2332:
replicas were built. Schickard's machine used clock wheels which were made stronger and were therefore heavier, to prevent them from being damaged by the force of an operator input. Each digit used a display wheel, an input wheel and an intermediate wheel. During a carry transfer all these wheels meshed with the wheels of the digit receiving the carry. The cumulative friction and inertia of all these wheels could "...potentially damage the machine if a carry needed to be propagated through the digits, for example like adding 1 to a number like 9,999". The great innovation in Pascal's calculator was that it was designed so that each input wheel is totally independent from all the others and carries are propagated in sequence. Pascal chose, for his machine, a method of re-zeroing that propagates a carry right through the machine. It is the most demanding operation to execute for a mechanical calculator and proved, before each operation, that the carry mechanism of the
Pascaline was fully functional. This could be taken as a testament to the quality of the Pascaline because none of the 18th century criticisms of the machine mentioned a problem with the carry mechanism and yet this feature was fully tested on all the machines, by their resets, all the time.
180:
132:
2336:
248:
2206:
20:
256:
28:
2125:
2159:), which provided the exclusive right to design and manufacture calculating machines in France, allowing the Pascaline to be the first calculator sold by a distributor. Pascal feared that craftsmen would not be able to accurately reproduce his Pascaline, which would result in false copies that would ruin his reputation along with the reputation of his machine. In 1645, in order to control the production of his invention, Pascal wrote to Monseigneur Le Chancelier (the chancellor of France,
2245:
2308:
293:", Pascal noted that a machine with 10,000 wheels would work as well as a machine with two wheels because each wheel is independent of the other. When it is time to propagate a carry, the sautoir, under the sole influence of gravity, is thrown toward the next wheel without any contact between the wheels. During its free fall the sautoir behaves like an acrobat jumping from one trapeze to the next without the trapezes touching each other ("sautoir" comes from the French verb
282:
3791:
2261:
2139:, Pascal hoped to provide a shortcut to hours of number crunching performed by workers in professions such as mathematics, physics, astronomy, etc. But, because of the intricacies of the device, the relationship Pascal had with craftsmen, and the intellectual property laws he influenced, the production of the Pascaline was far more limited than he had envisioned. Only 20 Pascalines were produced over the 10 years following its creation.
2130:“The second cause which I foresee capable of giving you umbrage, are (dear reader) the bad copies of this machine which might be produced by the presumption of the craftsmen: on these occasions, I conjure you to carry carefully the spirit of distinction, to keep you from surprise, to distinguish between leprosy and leprosy, and not to judge of the true originals by the imperfect productions of the ignorance and temerity of the workmen”
313:
3801:
3587:
235:
on it are barely visible. On a decimal machine, the digits 0 through 9 are carved clockwise, with each digit positioned between two spokes so that the operator can directly inscribe its value in the window of complements by positioning his stylus in between them and turning the wheel clockwise all the way to the stop lever. The marks on two adjacent spokes flank the digit 0 inscribed on this wheel.
2221:, one of Pascal's contemporaries also working on creating a calculating machine, likely succeeded because of his ability to manage good relations with his craftsmen. Morland proudly attributed part of his invention to the artisans by name– an odd thing for a nobleman to do for a commoner at the time. Morland was able to recruit the best talent in Europe. His first craftsmen was the famous
220:
the wheel clockwise all the way to the stop lever. The number displayed on the corresponding display register will be increased by 5 and, if a carry transfer takes place, the display register to the left of it will be increased by 1. To add 50, use the tens input wheel (second dial from the right on a decimal machine), to add 500, use the hundreds input wheel, etc...
65:, which adds 1 to 9 on one dial, and carries 1 to the next dial when the first dial changes from 9 to 0. His innovation made each digit independent of the state of the others, enabling multiple carries to rapidly cascade from one digit to another regardless of the machine's capacity. Pascal was also the first to shrink and adapt for his purpose a
191:
2346:
started to work on his own calculator after Pascal's death. He first tried to build a machine that could multiply automatically while sitting on top of the
Pascaline calculator, assuming incorrectly that all the dials on Pascal's calculator could be operated at the same time. Even though this could
613:
In other words, the 9's complement of the difference of two numbers is equal to the sum of the 9's complement of the minuend added to the subtrahend. The same principle is valid and can be used with numbers composed of digits of various bases (base 6, 12, 20), like in the surveying or the accounting
373:
The
Pascaline is a direct adding machine (it has no crank), so the value of a number is added to the accumulator as it is being dialed in. By moving a display bar, the operator can see either the number stored in the calculator or the complement of its value. Subtractions are performed like additions
2201:
understanding of the inventing process: ideas precede materialisation, as form precedes matter. This naturally led to an emphasis on theoretical purity and an underappreciation for practical work. As Pascal described artisans: “ work through groping trial and error, that is, without certain measures
955:
The method of re-zeroing that Pascal chose, which propagates a carry right through the machine, is the most demanding task for a mechanical calculator and proves, before each operation, that the machine is fully functional. This is a testament to the quality of the
Pascaline because none of the 18th
175:
when France was occupied by
Germany and therefore the main celebration was held in London, England. Speeches given during the event highlighted Pascal's practical achievements when he was already known in the field of pure mathematics, and his creative imagination, along with how ahead of their time
2393:
Pascal's calculator was the most successful mechanical calculator developed in the 17th century for the addition and subtraction of large numbers. The stepped reckoner had a problem in the carry mechanism after more than two consecutive carries, and the other devices had carry mechanisms (one tooth
234:
Four of the known machines have inner wheels of complements, which were used to enter the first operand in a subtraction. They are mounted at the center of each spoked metal wheel and turn with it. The wheel displayed in the picture above has an inner wheel of complements, but the numbers written
219:
For a 10-digit wheel (N), the fixed outside wheel is numbered from 0 to 9 (N-1). The numbers are inscribed in a decreasing manner clockwise going from the bottom left to the bottom right of the stop lever. To add a 5, one must insert a stylus between the spokes that surround the number 5 and rotate
198:
The calculator had spoked metal wheel dials, with the digit 0 through 9 displayed around the circumference of each wheel. To input a digit, the user placed a stylus in the corresponding space between the spokes and turned the dial until a metal stop at the bottom was reached, similar to the way the
272:
Pascal adapted a pawl and ratchet mechanism to his own turret wheel design; the pawl prevents the wheel from turning counterclockwise during an operator input, but it is also used to precisely position the display wheel and the carry mechanism for the next digit when it is pushed up and lands into
264:
Pascal went through 50 prototypes before settling on his final design; we know that he started with some sort of calculating clock mechanism which apparently "works by springs and which has a very simple design", was used "many times" and remained in "operating order". Nevertheless, "while always
2362:
The German calculating-machine inventor Arthur
Burkhardt was asked to attempt to put Leibniz' machine in operating condition. His report was favorable except for the sequence in the carry. and "therefore, especially in the case of multiple carry transfers, the operator had to check the result and
2188:
guild in 1631, half-way through Pascal's efforts to create the calculator. This affected Pascal’s ability to recruit talent as guilds often reduced the exchange of ideas and trade; sometimes, craftsmen would withhold their labour altogether to rebel against the nobles. Thus Pascal was in a market
259:
Pascal's adaptation. The blue gear (input) meshes with the yellow gears (processing), which themselves drive the red gear (output). The intersection of two perpendicular cylinders is one point and therefore, in theory, the blue gear and the yellow gear mesh in one single point. Pascal designed a
238:
On four of the known machines, above each wheel, a small quotient wheel is mounted on the display bar. These quotient wheels, which are set by the operator, have numbers from 1 to 10 inscribed clockwise on their peripheries (even above a non-decimal wheel). Quotient wheels seem to have been used
230:
These marks are used to set the corresponding cylinder to its maximum number, ready to be re-zeroed. To do so, the operator inserts the stylus in between these two spokes and turns the wheel all the way to the stopping lever. This works because each wheel is directly linked to its corresponding
2213:
Pascal operated his project with this hierarchy in mind: he invented and thought, while the artisans simply executed. He hid the theory from artisans, instead promoting that they should simply remember what to do, not necessarily why they should do it, i.e., until "practice has made the rules of
2331:
built the first replica of
Schickard's machine but not without adding wheels and springs to finish the design. This detail is not described in Schickard's two surviving letters and drawings. A problem in the operation of the Schickard machine, based on the surviving notes, was found after the
2323:
had written to his friend
Johannes Kepler in 1623 and 1624 which contain the drawings of a previously unknown working calculating clock, predating Pascal's work by twenty years. The 1624 letter stated that the first machine to be built by a professional had been destroyed in a fire during its
2354:
which was meant to perform additions, subtractions and multiplications automatically and division under operator control. Leibniz struggled for forty years to perfect this design and produced two machines, one in 1694 and one in 1706. Only the machine built in 1694 is known to exist; it was
207:
Each dial is associated with a one-digit display window located directly above it, which displays the value of the accumulator for this position. The complement of this digit, in the base of the wheel (6, 10, 12, 20), is displayed just above this digit. A horizontal bar hides either all the
227:, two adjacent spokes are marked; these marks differ from machine to machine. On the wheel pictured on the right, they are drilled dots, on the surveying machine they are carved; some are just scratches or marks made with a bit of varnish, some were even marked with little pieces of paper.
