| Pascal summing machine
Pascaline (Pascal's summing machine) is a mechanical calculating machine invented by the brilliant French scientist Blaise Pascal (1623-1662) in 1642.
Pascal was the first inventor of mechanical calculating machines. Blaise began work on the machine at the age of 19, overseeing the work of his father, who was a tax collector and often did long and tedious calculations.
For its time, Pascalina had, of course, a rather futuristic appearance: a mechanical "box" with a bunch of gears. In ten years, Pascal managed to collect more than 50 various options devices. The numbers to be added were entered into the machine by turning the typesetting wheels, each of which was marked with divisions from 0 to 9, because. one wheel corresponded to one decimal place of the number. Thus, to enter a number, the wheels scrolled to the corresponding number. When making a full turn, the excess over the number 9 was transferred by the wheel to the adjacent category, shifting the adjacent wheel by 1 position.
The first copies of Pascal's machine had five gears, after a while their number increased to six, and a little later to eight, which made it possible to work with multi-digit numbers, up to 9,999,999. Answer arithmetic operations was visible at the top of the metal body of the device. The rotation of the wheels was possible only in one direction, thereby excluding the possibility of working with negative numbers. It is noteworthy that the Pascal machine was able to perform both addition and other operations, however, it required the use of a rather inconvenient procedure for repeated additions. The subtraction was carried out by additions up to nine, which, as an aid to the one who counted, appeared in the window located above the original value set.
The advantages of automatic calculations did not change the situation in any way, since the use of a decimal machine for financial calculations within the framework of the monetary system in force in France until 1799 was not an easy task. Calculations were made in livres, sous and denier. In the "livre" there were 20 "sou", while in the "sou" - 12 "denier". A similar system was in the UK. As a result, the use of the decimal number system in non-decimal financial calculations complicated the already difficult process of calculations.
Despite the great enthusiasm caused by Pascalina, the machine did not make its creator rich. The technical complexity and high cost of the machine, combined with small computing abilities even for those years, served as a serious barrier to its wide distribution. And yet, Pascal's Machine deservedly went down in history, because the principle of connected wheels laid in its basis became the basis for most of the created computers for almost 300 years.
Pascal summing machine
The Frenchman Blaise Pascal began building the Pascaline adding machine in 1642 at the age of 19, overseeing the work of his father, who was a tax collector and often performed long and tedious calculations. Pascal's machine was a mechanical device in the form of a box with numerous gears connected to each other. The numbers to be added were entered into the machine by means of the appropriate rotation of the typesetting wheels. On each of these wheels, corresponding to one decimal place of the number, divisions from 0 to 9 were applied. 
When entering a number, the wheels scrolled to the corresponding number. Having made a full turn, the wheel transferred the excess over the number 9 to the next category, shifting the neighboring wheel by 1 position. The first versions of Pascalina had five gears, later their number increased to six or even eight, which made it possible to work with big numbers, up to 9999999. The answer appeared in the upper part of the metal case. The rotation of the wheels was possible only in one direction, excluding the possibility of directly operating with negative numbers. However, the Pascal machine allowed not only addition, but also other operations, but it required the use of a rather inconvenient procedure for repeated additions. The subtraction was carried out with the help of additions up to nine, which, to help the counter, appeared in the window located above the original value set. Despite the advantages of automatic calculations, the use of a decimal machine for financial calculations within the framework of the monetary system in force at that time in France was difficult. Calculations were made in livres, sous and denier. There were 20 sous in the livre, 12 deniers in the sous. The use of the decimal system in non-decimal financial calculations complicated the already difficult process of calculations. 
However, in about 10 years, Pascal built about 50 and even managed to sell about a dozen variants of his car. Despite the general delight it caused, the car did not bring wealth to its creator. The complexity and high cost of the machine, combined with little computing power, served as an obstacle to its wide distribution. Nevertheless, the principle of connected wheels laid down in the basis of Pascalina became the basis for most of the created computing devices for almost three centuries. Pascal's machine became the second really working computing device after Wilhelm Schickard's Counting Clock, created in 1623.
