Many a zero thinks it is the ellipse on which the Earth travels.
Stanisław Jerzy Lec
Around 1670 the Parisian doctor of medicine and self-taught architect Claude Perrault devised a simple calculating device, called Abaque Rhabdologique. The device was firstly described in a small book—Recueil de plusieurs machines, de nouvelle invention… (Collection of several newly invented machines…) published in 1770 in Paris, which 22 pages of text and several pages of sketches (see the book digitized of Google) contain nine inventions of Perrault, between them two machines for escalating and moving of burdens, a pendulum-controlled water clock, a pulley system to rotate the mirror of a reflecting telescope, etc.
Abaque Rhabdologique was described also in the journal of Academie Royale Des Sciences (Tome Premier, printed in 1735, see description of the Abaque Rhabdologique , pages 55-59). In this description is explained that the name of the machine Perrault derived from the mathematical practice of the ancients, who had used tablets (abacuses) to write numbers, and who had the capacity to perform many arithmetic operations by employing small rods marked with digits (rhabdology).
The device was devised probably between 1666 and 1675 (at that time Perrault was engaged mainly in architectural projects, designing the eastern facade of the Louvre, l’Observatoire de Paris, etc., so we can easily imagine that he needed some calculating tool). It is unknown whether a working copy of the device has been made by Perrault, and in the present day exist only several replicas.
In its contemporary reincarnations, the Abaque Rhabdologique is usually a small metal plate (30 cm x 12 cm x 0,7 cm) with a thickness of a finger and weight of some 1.15 kg. In the lower part of the lid is inscribed a multiplication table.
Over the plate are mounted seven small rules (marked with letters a, b, c, d, e, f and g on the sketch), which can be moved upwards and downwards. The rules are graduated to 26 parts by deep cuts, and the edge of the pin, which actually moves the rules, can be pushed in these cuts. Between the cuts are drawn ascending and descending rows of digits, with four empty divisions between zeroes. Rule a represents the units column, rule b—the decimal column, and so on to rule g, which represents the millions. The rules are separated by thin plates, which have perforations at the bottom.
Near the bottom of the each rule (with the exception of the rule for units), to the right side, there is a rule with 11 notches (marked with L), and the distance between notches is equal to the distance between digits, marked on the rules. From the other side of the rule with notches by means of springs are attached the hooks M. Due to the separating thin plates, the hook will be hidden in the body of the rule till the moment, when the hook will become symmetrical toward the opening in the plate. At this moment, the spring will push out the hook, which will pass the opening and will clutch to the notch of the lower rule and will move it one division downwards, making a carry to the next column.
On the front lid of the device ABCD are placed two long horizontal windows EF and GH. When the rulers are moving up or down, in these windows are seen the digits on the plates, and at every moment the sum of the digits of a particular ruler in upper and lower windows is always equal to 10. The window GH is used during adding operations, while the window EF is used during subtraction.
Between the windows are made 7 narrow vertical channels I-K, which are divided into 10 and marked with digits.
For entering a digit, in the particular cut of a ruler, which can be seen in the vertical channel, must be put a stylus, and then the ruler must be moved, until the stylus touched to the bottom edge of the channel. After this action, the number, which has been entered, will be shown simultaneously in both windows.
If to an entered number, for example 7, must be added 6, we have to perform the same action. During the movement of the ruler a to the bottom of the device, hook M will enter into cohesion with the cogs of the ruler b and will move it one division downwards. As a result of this in the decimal column will appear 1. In order to get the proper digit in the units column (which in this example must be 3), we have (without pulling the stylus out of the cut) to move the ruler upwards, until the stylus touched the bottom edge of the channel.
During the performing of subtraction, the actions of the operator are analogous, but the result must be read not in the lower, but in the upper window. If the minuend contains one or more zeroes, the result of the operation must be corrected.
Let’s see the original description of the device (pages 17 through 20 of the book Recueil de plusieurs machines, de nouvelle invention… are translated in the following section):
An excerpt from the book Recueil de plusieurs machines… (pp. 17-20)
I call this machine Rhabdological Abacus because the Ancients called abacuses small tables or boards on which they wrote arithmetical numerals and because they called rhabdology the ability to perform various arithmetical operations by means of several small rods marked with digits.
The machine that I propose does about the same thing. It is an abacus or small board about one finger thick, one foot long and half a foot wide. It is carved and made of thin ivory or copper plates, enclosing small rules marked with figures. In the cover plate, marked ABCD, two long and narrow windows in which the figures are displayed have been cut out, one EF at the top and one
GH at the bottom. These windows are about three inches apart and the area between them has cut out grooves IK, ending at about fives lines of the windows and distant also about five lines from each other.