304:
All the sautoirs are armed by either an operator input or a carry forward. To re-zero a 10,000-wheel machine, if one existed, the operator would have to set every wheel to its maximum and then add a 1 to the "unit" wheel. The carry would turn every input wheel one by one in a very rapid
273:
its next position. Because of this mechanism, each number displayed is perfectly centered in the display window and each digit is precisely positioned for the next operation. This mechanism would be moved six times if the operator dialed a six on its associated input wheel.
147:
By 1654 he had sold about twenty machines (only nine of those twenty machines are known to exist today), but the cost and complexity of the
Pascaline was a barrier to further sales and production ceased in that year. By that time Pascal had moved on to the study of
231:
display cylinder (it automatically turns by one during a carry operation). To mark the spokes during manufacturing, one can move the cylinder so that its highest number is displayed and then mark the spoke under the stopping lever and the one to the right of it.
265:
improving on it" he found reason to try to make the whole system more reliable and robust. Eventually he adopted a component of very large clocks, shrinking and adapting for his purpose the robust gears that can be found in a turret clock mechanism called a
300:
Pascal used gravity to arm the sautoirs. One must turn the wheel five steps from 4 to 9 in order to fully arm a sautoir, but the carry transfer will move the next wheel only one step. Thus, much extra energy is accumulated during the arming of a sautoir.
608:
2214:
theory so common that have finally been reduced into art”. This stemmed from his lack of faith in not only the artisanal work process, but in the artisans themselves: “artisans cannot regulate themselves to produce unified machines autonomously."
1408:
Move the display bar down to uncover the complement part of each result cylinder. From this point on, every number dialed into the machine adds its value to the accumulator and therefore decreases the total displayed in the complement window.
123:, the first mechanical calculator strong enough and reliable enough to be used daily in an office environment. It is not clear whether he ever saw Leibniz's device, but he either re-invented it or utilized Leibniz's invention of the step drum.
2389:
that is often mistaken for a mechanical calculator because it has a carry mechanism in between the numbers. But it is actually an abacus, since it requires the operator to handle the machine differently when a carry transfer takes place.
340:
positions it above this pin ready to push back on it. The sautoir keeps on moving up and suddenly the second carry pin drops it. The sautoir falls of its own weight. During the second phase, the sautoir and the two wheels are completely
139:
Blaise Pascal began to work on his calculator in 1642, when he was 18 years old. He had been assisting his father, who worked as a tax commissioner, and sought to produce a device which could reduce some of his workload. Pascal received a
333:. During the first phase, the active wheel touches the one that will receive the carry through the sautoir, but it never moves it or modifies it and therefore the status of the receiving wheel has no impact whatsoever on the active wheel.
2324:
construction and that he was abandoning his project. After careful examination it was found, in contradiction to Franz Hammer's understanding, that
Schickard's drawings had been published at least once per century starting from 1718.
1396:. It feels like an addition since the only two differences in between an addition and a subtraction are the position of the display bar (direct versus complement) and the way the first number is entered (direct versus complement).
3095:
2654:
2196:
Pascal’s own conduct led to difficulty in recruiting artisans for his project. This was rooted by his belief that matters of the mind trumped those of the body. Pascal was not alone, as many natural philosophers of his time had a
290:
2202:
and proportions regulated by art, produc nothing corresponding to what they had sought, or, what’s more, they make a little monster appear, that lacks its principal limbs, the others being deformed, lacking any proportion.”
1563:
and non-decimal varieties, both of which can be viewed in museums today. They were designed for use by scientists, accountants and surveyors. The simplest Pascaline had five dials; later variants had up to ten dials.
203:
of a telephone is used. This displayed the number in the windows at the top of the calculator. Then, one simply redialed the second number to be added, causing the sum of both numbers to appear in the accumulator.
208:
complement numbers when it is slid to the top, or all the direct numbers when it is slid toward the center of the machine. It thereby displays either the content of the accumulator or the complement of its value.
2163:) in his letter entitled "La Machine d’arithmétique. Lettre dédicatoire à Monseigneur le Chancelier". Pascal requested that no Pascaline be made without his permission. His ingenuity garnered the respect of
2167:
of France who granted his request, but it came at a price; craftsmen were not able to legally experiment with Pascal's design, nor were they able to distribute his machine without his permission/guidance.
324:
The first phase happens when the display register goes from 4 to 9. The two carry pins (one after the other) lift the sautoir pushing on its protruding part marked (3,4,5). At the same time the kicking
215:
was used. The only two differences between an addition and a subtraction are the position of the display bar (direct versus complement) and the way the first number is entered (direct versus complement).
1126:
The operator enters the second operand: 56,789. If he starts with the rightmost number, the second wheel will go from 4 to 5, during the inscription of the 9, because of a carry transmission....
467:
2770:
1841:
Most of the machines that have survived the centuries are of the accounting type. Seven of them are in European museums, one belongs to the IBM corporation and one is in private hands.
704:
1833:
The metric system was adopted in France on December 10, 1799, by which time Pascal's basic design had inspired other craftsmen, although with a similar lack of commercial success.
104:), which provided the exclusive right to design and manufacture calculating machines in France. Nine Pascal calculators presently exist; most are on display in European museums.
2135:
Pascal planned to distribute the Pascaline broadly in order to reduce the workload for people who needed to perform laborious arithmetic. Drawing inspiration from his father, a
462:
2193:, who built upon Pascal's calculator later in the 17th century, had the progress for his machine halted due to his artisan selling the machine's parts for financial solvency.
451:
933:
3073:
364:
positions the entire receiving mechanism in its proper place. During the third phase the sautoir, which no longer touches the active wheel, adds one to the receiving wheel.
1356:
806:
756:
or dial the complement of the minuend directly. The display bar is shifted to show the complement's window so that the operator sees the direct number displayed because
956:
century criticisms of the machine mentioned a problem with the carry mechanism and yet this feature was fully tested on all the machines, by their resets, all the time.
1302:
1254:
865:
1392:
1212:
746:
211:
Since the gears of the calculator rotated in only one direction, negative numbers could not be directly summed. To subtract one number from another, the method of
2367:, the principle of a two-motion mechanical calculator. He was also the first to have cursors to inscribe the first operand and a movable carriage for results.
1013:
Add 1 to the right-most wheel. Each wheel sends its sautoir to the next one, the zeros appear one after another, like in a domino effect, from right to left.
297:, which means to jump). All the wheels (including gears and sautoir) have therefore the same size and weight independently of the capacity of the machine.
2236:
In the end, Pascal succeeded in cementing his name as the sole creator of the Pascaline. The royal patent states that it was his invention exclusively.
2067:
The second wheel from the right has a wheel with 10 spokes contained in a fixed wheel with 20 segments. This could be attributed to a bad restoration.
58:. He designed the machine to add and subtract two numbers directly and to perform multiplication and division through repeated addition or subtraction.
54:
in 1642. Pascal was led to develop a calculator by the laborious arithmetical calculations required by his father's work as the supervisor of taxes in
3619:
2774:
948:
The machine has to be re-zeroed before each new operation. To reset his machine, the operator has to set all the wheels to their maximum, using the
2795:
2503:
3607:
2394:
wheel) that were limited in their capacity to carry across multiple digits or had no carry mechanism in between the digits of the accumulator.