The word "computer" means "computer", i.e. computing device. The need to automate data processing, including calculations, arose a very long time ago. More than \(1500\) years ago, counting sticks and pebbles were used for counting.
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The first inventor of mechanical calculating machines was the brilliant Frenchman Blaise Pascal.
The son of a tax collector, Pascal conceived the idea of building a computing device after watching his father's endless tedious calculations.
In \(1642\) when Pascal was only \(19\) years old, he began to work on the creation of an adding machine. Pascal died at the age of \(39\) years, but despite such short life, forever went down in history as an outstanding mathematician, physicist, writer and philosopher.
One of the most famous modern languages programming.
Pascal's summing machine, "Pascalina", was a mechanical device - a box with numerous gears.
In just over a decade, he built more than \(50\) different versions of the machine.
When working on the Pascaline, the added numbers were entered by correspondingly turning the typesetting wheels. Each wheel with divisions from \(0\) to \(9\) applied to it corresponded to one decimal place of the number - units, tens, hundreds, etc.
The wheel “transferred” the excess over \(9\), making a full turn and moving the “older” wheel adjacent to the left by \(1\) forward.
Other operations were performed using the rather inconvenient procedure of repeated additions.
"Pascalina" caused general delight; it did not bring wealth to Pascal. Nevertheless, the principle of connected wheels he invented was the basis on which most computing devices were built over the next three centuries.
The next milestone result was achieved by an outstanding German mathematician and philosopher Gottfried Wilhelm Leibniz.
In \(1672\), while in Paris, Leibniz met the Dutch mathematician and astronomer Christian Huygens. Seeing how many calculations an astronomer has to do, Leibniz decided to invent a mechanical device that would facilitate the calculations.
Since it is unworthy of such wonderful people, wrote Leibniz, like slaves, to waste time on computational work that could be entrusted to anyone when using a machine.
In \(1673\) he made a mechanical calculator.
Addition was carried out on it in essentially the same way as on the Pascaline, however, Leibniz included in the design a moving part and a handle with which it was possible to turn a stepped wheel or, in subsequent versions of the machine, cylinders located inside the device. This moving element mechanism made it possible to speed up the repetitive addition operations needed to multiply or divide numbers.
The repetition itself was also automatic.
The Leibniz machine required a special table to install, as it had an impressive size.
Leibniz demonstrated his machine at the French Academy of Sciences and the Royal Society of London. One copy of the Leibniz machine came to Peter the Great, who presented it Chinese emperor wanting to impress him with European technical achievements.
In \(1812\), the English mathematician Charles Babbage began working on the so-called difference engine, which was supposed to calculate any functions, including trigonometric ones, and also compile tables.
Pascaline
The first computing device that gained popularity during the author's lifetime was the Pascaline or, as it is sometimes called, the Pascal Wheel. It was created in 1644 by Blaise Pascal (06/19/1623-08/19/1662) and for centuries took the place of the first calculating machine, since at that time an extremely narrow circle of people knew about Schickard's "Computing Clock".
The creation of "Pascalina" was caused by Pascal's desire to help his father. The fact is that the father of the great scientist Etienne Pascal in 1638 led a group of rentiers who protested against the government's decision to abolish the payment of rent, for which he fell out of favor with Cardinal Richelieu, who ordered the arrest of the rebel. Pascal's father had to flee.
On April 4, 1939, thanks to Jacqueline, the youngest daughter of the scientist's father, and the Duchess d "Aiguillon, they managed to get the forgiveness of the cardinal. Etienne Pascal was appointed to the post of intendant of the Rouen generalship, and on January 2, 1640, the Pascal family arrived in Rouen. Pascal's father immediately plunged In 1642, at the age of 19, Blaise Pascal, wanting to make his father's job easier, began work on an adding machine.
