must know the multiplication table (during the multiplication operation), and be able to determine a complement to 9 for digits (for division and subtraction). This is an easy task even for 8-year-old children now, but not for the men of the 17^th century. Of course, the calculations can be done without following the two upper-mentioned requirements, but it will be necessary more attention and additional movements of the wheels.

First, let’s make an addition, for example, 64 + 83. We have to put the stylus between the spokes of the units wheels, against 4, and to rotate the wheel to the stop. In the lower row of windows (the upper was hidden by the plate) we will see 4. Then we rotate the wheels of the tens in the same way to 6. Then we have to enter the second addend, 83, and we will see the result, 147, meanwhile, one carry will be performed.

The subtraction will be a little more difficult and will require not only rotating but also some mental work. Let’s make, for example, 182–93.

After zeroing the mechanism (to see 000 in the lower windows), the plate of the windows must be moved to the lower position, and at this moment in the windows can be seen the number 999. Then the minuend is entered as a complement to 9, i.e. the units-wheel is rotated for 7, the tens-wheel for 1, and the hundreds-wheel to 8 (the complement to 9 of 182 is 817). As the upper row of digits actually is moved to descending order, thus we have made a subtraction 999-817 and the result is 182 (see the lower sketch).

Then must be entered the subtrahend (93), making a subtraction 182–93 (during rotating of the wheels two carries will happen—during the entering of the units (3), the units wheel will come to 9, and a carry to the tens-wheel wheel will be done, moving the tens-wheel to 7; then during the entering of 9 to the tens-wheel, it will be rotated to 8, and a carry will be transferred to the hundreds-wheel, making it to show 0). So, we have the right result 182–93=089 (see the lower sketch).

It wasn’t that difficult, but the operator must be able to determine the complement to 9 of a number.

To be able to use the fastest way for multiplication, the operator must know (or use) a multiplication table. Let’s make the multiplication 24 x 38. First, we have to multiply (mentally or looking at the table) units of the multiplicand to the units of the multiplier (8 x 4 = 32) and enter the result 32 in the mechanism (see the lower sketch).

Then we have to multiply units of the multiplier to the tens of the multiplicand (8 x 2 =16), but to enter the result (16) not in the right-most digital positions (for units and tens), but in the next (the positions for tens and hundreds). This we will have the result 192 (32 + 160) (see the lower sketch).

Then we have to repeat the same operation for the multiplication of the units of the multiplicand to the tens of the multiplier (3 x 4 =12) and for the multiplication of the tens of the multiplier to the tens of the multiplicand (3 x 2 = 6), entering the intermediate results into wheels of tens and hundreds (12), and into the hundreds and thousands (06). We have the right result (912) (see the lower sketch).

The division with the Pascaline can be done in a way, similar to the manual division of the numbers—first, we have to separate the dividend into 2 parts (according to the value of the divisor). Then we have to perform consecutive subtractions of the divisor from the selected part of the dividend until the remainder will become smaller than the part. At this moment we have to write down the number of subtractions, this will be the first digit of the result. Then we have to attach to the remainder (if any) 1 or more digits from the remained part of the dividend and start again the consecutive subtractions until we receive the second digit of the result and to continue this operation again and again until the last digit of the dividend will be used. In the end, we will have the remainder of the division in the windows, while the result will be written.

It’s quite obvious, that the work with the Pascaline is not very easy, but the machine is completely usable for simple calculations.

Some people at the time almost suggested Pascal was in possession of some kind of magical powers during his work on Pascaline. e.g. in Entretien avec M. de Sacy: It was common knowledge that [Pascal] seemed able to animate copper, and to give to brass the power of thought. Little unthinking wheels, each rimmed with then ten digits, were so arranged by him that they could give accounts even to the most reasonable persons, and he could in a sense make dumb machines speak.

Pierre Petit (1617–1687)—a French scholar and an inventor of a tool with Napier’s rods wrote: I find that since the invention of logarithms and rabdology, nothing of significance occurred regarding the practice of numbers other than Monsieur Pascal’s instrument. It is a device truly invented with as much success and speculation as his author has intelligence and knowledge. It consists, however, of a number of wheels, springs, and movements, and one needs the head and hands of a good clockmaker to understand how it works and to manufacture it, as well as the skills and knowledge of a good arithmetician to operate it. [For all these reasons], one fears that its use will never become widespread and that instead of being employed in financial bureaux and regional administrations to calculate taxes, or in merchant offices to compute their rules of discount and company, [the machine] will be stored in cabinets and libraries, there to be admired.

Admittedly, not all impressions from Pascal’s contemporaries were positive. Some were unfavorable, such as the October 1648 letter of the English gentleman traveler Balthasar Gerbier to Samuel Hartlib. Gerbier came upon Pascaline not long after a model in wood was finished, and thought it resembled something invented in England 30 years earlier. (Gerbier most likely meant William Pratt’s Arithmetical Jewel from 1616, a simple calculating instrument, that was nothing more than a variant of the common abacus). Gerbier though found many problems with Pascaline.

First, its user had to be knowledgeable in arithmetic, which ran contrary to Pascal’s rhetorical stance. Multiplications and divisions were complicated and it even took two Pascalines to make a simple rule of three. Gerbier also found Pascaline rather big (two feet in length, 9 inches broad), heavy, difficult to move, expensive (50 pistoles, or 500 lives), and useless to anyone who would like to learn the art of arithmetic. In other words, Gerbier did not admire this mechanical contraption supposed to “think” by itself. He ended his letter to Hartlib quoting a former ruler of Netherlands: Infine a Rare Invention farre saught, and deare baught: putt them jn the Storre house was the old Prince of Orange wont to saye and lett us proceede on the ordinary readdy way.

Pascaline was described in many other sources also, e.g. in the 18^th century books of Jean Gaffin Gallon—Machines et inventions approuvées par l’Academie Royale des Sciences, depuis son établissment jusqu’a présent; avec leur description (see description of Pascaline from Gallon).