1177:
Subtractions are performed with the display bar moved closest to the center of the machine showing the complement value of the accumulator.
2597:, p. 29 (1988). "Toutes les machines arithmétiques inventoriées....sauf la machine tardive du C.N.A.M....ont deux rayons contigus marqués".
2363:
manually correct the possible errors". Leibniz had not succeeded in creating a calculator that worked properly, but he had invented the
2229:
for his contributions in producing coinage for England. Morland's other craftsmen were similarly accomplished: the third, Dutchman John
107:
Many later calculators were either directly inspired by or shaped by the same historical influences that had led to Pascal's invention.
2733:
2507:
1643:. Therefore, the pascaline needed wheels in base 6, 10, 12 and 20. Non-decimal wheels were always located before the decimal part.
1508:
Dial the subtrahend (12,345) on the spoked metal wheels. This is an addition. The result, 41,976, is in the 9's complement window.
2370:
There were five additional attempts at designing "direct entry" calculating machines in the 17th century (including the designs of
1064:
Additions are performed with the display bar moved closest to the edge of the machine, showing the direct value of the accumulator.
3617:"Avis nécessaire à ceux qui auront curiosité de voir ladite Machine et s'en servir" (Pascaline, 1635), online text and analysis on
3650:
92:. Pascal built around twenty more machines during the next decade, many of which improved on his original design. In 1649, King
2248:
Pascaline made for French currency which once belonged to Louis Perrier, Pascal's nephew. The least significant denominations,
2189:
that had a scarcity of skills and willing workers. Importantly, artisans were not free as intellectuals to create the machine:
965:
Set all the wheels to their maximum using the marks on two adjacent spokes. Every single wheel is ready for a carry transfer.
2530:
3343:
3288:
3242:
260:
gear that could easily take the strength of the strongest operator and yet added almost zero friction to the entire mechanism
2275:
the first calculator to have a controlled carry mechanism that allowed for an effective propagation of multiple carries
3612:
3478:
3439:
3394:
3373:
3028:
2185:
2043:
937:. The last step can be repeated as long as the subtrahend is smaller than the minuend displayed in the accumulator.
336:
The second phase starts when the display register goes from 9 to 0. The kicking pawl passes its guiding pin and its
2209:
Letter from the French Royal allowing Pascal exclusive rights to his invention. This was arguably the first patent.
2405:, the first machine strong enough to be used daily in an office environment. The Arithmometer was designed around
77:. This innovation allowed the device to resist the strength of any operator input with very little added friction.
2038:
This is the only known machine that came with a box. This is the smallest machine. Was it meant to be portable?
329:
is pulled up, using a pin on the receiving wheel as guidance, but without effect on this wheel because of the top
3825:
2128:
The above is an excerpt from Pascal's letter to the Chancellor of France. When translated to English, it states:
390:. So the 9's complement of 4 is 5 and the 9's complement of 9 is 0. Similarly, the 11's complement of 3 is 8.
3804:
2935:
1877:
623:
3355:
Science and Civilization in China: Volume 4, Physics and Physical Technology, Part 2, Mechanical Engineering
3131:
3021:
Reckoning with Matter: Calculating Machines, Innovation, and Thinking about Thinking from Pascal to Babbage
269:, itself derived from a water wheel mechanism. This could easily handle the strength of an operator input.
179:
2347:
not be done, it was the first time that a pinwheel was described and used in the drawing of a calculator.
603:{\displaystyle {\begin{aligned}CP(A-B)&=10^{n}-1-(A-B)&=10^{n}-1-A+B\\&=CP(A)+B\end{aligned}}}
3643:
1606:
3597:
2912:
Oeuvres: Avis nécessaire à ceux qui auront curiosité de voir la Machine d'Arithmétique et de s'en servir
3835:
3591:
1911:
2799:
2356:
399:
2190:
876:
89:
2328:
3416:
2379:
239:
during a division to memorize the number of times the divisor was subtracted at each given index.
2355:
rediscovered at the end of the 19th century, having spent 250 years forgotten in an attic at the
1311:
761:
2268:
Besides being the first calculating machine made public during its time, the pascaline is also:
171:
The tercentenary celebration of Pascal's invention of the mechanical calculator occurred during
3830:
3794:
3636:
3096:
Avis nécessaire à ceux qui auront curiosité de voir la Machine d'Arithmétique et de s'en servir
2655:
Avis nécessaire à ceux qui auront curiosité de voir la Machine d'Arithmétique et de s'en servir
1263:
115:
after 1671, after trying to add an automatic multiplication feature to the Pascaline. In 1820,
3281:
Histoire des instruments et machines à calculer, trois siècles de mécanique pensante 1642–1942
131:
2398:
1221:
832:
47:
2569:
3719:
3697:
3547:
3512:
3418:
Annales du Conservatoire national des arts et métier, 2e série, tome 5, Le calcul simplifié
2850:
2737:
2371:
2230:
1365:
1185:
719:
158:
144:
in 1649 that granted him exclusive rights to make and sell calculating machines in France.
3773:
1996:
8:
3692:
3405:
2335:
2148:
93:
3551:
3516:
2854:
251:
A lantern gear used in turret clocks powered by weights that can weigh hundreds of kilos
247:
3467:
3428:
2996:
2980:
2876:
2226:
2205:
3765:
255:
19:
3757:
3702:
3474:
3451:
3435:
3390:
3369:
3339:
3284:
3238:
3024:
2988:
2972:
2931:
2868:
2447:
2442:
2343:
2320:
2124:
1258:
after adding B. In displaying that data in the complement window, the operator sees
1070:
The following table shows all the steps required to compute 12,345 + 56,789 = 69,134
108:
27:
3749:
3000:
2821:
2160:
1666:. In a surveyor's machine (..10,10,6,12,12), the decimal part counted the number of
85:
3555:
3520:
2964:
2880:
2858:
2427:
2351:
2307:
2136:
1988:
116:
2177:
3687:
3489:
3384:
3363:
3045:
2910:
2316:
1646:
In an accounting machine (..10,10,20,12), the decimal part counted the number of
1399:
The following table shows all the steps required to compute 54,321-12,345=41,976
752:
First the complement of the minuend is entered. The operator can either use the
190:
2089:
This machine was bought as a broken music box in a French antique shop in 1942.
3462:
2823:
La Machine d'arithmétique. Lettre dédicatoire à Monseigneur le Chancelier, 1645
2422:
2375:
2222:
2218:
3602:
2968:
2621:, Courrier du centre international Blaise Pascal, Clermont-Ferrand, no 8, 1986
2171:
135:
Four Pascalines and a clone from LĂ©pine on display at the CNAM museum in Paris
3819:
3659:
2976:
2872:
2452:
2406:
2364:
2292:
2244:
306:
112:
51:
2278:
the first calculator to be used in an office (his father's to compute taxes)
2225:, who had already received protection and recognition from French statesman
3085:
Encyclopédie de Diderot & d'Alembert, Tome I, 1ère édition, pp. 680-681
2992:
2432:
2402:
2198:
1568:
823:
Then the second number is dialed in and adds its value to the accumulator.
289:
The sautoir is the centerpiece of the pascaline's carry mechanism. In his "
266:
172:
120:
74:
70:
2953:"Reinventing machines: the transmission history of the Leibniz calculator"
1457:
Enter the 9's complement of the minuend. The operator can either use the
1401:
1072:
958:
281:
2437:
2397:
Calculating machines did not become commercially viable until 1851, when
2152:
1984:
1067:
After re-zeroing the machine, numbers are dialed in one after the other.
200:
97:
2984:
2952:
2771:"Staatliche Kunstsammlungen Dresden - Mathematisch-Physikalischer Salon"
348:
pushes the pin on the receiving wheel and starts turning it. The upper
2281:
the first calculator commercialized (with around twenty machines built)
2260:
393:
In a decimal machine with n dials the 9's complement of a number A is:
153:
66:
3729:
3608:
More detail on the history of the Pascaline and contemporary replicas.
3327:
Catalogue du musée – Section A Instruments et machines à calculer
3274:(in French). Clermont-Ferrand: La Française d'Edition et d'Imprimerie.