The first created model did not satisfy him, and he immediately proceeded to improve it. In total, about 50 different models of computing devices were created. Pascal wrote about his work this way: “I did not save either time, labor or money to bring it to the state of being useful to you ... I had the patience to make up to 50 different models: some wooden, others made of Ivory, from ebony, from copper ... ". The final version of the device was created in 1645.
The description of Pascalina first appeared in Diderot's Encyclopedia in the 18th century.
It was a small brass box 36x13x8 cm in size, containing inside a lot of interconnected gears and having several typesetting wheels with divisions from 0 to 9, with the help of which control was carried out - entering numbers for operations on them and displaying the results of operations in windows.
Each dial corresponded to one digit of the number. The first versions of the device were five-bit, later Pascal created six- and even eight-bit versions.
The two least significant digits of the eight-digit "Pascaline" were adapted for operating with denier and sous, i.e. the first place was vigesimal, and the second duodecimal, because in those days the French monetary system was more complicated than the modern one. The livre was 12 denier and the denier was 20 sous. When performing normal decimal operations, it was possible to turn off the digits intended for a token coin. Six- and five-digit versions of the machines could only work with decimal digits.
The dialing wheels were turned manually by means of a driving pin, which was inserted between the cloves, the number of which was ten for decimal places, twelve for duodecimal, and twenty for twenty. For the convenience of data entry, a fixed stop was used, fixed at the bottom of the type wheel, slightly to the left of the number 0.
The rotation of the type wheel was transmitted to the counting drum using a special device shown in the figure on the left. The type-setting wheel (A) was rigidly connected to the crown wheel (C) using a rod (B). The crown wheel (C) was engaged with the crown wheel (D) at right angles to the crown wheel (C). Thus, the rotation of the dial wheel (A) was transmitted to the crown wheel (D), which was rigidly connected to the rod (E), on which the crown wheel (F) was fixed, used to transmit overflow to the most significant digit using teeth (F1) and to receive overflow from the least significant digit with the teeth (F2). Also fixed on the rod (E) was a crown wheel (G) used to transmit the rotation of the type wheel (A) to the counting drum (J) using a gear wheel (H).
When the dial wheel was fully turned to the senior digit of Pascaline, the overflow result was transmitted using the mechanism shown in the figures “Overflow transfer mechanism in Pascaline”.
Two crown wheels (B and H) of adjacent bits were used to convey overflow. The low order crown wheel (B) had two pins (C) that could engage with a fork (A) attached to a double crank arm D. This lever rotated freely about the high order axle (E). A spring-loaded pawl (F) was also attached to this lever.
When the low-order dial reached the number 6, the rods (C) engaged with the fork (A). At the moment when the dial went from the number 9 to the number 0, the fork disengaged from the pins (C) and fell down under its own weight, while the pawl engaged with the pins (G) of the crown wheel (E) of the highest order and moved him one step forward.
The principle of operation of the overflow transfer mechanism in Pascaline is illustrated in the animation below.
The main purpose of the device was addition. For addition, it was necessary to do a number of simple operations:
1. Reset the previous result by turning the dials starting from the least significant digit until zeros appear in each of the windows.
2. Using the same wheels, the first term is entered, starting from the least significant digit.
The animation below illustrates the work of Pascalina using the example of adding 121 and 32.
The subtraction was a bit more complicated, since the transfer of overflow bits occurred only when the dials were rotated clockwise. A locking lever (I) was used to prevent counterclockwise rotation of the dials.
Such an overflow discharge device led to a problem in implementing subtraction on Pascaline by turning the dials in the opposite direction, as was done in Schickard's "Counting Clock". Therefore, Pascal replaced the operation of subtraction with addition with nine's complement.