Under the cover plate, several small rules a, b, c, d, e, f, g, lying side by side, can slide up and down: they are about 4 lines wide and seven and a half inches long: their length is divided into 26 equally spaced parts by engraved crossing lines. These lines are deep enough to hold in position the tip of a stylus used to move them. Twenty-two figures have been marked in the spaces between the engraved lines, eleven upwards and also eleven downwards: this is done in a way that four spacings are left empty between each series of figures. Thus we find, beginning from above, 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 0. and continuing downward, after having left four empty spacings, 0. 9. 8. 7. 6. 5. 4. 3. 2. 1. 0.
Between the grooves, the cover plate is marked upwards with the nine digits 1. 2. 3. 4. 5. 6. 7. 8. 9. keeping the same spacing as on the rules.
When the rules are lowered or lifted, the digits show one by one in the windows, but in a way that two digits of the same rule appearing in the two windows always sum up to 10. That’s to say, if the figure 9 shows in the upper window, the figure 1 will show in the bottom window, and if there is 6 in one window there will be 4 in the other one.
These rules, lying side by side, represent the decimal order; the first rule at the right, marked N above the upper window EF, being for the units; the second one, marked D, being for the tens; the third, marked C, for the hundreds, etc. They are separated by very thin blades, which are interrupted by the value of three spacings; the middle of this interruption being opposite the
bottom window. Each rule has LL rack-type notches at one side of the bottom, each notch being opposite the eleven figures, and at the other side a pawl M, to pull downwards the adjoining left-hand rule. To ensure that the pawl does not lower the rule it has to pull, more than one spacing, as is necessary, it needs to enter into the rule and stay hidden there, without being able to get out, until it is opposite the bottom window. Furthermore it has to retract as soon as the rule it is pulling has moved a value of one spacing. This is done thanks to two features: the first one is that a spring N shoves the pawl outwards; the second one is that the interruption of the blades separating the rules, enables the pawl to get out and engage into the notches of the rack. This engagement is possible only opposite the interruption and when the rule slides up or down; at the places where the blades are not interrupted, the pawl stays enclosed and is not in a state to engage.
To use the machine, one puts the tip of a stylus in one of the grooves, opposite one of the digits marked from top to bottom between the grooves. Pressing the stylus in the engraving between the digits, one slides it until it reaches the bottom of the groove: the same number chosen by the stylus will then appear in one of the windows, the bottom window being for addition and multiplication and the upper window for subtraction.
For instance, if one wants to obtain the number 8, one lowers this number in the window as previously explained: but if one wants to add 7, instead of this number, a digit 1 would show in the window as being the number of tens and nothing would show at the units location. In this case, without removing the tip of the stylus from the engraving where it presses, one has to slide it upwards to the top of the groove, and the digit 5 will then appear in the window at the units position. Thus, each time that the rule has been lowered as much as possible, nothing or only a 0 would show in the window, the stylus would have to be slid upwards.
For subtraction, one needs to set in the top window the number from which another one has to be subtracted.
For instance to subtract 34 from 123, one needs to put the stylus on the 4 of the units location and pull it to the bottom and then pull in the same way the 3 of the tens location. The number 123, which showed in the window, will then be replaced by the number 89.
It must be pointed out that when the number from which another one is subtracted contains one or several 0s, one unit needs to be subtracted from the remaining number, that is to say the one after the 0 toward the left.
For instance, if one wants to subtract 92 from 150, the machine will give 68 instead of 58, but the latter will be obtained if we subtract one from the 6 appearing at the tens location, and after the 0 of 150 which is of the units order. The same applies when there are several 0s.
For instance, if one wants to subtract 264 from 1500, the machine will give 1346 instead of 1236, but the latter will be obtained by subtracting one unit from 4, because of the first 0, and another unit from 3, because of the second 0.
For multiplication, one needs to do the same as for addition. For instance, if one wants to multiply 15 by 15, one needs to mark five times 5 which is 25 in the lower window by setting a 5 in the units location and a two in the tens location; finally mark one time 5 in the tens location and one time 1 in the hundreds location: this will give the result 225.
End of the excerpt
The simple and ingenious idea of the calculator of Claude Perrault was a step aside from the common development of mechanical calculating devices, which are based on the gear-wheels. This same idea will be applied by many inventors later in several cheap, simple, and reliable calculating devices, such as the adding devices of César Caze and Heinrich Kummer, and even in more sophisticated devices as the multi-column adding machine, designed in 1891 by Peter J. Landin of Minneapolis (US Patent No. 482312), which will be later produced in several countries in great quantities and many varieties, e. g. popular Comptator in Germany.
Biography of Claude Perrault
Claude Perrault was born in Paris on 25 September 1613, in the wealthy bourgeois family of a Parisian barrister—Pierre Perrault (1570-1652), and his wife Pâquette Le Clerc (or Leclerc) (d. 1657). Perrault was a numerous, talented, versatile, and close-knit Parisian family. Its founder, Pierre Perrault, born to a royal embroiderer from Tours, moved in 1592 only 22 years old to Paris, and developed a career as an avocat (barrister) in the city.