3132:
The calculating Clock of Wilhelm Schickard. Retrieved January 31, 2012
164:
3560:
3535:
3525:
3500:
3421:(in French). Paris: Gauthiers-Villars et files, Imprimeurs-Libraires.
2863:
2838:
2164:
352:
is moved to the next space. The operation stops when the protruding
81:
312:
3536:"Blaise Pascal (1623–1662) Tercentenary of the calculating machine"
2499:
2180:. During his time, craftsmen in Europe increasingly organised into
149:
61:
Pascal's calculator was especially successful in the design of its
2086:
5 x 10 + 6 + 12 + 12
1978:
This machine was assembled in the 18th century with unused parts.
84:, he presented the device to the public in 1645, dedicating it to
2264:
View through the back of the above calculator, showing the wheels
2047:
1560:
3628:
2233:, came a famous Dutch family who pioneered the pendulum clock.
3586:
3329:(in French). Paris: Conservatoire National des Arts et MĂ©tiers.
3260:
2609:, p. 29 (1988). "...palmette, petits ronds, griffures, vernis".
2156:
871:
The result (A-B) is displayed in the complement window because
141:
101:
3311:(in French). Presses universitaires de France. pp. 20–28.
2272:
the only operational mechanical calculator in the 17th century
3407:
Mechanical arithmetic, or The history of the counting machine
2327:
Bruno von Freytag Loringhoff, a mathematics professor at the
2181:
1601:
55:
2401:
released, after thirty years of development, his simplified
223:
On all the wheels of all the known machines, except for the
2172:
Social context of intellectual collaboration with craftsmen
2119:
2094:
1461:
or dial the 9's complement of 54,321 (45,678) directly.
3603:
Detailed animation explaining how the Pascaline works.
309:
fashion and all the display registers would be reset.
3613:
More on the 'operating instructions' for a Pascaline.
1368:
1314:
1266:
1224:
1188:
879:
835:
764:
722:
626:
465:
402:
2796:"IBM Archives: Artifacts list for vol. 3, items M-Z"
2657:
Wikisource: La Machine d’arithmétique, Blaise Pascal
1079:
The machine is at zero, the operator enters 12,345.
374:
using some properties of 9's complement arithmetic.
3491:
Recueil de plusieurs machines de nouvelle invention
3434:. Los Alamitos, California: IEEE Computer Society.
3237:(in French). Clermont-Ferrand: Muséum Henri-Lecoq.
2928:
Labour, Science and Technology in France, 1500-1620
382:The 9's complement of any one-digit decimal number
3466:
3450:
3427:
3261:Ellenberger, Michel; Collin, Marie–Marthe (1993).
3023:. The University of Chicago Press. pp. 5–34.
1386:
1350:
1296:
1248:
1206:
927:
859:
800:
740:
698:
602:
445:
2581:Pascal tercentenary celebration, London, (1942).
2184:, such as the English clockmakers who formed the
2010:Marguerite (1646–1733) was Pascal's goddaughter.
1949:Louis PĂ©rier, Pascal's nephew, offered it to the
1830:The decimal part of each machine is highlighted.
949:
3817:
3598:Website explaining the operation of a Pascaline.
2734:"Muséum Henri-Lecoq - Ville de Clermont-Ferrand"
2339:Leibniz' drawing showing 365 multiplied by 124.
1694:. Scientific machines just had decimal wheels.
1458:
753:
3573:(in French) (8). Clermont-Ferrand: 4–25. 1986.
3571:Courrier du Centre International Blaise Pascal
3336:Scripta Mathematica (Septembre 1932-Juin 1933)
3320:(in French). Presses universitaires de France.
3309:Le calcul mécanique. Que sais-je ? n° 367
3302:(in French). Presses universitaires de France.
3300:Le calcul mécanique. Que sais-je ? n° 367
3074:Privilège du Roi, pour la Machine Arithmétique
2957:The British Journal for the History of Science
2930:. Cambridge university press. pp. 29–31.
2319:, announced the discovery of two letters that
456:and therefore the 9's complement of (A-B) is:
316:The three phases of a carry transfer operation
80:Pascal designed the machine in 1642. After 50
3644:
3318:Histoire du calcul. Que sais-je ? n° 198
31:Top view and overview of the entire mechanism
3272:Les machines arithmétiques de Blaise Pascal
3235:Les Machines Arithmétiques de Blaise Pascal
3050:(in French). La Haye. pp. vol 4, pg 7.
2896:Les machines arithmétiques de Blaise Pascal
2689:
2687:
2291:the first calculator to be described in an
3651:
3637:
2704:
2702:
2298:the first calculator sold by a distributor
3559:
3524:
3469:Computers: The Life Story of a Technology
3324:
3233:Vidal, Nathalie; Vogt, Dominique (2011).
3232:
2893:
2862:
1855: Machine Name
952:, and then add 1 to the rightmost wheel.
709:This principle applied to the Pascaline:
320:The carry transmission has three phases:
183:Detail of the carry mechanism and of the
3098:La Machine d’arithmétique, Blaise Pascal
3076:La Machine d’arithmétique, Blaise Pascal
2684:
2541:
2539:
2531:La Machine d’arithmétique, Blaise Pascal
2385:Around 1660 Claude Perrault designed an
2350:He then devised a competing design, the
2334:
2306:
2259:
2243:
2204:
2142:
2123:
2120:Limits to distribution and controversies
943:
311:
280:
254:
246:
189:
178:
176:both the machine and its inventor were.
130:
26:
18:
3494:. Paris, France: Jean Batiste Coignard.
3177:
3175:
2836:
2699:
2410:
2315:In 1957, Franz Hammer, a biographer of
2176:Pascal lived in France during France's
699:{\displaystyle CP(A-B-C-D)=CP(A)+B+C+D}
212:
3818:
3263:La machine Ă calculer de Blaise Pascal
3251:
3043:
2925:
2908:
2819:
3632:
3534:Prof. S. Chapman (October 31, 1942).
3297:
3066:
3018:
3014:
3012:
3010:
2950:
2815:
2813:
2811:
2809:
2536:
2284:the first calculator to be patented (
3800:
3172:
3088:
2498:
2302:
62:
23:A Pascaline signed by Pascal in 1652
3457:. New York: Reynal & Hitchcock.
3382:
13:
3386:The Universal History of Computing
3256:(in French). La Haye: Chez Detune.
3007:
2919:
2806:
2480:
2015:Musée Henri Lecoq
276:
242:
14:
3847:
3658:
3579:
3501:"Pascal tercentenary celebration"
3361:
2798:. 23 January 2003. Archived from
2044:Mathematisch-Physikalischer Salon
377:
3799:
3790:
3789:
3585:
3410:. Chicago: Washington Institute.
3365:The Universal History of Numbers
2295:(Diderot & d'Alembert, 1751)
446:{\displaystyle CP(A)=10^{n}-1-A}
3430:History of Computing Technology
3210:
3198:
3186:
3160:
3148:
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2726:
2714:
2672:
2660:
2648:
2636:
2624:
2612:
2600:
2239:
2072:Léon Parcé collection
928:{\displaystyle CP(CP(A-B))=A-B}
3389:. John Wiley & Sons, Inc.
3368:. John Wiley & Sons, Inc.
3182:Jean Marguin, pp. 64–65 (1994)
2588:
2575:
2572:, (2022). Retrieved 2022-09-02
2563:
2551:
2523:
2492:
2464:
1951:Académie des sciences de Paris
1381:
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633:
617:This can also be extended to:
587:
581:
529:
517:
488:
476:
415:
409:
1:
3568:
3533:
3487:
3426:Williams, Michael R. (1997).
3425:
3338:. Kessinger Publishing, LLC.
3216:
3154:
3142:
3107:
2951:MORAR, FLORIN-STEFAN (2015).
2693:
2486:
2311:Schickard's calculating clock
1836:
3498:
3414:
3352:
3334:Ginsburg, Jekuthiel (2003).
3306:
3204:
2666:
2582:
2409:and initially used Pascal's
2107:
2104:
2099:
2082:
2079:
2074:
2060:
2057:
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2019:
2003:
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1992:
1971:
1968:
1962:
1942:
1939:
1933:
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1889:
1883:
1505:
1453:
1404:
1123:
1075:
961:
950:marks on two adjacent spokes
368:
7:
3473:. Westport, CT: Greenwood.
3448:
3357:. Taipei: Caves Books, Ltd.
3265:(in French). Paris: Nathan.
2839:"Blaise Pascal (1623–1662)"
2504:"Blaise Pascal's Pascaline"
2416:
1459:inner wheels of complements
1351:{\displaystyle CP(CP(A-B))}
1059:
801:{\displaystyle CP(CP(A))=A}
754:inner wheels of complements
16:Early mechanical calculator
10:
3852:
3499:M.E.P (October 31, 1942).
3465:; Ferro, David L. (2005).
3453:Pascal, The life of genius
3415:d'Ocagne, Maurice (1893).
3225:
2837:Champan, S. (1942-10-01).
1912:Christina, Queen of Sweden
1216:during the first step and
827:
814:
714:
126:
3785:
3742:
3711:
3666:
3488:Perrault, Claude (1700).
3461:
3403:
3333:
3315:
3278:
3269:
3192:
3181:
3166:
3119:
3060:
3047:Oeuvres: Privilege Du Roi
2969:10.1017/S0007087414000429
2757:
2720:
2708:
2678:
2642:
2630:
2606:
2594:
2557:
2545:
2413:method for subtractions.
1599:. Length was measured in
1297:{\displaystyle CP(CP(A))}
1180:The accumulator contains
156:, which gave us both the
3353:Needham, Joseph (1986).
3254:Oeuvres de Blaise Pascal
2898:(in French). p. 12.
2458:
2149:King Louis XIV of France
1559:Pascalines came in both
3569:"Usage de la machine".
3449:Bishop, Morris (1936).
3383:Ifrah, Georges (2001).
3362:Ifrah, Georges (2000).
3270:Mourlevat, Guy (1988).
3252:Pascal, Blaise (1779).
3044:Pascal, Blaise (1779).
3019:Jones, Matthew (2016).
2909:Pascal, Blaise (1779).
2894:Mourlevat, Guy (1988).
2820:Pascal, Blaise (1645).
2357:University of Göttingen
1554:
1249:{\displaystyle CP(A-B)}
860:{\displaystyle CP(A-B)}
3826:Mechanical calculators
3404:Felt, Dorr E. (1916).
3283:(in French). Hermann.
3279:Marguin, Jean (1994).
2926:Heller, Henry (2002).
2340:
2329:University of TĂĽbingen
2312:
2265:
2257:
2210:
2132:
2105: Accounting
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195:
187:
136:
32:
24:
3511:(3809). London: 527.
3157:, pp. 124, 128 (1997)
2915:(in French). La Haye.
2802:on November 21, 2005.
2502:(November 14, 2014).
2338:
2310:
2263:
2247:
2208:
2143:Intellectual property
2127:
1723:Decimal / scientific
1405:Change display space
1389:
1387:{\displaystyle (A-B)}
1353:
1299:
1251:
1209:
1207:{\displaystyle CP(A)}
944:Resetting the machine
930:
862:
803:
743:
741:{\displaystyle CP(A)}
701:
605:
448:
315:
284:
258:
250:
193:
182:
134:
48:mechanical calculator
30:
22:
3720:Lettres provinciales
3594:at Wikimedia Commons
3316:Taton, René (1969).
3307:Taton, René (1963).
3298:Taton, René (1949).
2387:abaque rhabdologique
2155:(a precursor to the
1366:
1312:
1306:which is A and then
1264:
1222:
1186:
877:
833:
762:
720:
624:
463:
400:
159:Lettres provinciales
90:chancellor of France
3683:Pascal's calculator
3552:1942Natur.150..508C
3546:. London: 508–509.
3517:1942Natur.150..527M
3193:Scripta Mathematica
2855:1942Natur.150..508C
2760:, Genealogy, (1988)
2696:, N°8, p. 9, (1986)
2619:Usage de la machine
2548:, p. 12 (1988)
1699:
820:
94:Louis XIV of France
38:(also known as the
36:Pascal's calculator
3325:Collectif (1942).
3122:, pp. 46-48 (1994)
2633:, pp. 31–33 (1988)
2341:
2313:
2266:
2258:
2256:, are on the right
2211:
2133:
1887:Chancelier SĂ©guier
1697:
1384:
1348:
1294:
1246:
1204:
925:
857:
798:
738:
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600:
598:
443:
318:
291:Avis nécessaire...
287:
262:
253:
196:
188:
137:
40:arithmetic machine
33:
25:
3836:French inventions
3813:
3812:
3774:Marguerite PĂ©rier
3758:Jacqueline Pascal
3724:(1656–1657)
3698:Pascal's triangle
3624:
3590:Media related to
3345:978-0-7661-3835-3
3290:978-2-7056-6166-3
3244:978-2-9528068-4-8
3072:(fr) Wikisource:
2849:(3809): 508–509.
2570:Magazine Priciest
2509:Things that Count
2448:Analytical engine
2443:Difference engine
2344:Gottfried Leibniz
2321:Wilhelm Schickard
2303:Competing designs
2191:Gottfried Leibniz
2117:
2116:
1997:Marguerite PĂ©rier
1828:
1827:
1567:The contemporary
1552:
1551:
1548:
1547:
1501:
1500:
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1448:
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1165:
1119:
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1005:
1004:
941:
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213:nine's complement
109:Gottfried Leibniz
3843:
3803:
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3793:
3792:
3778:
3770:
3762:
3754:
3735:
3725:
3693:Pascal's theorem
3653:
3646:
3639:
3630:
3629:
3623:
3589:
3574:
3565:
3563:
3561:10.1038/150508a0
3530:
3528:
3526:10.1038/150527a0
3495:
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3155:Michael Williams
3152:
3146:
3143:Michael Williams
3140:
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2864:10.1038/150508a0
2834:
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2803:
2792:
2786:
2785:
2783:
2782:
2773:. Archived from
2767:
2761:
2755:
2749:
2748:
2746:
2745:
2736:. Archived from
2730:
2724:
2718:
2712:
2706:
2697:
2694:Courrier du CIBP
2691:
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2490:
2484:
2478:
2471:Ĺ’uvres de Pascal
2468:
2428:Stepped reckoner
2399:Thomas de Colmar
2352:Stepped Reckoner
2137:tax commissioner
2111:6 x 10 + 20 + 12
2064:8 x 10 + 20 + 12
2035:3 x 10 + 20 + 12
2026:
2017:Clermont-Ferrand
1989:Clermont-Ferrand
1975:4 x 10 + 20 + 12
1946:6 x 10 + 20 + 12
1896:6 x 10 + 20 + 12
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362:pawl/ratchet (C)
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350:pawl/ratchet (C)
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331:pawl/ratchet (C)
328:
117:Thomas de Colmar
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3842:
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3766:Gilberte PĂ©rier
3760:
3752:
3738:
3733:
3723:
3707:
3676:
3662:
3657:
3582:
3577:
3481:
3463:Swedin, Eric G.
3442:
3397:
3376:
3346:
3291:
3245:
3228:
3223:
3219:, p. 38 (1700).
3217:Claude Perrault
3215:
3211:
3203:
3199:
3195:, p. 149 (1932)
3191:
3187:
3180:
3173:
3165:
3161:
3153:
3149:
3145:, p. 122 (1997)
3141:
3137:
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3114:
3110:, p. 20, (1984)
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2605:
2601:
2593:
2589:
2583:Magazine Nature
2580:
2576:
2568:
2564:
2560:, p. 316 (1933)
2556:
2552:
2544:
2537:
2528:
2524:
2514:
2512:
2497:
2493:
2487:Magazine Nature
2485:
2481:
2469:
2465:
2461:
2419:
2317:Johannes Kepler
2305:
2286:royal privilege
2242:
2174:
2153:royal privilege
2145:
2122:
2055:Queen of Poland
2024:
2016:
1987:
1959:
1930:
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1698:Configurations
1569:French currency
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358:buffer stop (R)
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279:
277:Carry mechanism
245:
243:Inner mechanism
225:machine tardive
142:Royal Privilege
129:
98:royal privilege
63:carry mechanism
17:
12:
11:
5:
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3763:
3755:
3750:Étienne Pascal
3746:
3744:
3740:
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3737:
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3726:
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3713:
3709:
3708:
3706:
3705:
3703:Pascal's wager
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3580:External links
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3331:
3322:
3313:
3304:
3295:
3289:
3276:
3267:
3258:
3249:
3243:
3229:
3227:
3224:
3222:
3221:
3209:
3197:
3185:
3171:
3169:, p. 11 (2005)
3159:
3147:
3135:
3124:
3112:
3100:
3087:
3078:
3065:
3063:, p. 46 (1994)
3053:
3036:
3029:
3006:
2963:(1): 123–146.