After their marriage on 27 January 1607, Pierre Perrault and Pâquette Le Clerc had seven children, but two of them died young, so Claude had four remaining brothers. The eldest brother—Jean Perrault (1609-1669), was (just like his father) a lawyer and advocate at the Parliament, and later was in the service of Henri II de Bourbon, Prince de Condé. Pierre Perrault (1611-1680), who was also a lawyer and Receiver General of Finances in Paris (1654-1664), later became a famous scientist (he developed the concept of the hydrological cycle, and together with Edme Mariotte, he was primarily responsible for making hydrology an experimental science). Nicolas Perrault (1624-1662), was an amateur mathematician and doctor of theology in Sorbonne, known for his denunciation of the Jesuits, and who was excluded from the Sorbonne for Jansenism and for defending Antoine Arnauld. However, the genuine celebrity of the Parisian branch of Perrault family was found to be the youngest brother—Charles Perrault (1628-1703), who became the world-renowned author of Tales of Mother Goose. The only daughter of the family—Marie, died at thirteen, and François, a twin of Charles, died in July 1628, only 6 months.
As boys, the Perrault brothers collaborated in such things as writing mock-heroic verse, and in adult life, each brother aided the career of the other. Claude Perrault was educated at the prestigious Collège de Beauvais (later he was followed by his younger brother Charles), one of the leading schools of France, educating pupils whose parents were prominent in the French establishment. Pierre Perrault wanted his son to study medicine, anatomy, and mathematics, so in 1634 Claude enrolled at the University of Paris to study medicine. He received a bachelor’s degree in 1639, and two years later, on 19 December 1641, he received a master’s degree (doctor of medicine).
After graduation, Perrault started his career as a physician and later on became a leader of a group of anatomists, who undertook dissections and descriptions of various animals. He proposed two theories, concerning the circulation of sap in plants and embryonic growth from preformed germs. These theories were highly influential in his lifetime and for many years thereafter. In 1681 Perrault began publishing of an all-embracing natural philosophy, which comprehended his research in anatomy, various aspects of animal and plant physiology, and acoustics. In his longest essay, he explained sound as an agitation of air, rather than by the concept of sound waves.
After twenty years of practicing medicine, around 1660 Claude Perrault turned his attention to architecture and now he is best known as one of the architects of the eastern facade of the Louvre (see the photo below), known as the Colonnade, built between 1665 and 1680 and cited everywhere as an example of the classicist phase of the French baroque style. Perrault’s architectural career was actually inspired by the translation into the French language he had started of the ten books of Vitruvius (published in 1673, with the help of Jean Baptiste Colbert), the only surviving Roman work on architecture.
When King Louis XIV decided to rebuild the Louvre in the 1660s, Perrault collaborated with the famous architects Louis Le Vau, Charles Le Brun and Francois d’Orbay to submit a worthy design for the competition, and his design was selected (not without the support of his brother Charles, who was at that time the First Commissioner of Royal Buildings, and who was promoted to this position from his brother Pierre, the Receiver General of Finances for Paris from 1654 until 1664).
The Colonnade was begun in 1668 and was almost completed in 1680, by which time Louis XIV had abandoned the Louvre and focused his attention on the Palace of Versailles. Nevertheless, the Colonnade may justly be regarded as the masterpiece of French architecture, and the finest edifice that exists in Paris.
Perrault’s architecture projects include also several other buildings in Paris like: l’Observatoire de Paris; the church of St-Benoît-le-Bétourné; the church of St-Geneviève; the altar in the Church of the Little Fathers; the triumphal arch on Rue St-Antoine, started in 1670 (Perrault’s design was preferred to competing designs of Le Brun and Le Vau, but was only partly executed in stone, and when the arch was taken down in the 19th century, it was found that the ingenious master had devised a means of so interlocking the stones, without mortar, that it had become an inseparable mass); a house for Louis XIV’s prime minister— Jean Baptiste Colbert, in Sceaux in 1673.
Although Claude Perrault stopped practicing medicine around 1661, he continued to treat family, friends, and the poor. At that time, besides the calculating device, he designed several other machines, which he occasionally displayed to the Academy: a pendulum-controlled water clock, a pulley system to rotate the mirror of a reflecting telescope, a machine to produce roper for ships, a machine for testing projectiles, machines to overcome the effects of friction. Many of his machines were used in the Louvre and by 1691 at Les Invalides. Perrault also wrote an essay on ancient music, to show its inferiority to that of his own day.
After Colbert’s death in 1683, the position of the Perrault family gradually declined. In the middle 1680s Claude Perrault’s house was among those torn down to make room for the Place des Victoires, and he seems to have spent his last years writing his essays (like Essais de Physique, and his own attempt to apply a modern approach to beauty, his architectural treatise, Ordonnance des cinq espèces de colonnes selon la méthode des Anciens), living at his brother Charles’ house.
Claude Perrault became a founding member of the French Academy of Sciences (Académie des Sciences) when it was founded in 1666. He remained a keen academician until his death and died as a genuine researcher in Paris on 9 October 1688, of an infection, caught during a dissection of a camel in the Botanical Garden of Paris.