2943:
2936:
2918:
2901:
2886:
2829:
2805:
2787:
2762:
2750:
2725:
2723:, p. 38 (1988)
2713:
2711:, p. 30 (1988)
2698:
2683:
2681:, p. 17 (1988)
2671:
2669:, p. 41 (1994)
2659:
2647:
2645:, p. 27 (1988)
2635:
2623:
2611:
2599:
2587:
2574:
2562:
2550:
2535:
2522:
2491:
2479:
2473:in 5 volumes,
2462:
2460:
2457:
2456:
2455:
2450:
2445:
2440:
2435:
2430:
2425:
2423:Adding machine
2418:
2415:
2411:9's complement
2407:Leibniz wheels
2376:Samuel Morland
2372:Tito Burattini
2304:
2301:
2300:
2299:
2296:
2289:
2282:
2279:
2276:
2273:
2241:
2238:
2223:Peter Blondeau
2219:Samuel Morland
2173:
2170:
2165:King Louis XIV
2161:Pierre SĂ©guier
2151:gave Pascal a
2144:
2141:
2121:
2118:
2115:
2114:
2112:
2109:
2106:
2103:
2101:
2098:
2091:
2090:
2087:
2084:
2081:
2078:
2076:
2073:
2069:
2068:
2065:
2062:
2059:
2056:
2053:
2050:
2040:
2039:
2036:
2033:
2030:
2027:
2021:
2018:
2012:
2011:
2008:
2005:
2002:
1999:
1994:
1991:
1980:
1979:
1976:
1973:
1970:
1967:
1966:Late (Tardive)
1964:
1961:
1955:
1954:
1947:
1944:
1941:
1938:
1935:
1932:
1926:
1925:
1923:
1920:
1917:
1914:
1909:
1906:
1900:
1899:
1897:
1894:
1891:
1888:
1885:
1882:
1874:
1873:
1869:
1865:
1861:
1857:
1853:
1849:
1838:
1835:
1826:
1825:
1818:
1811:
1804:
1797:
1792:
1788:
1787:
1780:
1773:
1766:
1761:
1756:
1752:
1751:
1744:
1739:
1734:
1729:
1728:Ten thousands
1724:
1720:
1719:
1716:
1713:
1710:
1707:
1704:
1556:
1553:
1550:
1549:
1546:
1545:
1544: 3
1542:
1539:
1536:
1533:
1529:
1528:
1527: 6
1525:
1522:
1519:
1516:
1509:
1506:
1503:
1502:
1499:
1498:
1497: 8
1495:
1492:
1489:
1486:
1482:
1481:
1480: 1
1478:
1475:
1472:
1469:
1462:
1455:
1451:
1450:
1447:
1446:
1445: 0
1443:
1440:
1437:
1434:
1430:
1429:
1428: 9
1426:
1423:
1420:
1417:
1410:
1406:
1383:
1380:
1377:
1374:
1371:
1347:
1344:
1341:
1338:
1335:
1332:
1329:
1326:
1323:
1320:
1317:
1293:
1290:
1287:
1284:
1281:
1278:
1275:
1272:
1269:
1245:
1242:
1239:
1236:
1233:
1230:
1227:
1203:
1200:
1197:
1194:
1191:
1174:
1171:
1168:
1167:
1164:
1163:
1162: 4
1160:
1157:
1154:
1151:
1147:
1146:
1145: 5
1143:
1140:
1137:
1134:
1127:
1124:
1121:
1120:
1117:
1116:
1115: 5
1113:
1110:
1107:
1104:
1100:
1099:
1098: 4
1096:
1093:
1090:
1087:
1080:
1077:
1061:
1058:
1055:
1054:
1051:
1050:
1049: 0
1047:
1044:
1041:
1038:
1034:
1033:
1032: 9
1030:
1027:
1024:
1021:
1014:
1011:
1007:
1006:
1003:
1002:
1001: 9
999:
996:
993:
990:
986:
985:
984: 0
982:
979:
976:
973:
966:
963:
945:
942:
939:
938:
924:
921:
918:
915:
912:
909:
906:
903:
900:
897:
894:
891:
888:
885:
882:
869:
856:
853:
850:
847:
844:
841:
838:
825:
824:
821:
812:
811:
797:
794:
791:
788:
785:
782:
779:
776:
773:
770:
767:
750:
737:
734:
731:
728:
725:
707:
706:
695:
692:
689:
686:
683:
680:
677:
674:
671:
668:
665:
662:
659:
656:
653:
650:
647:
644:
641:
638:
635:
632:
629:
611:
610:
595:
592:
589:
586:
583:
580:
577:
574:
571:
569:
567:
564:
561:
558:
555:
552:
549:
544:
540:
536:
533:
531:
528:
525:
522:
519:
516:
513:
510:
505:
501:
497:
494:
492:
490:
487:
484:
481:
478:
475:
472:
469:
468:
454:
453:
442:
439:
436:
433:
428:
424:
420:
417:
414:
411:
408:
405:
379:
378:9's complement
376:
370:
367:
366:
365:
342:
334:
278:
275:
244:
241:
128:
125:
113:Leibniz wheels
100:(similar to a
96:gave Pascal a
86:Pierre SĂ©guier
15:
9:
6:
4:
3:
2:
3848:
3837:
3834:
3832:
3831:Blaise Pascal
3829:
3827:
3824:
3823:
3821:
3806:
3798:
3796:
3788:
3787:
3784:
3775:
3772:
3767:
3764:
3759:
3756:
3751:
3748:
3747:
3745:
3741:
3732:
3731:
3727:
3722:
3721:
3717:
3716:
3714:
3710:
3704:
3701:
3699:
3696:
3694:
3691:
3689:
3686:
3684:
3681:
3680:
3678:
3672:
3669:
3668:
3665:
3661:
3660:Blaise Pascal
3654:
3649:
3647:
3642:
3640:
3635:
3634:
3631:
3622:
3621:
3616:
3614:
3611:
3609:
3606:
3604:
3601:
3599:
3596:
3593:
3588:
3584:
3583:
3572:
3567:
3562:
3557:
3553:
3549:
3545:
3541:
3537:
3532:
3527:
3522:
3518:
3514:
3510:
3506:
3502:
3497:
3493:
3492:
3486:
3482:
3480:0-8018-8774-7
3476:
3471:
3470:
3464:
3460:
3455:
3454:
3447:
3443:
3441:0-8186-7739-2
3437:
3432:
3431:
3424:
3420:
3419:
3413:
3409:
3408:
3402:
3398:
3396:0-471-39671-0
3392:
3388:
3387:
3381:
3377:
3375:0-471-39671-0
3371:
3367:
3366:
3360:
3356:
3351:
3347:
3341:
3337:
3332:
3328:
3323:
3319:
3314:
3310:
3305:
3301:
3296:
3292:
3286:
3282:
3277:
3273:
3268:
3264:
3259:
3255:
3250:
3246:
3240:
3236:
3231:
3230:
3218:
3213:
3206:
3201:
3194:
3189:
3183:
3178:
3176:
3168:
3163:
3156:
3151:
3144:
3139:
3133:
3128:
3121:
3116:
3109:
3108:Stan Augarten
3104:
3097:
3091:
3082:
3075:
3069:
3062:
3057:
3049:
3048:
3040:
3032:
3030:9780226411460
3026:
3022:
3015:
3013:
3011:
3002:
2998:
2994:
2990:
2986:
2982:
2978:
2974:
2970:
2966:
2962:
2958:
2954:
2947:
2939:
2933:
2929:
2922:
2914:
2913:
2905:
2897:
2890:
2882:
2878:
2874:
2870:
2865:
2860:
2856:
2852:
2848:
2844:
2840:
2833:
2825:
2824:
2816:
2814:
2812:
2810:
2801:
2797:
2791:
2777:on 2011-10-19
2776:
2772:
2766:
2759:
2758:Guy Mourlevat
2754:
2740:on 2011-10-15
2739:
2735:
2729:
2722:
2721:Guy Mourlevat
2717:
2710:
2709:Guy Mourlevat
2705:
2703:
2695:
2690:
2688:
2680:
2679:Guy Mourlevat
2675:
2668:
2663:
2656:
2651:
2644:
2643:Guy Mourlevat
2639:
2632:
2631:Guy Mourlevat
2627:
2620:
2615:
2608:
2607:Guy Mourlevat
2603:
2596:
2595:Guy Mourlevat
2591:
2584:
2578:
2571:
2566:
2559:
2554:
2547:
2546:Guy Mourlevat
2542:
2540:
2532:
2526:
2511:
2510:
2505:
2501:
2495:
2488:
2483:
2476:
2472:
2467:
2463:
2454:
2453:Z1 (computer)
2451:
2449:
2446:
2444:
2441:
2439:
2436:
2434:
2431:
2429:
2426:
2424:
2421:
2420:
2414:
2412:
2408:
2404:
2400:
2395:
2391:
2388:
2383:
2381:
2377:
2373:
2368:
2366:
2365:Leibniz wheel
2360:
2358:
2353:
2348:
2345:
2337:
2333:
2330:
2325:
2322:
2318:
2309:
2297:
2294:
2293:encyclopaedia
2290:
2287:
2283:
2280:
2277:
2274:
2271:
2270:
2269:
2262:
2255:
2251:
2246:
2237:
2234:
2232:
2228:
2224:
2220:
2217:In contrast,
2215:
2207:
2203:
2200:
2194:
2192:
2187:
2183:
2179:
2178:Ancien RĂ©gime
2169:
2166:
2162:
2158:
2154:
2150:
2140:
2138:
2131:
2126:
2113:
2110:
2102:
2096:
2093:
2092:
2088:
2085:
2077:
2071:
2070:
2066:
2063:
2054:
2049:
2045:
2042:
2041:
2037:
2034:
2025:Durant-Pascal
2022:
2014:
2013:
2009:
2006:
1998:
1995:
1990:
1986:
1982:
1981:
1977:
1974:
1965:
1957:
1956:
1952:
1948:
1945:
1936:
1928:
1927:
1924:
1921:
1913:
1910:
1902:
1901:
1898:
1895:
1886:
1879:
1876:
1875:
1870:
1867:Configuration
1866:
1862:
1858:
1854:
1850:
1846:
1845:
1842:
1834:
1831:
1824:
1819:
1817:
1812:
1810:
1805:
1803:
1798:
1793:
1790:
1789:
1786:
1781:
1779:
1774:
1772:
1767:
1762:
1757:
1754:
1753:
1750:
1745:
1740:
1735:
1730:
1725:
1722:
1721:
1717:
1714:
1711:
1708:
1706:Other wheels
1705:
1703:Machine type
1702:
1701:
1695:
1693:
1689:
1685:
1681:
1677:
1673:
1669:
1665:
1661:
1657:
1653:
1649:
1644:
1642:
1638:
1634:
1630:
1626:
1622:
1618:
1617:
1613:
1609:
1604:
1603:
1598:
1594:
1590:
1586:
1582:
1578:
1574:
1570:
1565:
1562:
1543:
1541: 2
1540:
1538: 0
1537:
1535: 8
1534:
1532: 5
1531:
1530:
1526:
1524: 7
1523:
1521: 9
1520:
1518: 1
1517:
1515: 4
1514:
1513:
1510:
1507:
1504:
1496:
1494: 7
1493:
1491: 6
1490:
1488: 5
1487:
1485: 4
1484:
1483:
1479:
1477: 2
1476:
1474: 3
1473:
1471: 4
1470:
1468: 5
1467:
1466:
1463:
1460:
1456:
1452:
1444:
1442: 0
1441:
1439: 0
1438:
1436: 0
1435:
1433: 0
1432:
1431:
1427:
1425: 9
1424:
1422: 9
1421:
1419: 9
1418:
1416: 9
1415:
1414:
1411:
1407:
1403:
1400:
1397:
1378:
1375:
1372:
1339:
1336:
1333:
1327:
1324:
1318:
1315:
1285:
1279:
1276:
1270:
1267:
1240:
1237:
1234:
1228:
1225:
1198:
1192:
1189:
1178:
1161:
1159: 3
1158:
1156: 1
1155:
1153: 9
1152:
1150: 6
1149:
1148:
1144:
1142: 6
1141:
1139: 8
1138:
1136: 0
1135:
1133: 3
1132:
1131:
1128:
1125:
1122:
1114:
1112: 4
1111:
1109: 3
1108:
1106: 2
1105:
1103: 1
1102:
1101:
1097:
1095: 5
1094:
1092: 6
1091:
1089: 7
1088:
1086: 8
1085:
1084:
1081:
1078:
1074:
1071:
1068:
1065:
1048:
1046: 0
1045:
1043: 0
1042:
1040: 0
1039:
1037: 0
1036:
1035:
1031:
1029: 9
1028:
1026: 9
1025:
1023: 9
1022:
1020: 9
1019:
1018:
1015:
1012:
1009:
1008:
1000:
998: 9
997:
995: 9
994:
992: 9
991:
989: 9
988:
987:
983:
981: 0
980:
978: 0
977:
975: 0
974:
972: 0
971:
970:
967:
964:
960:
957:
953:
951:
922:
919:
916:
913:
904:
901:
898:
892:
889:
883:
880:
870:
851:
848:
845:
839:
836:
826:
822:
813:
795:
792:
783:
777:
774:
768:
765:
755:
751:
732:
726:
723:
713:
710:
693:
690:
687:
684:
681:
678:
672:
666:
663:
660:
654:
651:
648:
645:
642:
639:
636:
630:
627:
620:
619:
618:
615:
593:
590:
584:
578:
575:
572:
570:
562:
559:
556:
553:
550:
547:
542:
538:
534:
526:
523:
520:
514:
511:
508:
503:
499:
495:
493:
485:
482:
479:
473:
470:
459:
458:
457:
440:
437:
434:
431:
426:
422:
418:
412:
406:
403:
396:
395:
394:
391:
389:
385:
375:
360:. The upper
343:
341:disconnected.
335:
323:
322:
321:
314:
310:
308:
307:Domino effect
302:
298:
296:
292:
283:
274:
270:
268:
257:
249:
240:
236:
232:
228:
226:
221:
217:
214:
209:
205:
202:
192:
186:
181:
177:
174:
169:
167:
166:
161:
160:
155:
151:
145:
143:
133:
124:
122:
119:designed his
118:
114:
111:invented his
110:
105:
103:
99:
95:
91:
87:
83:
78:
76:
72:
71:turret clocks
68:
64:
59:
57:
53:
52:Blaise Pascal
49:
45:
41:
37:
29:
21:
3728:
3718:
3688:Pascal's law
3682:
3618:
3570:
3543:
3539:
3508:
3504:
3490:
3468:
3452:
3429:
3417:
3406:
3385:
3364:
3354:
3335:
3326:
3317:
3308:
3299:
3280:
3271:
3262:
3253:
3234:
3212:
3205:Jean Marguin
3200:
3188:
3162:
3150:
3138:
3127:
3120:Jean Marguin
3115:
3103:
3094:Wikisource:
3090:
3081:
3068:
3061:Jean Marguin
3056:
3046:
3039:
3020:
2960:
2956:
2946:
2927:
2921:
2911:
2904:
2895:
2889:
2846:
2842:
2832:
2822:
2800:the original
2790:
2779:. Retrieved
2775:the original
2765:
2753:
2742:. Retrieved
2738:the original
2728:
2716:
2674:
2667:Jean Marguin
2662:
2650:
2638:
2626:
2618:
2614:
2602:
2590:
2577:
2565:
2558:Leland Locke
2553:
2533:, Wikisource
2525:
2513:. Retrieved
2508:
2494:
2482:
2474:
2470:
2466:
2433:Arithmometer
2403:arithmometer
2396:
2392:
2386:
2384:
2380:René Grillet
2369:
2361:
2349:
2342:
2326:
2314:
2285:
2267:
2253:
2249:
2240:Achievements
2235:
2216:
2212:
2195:
2175:
2146:
2134:
2129:
1950:
1937:Louis PĂ©rier
1840:
1832:
1829:
1822:
1815:
1808:
1801:
1784:
1777:
1770:
1748:
1691:
1687:
1683:
1679:
1675:
1671:
1667:
1663:
1659:
1655:
1651:
1647:
1645:
1640:
1636:
1632:
1628:
1624:
1620:
1615:
1611:
1607:
1600:
1596:
1592:
1588:
1584:
1580:
1576:
1572:
1571:system used
1566:
1558:
1454:Subtraction
1398:
1179:
1176:
1069:
1066:
1063:
954:
947:
708:
616:
612:
455:
392:
387:
383:
381:
372:
344:The kicking
338:spring (z,u)
319:
303:
299:
294:
288:
271:
267:lantern gear
263:
237:
233:
229:
224:
222:
218:
210:
206:
197:
184:
173:World War II
170:
163:
157:
146:
138:
121:arithmometer
106:
79:
75:water wheels
67:lantern gear
60:
50:invented by
43:
39:
35:
34:
3670:Innovations
3167:Eric Swedin
2515:January 31,
2438:Comptometer
2199:hylomorphic
2186:Clockmakers
1985:Henri Lecoq
1983:Musée
1958:CNAM museum
1929:CNAM museum
1903:CNAM museum
1878:CNAM museum
1755:Accounting
1173:Subtraction
285:The sautoir
201:rotary dial
194:Input wheel
3820:Categories
2937:0521893801
2781:2011-11-05
2744:2011-11-19
2231:Fromanteel
2097:collection
2058:Accounting
2029:Accounting
2023:Chevalier
2001:Scientific
1969:Accounting
1940:Accounting
1916:Scientific
1890:Accounting
1837:Production
1791:Surveying
1733:Thousands
614:machines.
154:philosophy
82:prototypes
69:, used in
3592:Pascaline
2977:0007-0874
2873:1476-4687
2500:Falk, Jim
2227:Richelieu
2147:In 1649,
2080:Surveying
1953:in 1711.
1760:Hundreds
1738:Hundreds
1376:−
1360:which is
1337:−
1238:−
1076:Addition
920:−
902:−
849:−
652:−
646:−
640:−
554:−
548:−
524:−
515:−
509:−
483:−
438:−
432:−
369:Operation
356:hits the
44:Pascaline
3795:Category
3769:(sister)
3761:(sister)
3753:(father)
3001:38193192
2993:25833800
2985:43820570
2585:, (1942)
2489:, (1942)
2417:See also
2288:of 1649)
1847:Location
1583:with 20
1060:Addition
962:Re-zero
354:part (T)
346:pawl (1)
327:pawl (1)
162:and the
150:religion
3805:Commons
3777:(niece)
3730:Pensées
3548:Bibcode
3513:Bibcode
3226:Sources
3207:, p. 66
2881:4097256
2851:Bibcode
2475:La Haye
2254:deniers
2052:Germany
2048:Dresden
1851:Country
1820:base 12
1813:base 12
1799:base 10
1794:base 10
1785:Deniers
1782:base 12
1775:base 20
1768:base 10
1763:base 10
1758:base 10
1746:base 10
1741:base 10
1736:base 10
1731:base 10
1726:base 10
1664:deniers
1660:deniers
1635:and 12
1619:with 6
1593:deniers
1591:and 12
1581:deniers
1561:decimal
1394:
1362:
1358:
1308:
1304:
1260:
1256:
1218:
1214:
1182:
1010:
935:
873:
867:
829:
808:
758:
748:
716:
185:sautoir
165:Pensées
127:History
88:, then
46:) is a
3743:Family
3734:(1669)
3673:Career
3620:BibNum
3540:Nature
3505:Nature
3477:
3438:
3393:
3372:
3342:
3287:
3241:
3027:
2999:
2991:
2983:
2975:
2934:
2879:
2871:
2843:Nature
2477:, 1779
2182:guilds
2157:patent
2075:France
2020:France
2007:8 x 10
1993:France
1963:France
1934:France
1922:6 x 10
1908:France
1884:France
1863:Wheels
1823:Lignes
1816:Pouces
1806:base 6
1802:Toises
1771:Livres
1692:lignes
1690:) and
1688:lignes
1684:pouces
1680:pouces
1668:toises
1662:) and
1648:livres
1637:lignes
1629:pouces
1616:lignes
1612:pouces
1602:toises
1573:livres
295:sauter
102:patent
3712:Works
2997:S2CID
2981:JSTOR
2877:S2CID
2529:(fr)
2459:Notes
1960:Paris
1931:Paris
1905:Paris
1881:Paris
1871:Notes
1809:Pieds
1796:Tens
1765:Tens
1749:Units
1743:Tens
1676:pieds
1672:pieds
1641:pouce
1639:to a
1631:to a
1627:, 12
1625:toise
1623:to a
1621:pieds
1608:pieds
1595:to a
1589:livre
1587:to a
386:is 9-
56:Rouen
3475:ISBN
3436:ISBN
3391:ISBN
3370:ISBN
3340:ISBN
3285:ISBN
3239:ISBN
3025:ISBN
2989:PMID
2973:ISSN
2932:ISBN
2869:ISSN
2517:2016
2378:and
2252:and
2250:sols
1859:Type
1778:Sols
1718:1st
1715:2nd
1712:3rd
1709:4th
1686:(12
1678:(12
1658:(12
1656:sols
1652:sols
1650:(20
1633:pied
1614:and
1585:sols
1579:and
1577:sols
1555:Uses
152:and
73:and
3556:doi
3544:150
3521:doi
3509:150
2965:doi
2859:doi
2847:150
2382:).
2100:USA
2095:IBM
1682:),
1674:),
1670:(6
1654:),
1597:sol
42:or
3822::
3554:.
3542:.
3538:.
3519:.
3507:.
3503:.
3174:^
3009:^
2995:.
2987:.
2979:.
2971:.
2961:48
2959:.
2955:.
2875:.
2867:.
2857:.
2845:.
2841:.
2808:^
2701:^
2686:^
2538:^
2506:.
2374:,
2359:.
2061:10
2046:,
1610:,
1605:,
1575:,
810:.
539:10
500:10
423:10
168:.
3652:e
3645:t
3638:v
3625:.
3564:.
3558::
3550::
3529:.
3523::
3515::
3483:.
3444:.
3399:.
3378:.
3348:.
3293:.
3247:.
3033:.
3003:.
2967::
2940:.
2883:.
2861::
2853::
2826:.
2784:.
2747:.
2519:.
2108:8
2083:8
2032:5
2004:8
1972:6
1943:8
1919:6
1893:8
1382:)
1379:B
1373:A
1370:(
1346:)
1343:)
1340:B
1334:A
1331:(
1328:P
1325:C
1322:(
1319:P
1316:C
1292:)
1289:)
1286:A
1283:(
1280:P
1277:C
1274:(
1271:P
1268:C
1244:)
1241:B
1235:A
1232:(
1229:P
1226:C
1202:)
1199:A
1196:(
1193:P
1190:C
923:B
917:A
914:=
911:)
908:)
905:B
899:A
896:(
893:P
890:C
887:(
884:P
881:C
855:)
852:B
846:A
843:(
840:P
837:C
817:B
796:A
793:=
790:)
787:)
784:A
781:(
778:P
775:C
772:(
769:P
766:C
736:)
733:A
730:(
727:P
724:C
694:D
691:+
688:C
685:+
682:B
679:+
676:)
673:A
670:(
667:P
664:C
661:=
658:)
655:D
649:C
643:B
637:A
634:(
631:P
628:C
594:B
591:+
588:)
585:A
582:(
579:P
576:C
573:=
563:B
560:+
557:A
551:1
543:n
535:=
530:)
527:B
521:A
518:(
512:1
504:n
496:=
489:)
486:B
480:A
477:(
474:P
471:C
441:A
435:1
427:n
419:=
416:)
413:A
410:(
407:P
404:C
388:d
384:d
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