Let me explain the method used by Pascal with an example. Let's say you need to solve the equation Y=64-37=27. Using the complement method, we represent the number 64 as the difference between the numbers 99 and 35 (64=99-35), so our equation is reduced to the following form: Y=64-37=99-35-37=99-(35+37)= 27. As can be seen from the transformation, the subtraction was partially replaced by addition and subtraction of the result of addition from 99, which is the inverse addition transformation. Consequently, Pascal had to solve the problem of automatic addition to nine, for which he entered two rows of numbers on the counting drum so that the sum of two numbers located one below the other always equaled 9. Thus, the number displayed in the top row of the calculation result window, was the addition of the number of the bottom row to 9.
In expanded form, the rows printed on the cylinder are shown in the figure on the left.
The bottom row was used for addition and the top row for subtraction. In order for the unused row not to distract from the calculations, it was covered with a bar.
Consider the work of Pascalina using the example of subtracting 132 from 7896 (7896-132=7764):
1. Close the bottom row of windows used for addition.
2. Turn the dials so that the number 7896 is displayed in the top row, while the number 992103 will be displayed in the bottom closed row.
3. Enter the subtrahend in the same way as we enter the terms in addition. For the number 132, this is done like this:
A pin is installed opposite the number 2 of the least significant digit of "Pascaline", and the dial is turned clockwise until the pin rests against the stop.
A pin is installed opposite the number 3 of the second category of "Pascaline", and the dial is turned clockwise until the pin rests against the stop.
A pin is installed opposite the number 1 of the third category of "Pascaline", and the dial is turned clockwise until the pin rests against the stop.
The rest of the digits do not change.
4. The result of subtraction 7896-132=7764 will be displayed in the top row of windows.
Multiplication in the device was performed in the form of multiple addition; multiple subtraction could be used to divide a number.
When developing a calculating machine, Pascal faced many problems, the most acute of which was the manufacture of nodes and gears. The workers did not understand the ideas of the scientist well, and the technology of instrumentation was low. Sometimes Pascal himself had to pick up the tools and bring to mind certain parts of the machine, or simplify their configuration so that the masters could make them.
The inventor presented one of the first successful Pascalina models to Chancellor Séguier, which helped him to receive a royal privilege on May 22, 1649, confirming the authorship of the invention and securing Pascal's right to manufacture and sell the machine. For 10 years, about 50 models of a computer were created and about a dozen were sold. 8 samples have survived to our time.
Although the machine was revolutionary for its time and caused general delight, it did not bring wealth to the creator, since practical application not received, although a lot has been said and written about them. Perhaps because the clerks who the car was intended to help were afraid of losing their jobs because of it, and employers were stingy to buy an expensive device, preferring cheap labor.
Nevertheless, the ideas underlying the construction of Pascalina became the basis for the development computer science. Pascal also had immediate successors. So Rodriguez Pereira, known for his system of teaching the deaf and dumb, designed two calculating machines based on the principles of the Pascalina, but as a result of a number of improvements, which turned out to be more perfect.
Brilliant people are brilliant in everything. This commonplace statement is fully applicable to the French scientist Blaise Pascal. The research interests of the inventor included physics and mathematics, literature and philosophy. It is Pascal who is considered one of the founders of mathematical analysis, the author of the fundamental law of hydrodynamics. He is also known as the first creator of mechanical computers. These devices are prototypes of modern computers.
At that time, the models were in many ways unique. In terms of their technical features, they surpassed many analogues invented before Blaise Pascal. What is the history of "Pascalina"? Where can you find these structures now?
First prototypes
Attempts to automate computing processes have been made for a long time. The Arabs and the Chinese were the most successful in these matters. It is they who are considered the discoverers of such a device as the abacus. The principle of operation is quite simple. To carry out the calculation, it is necessary to shift the bones from one part to another. The products additionally made it possible to carry out subtraction operations. The inconvenience of the first Arabic and Chinese abacuses was associated only with the fact that the stones easily crumbled during the transfer. In some shops in the outback, you can still find the simplest types of Arab abacus, however, now they are called accounts.
Relevance of the problem
Pascal began designing his car at the age of 17. The idea of the need to automate the routine computing processes of a teenager was prompted by the experience of his own father. The fact is that the parent of a brilliant scientist worked as a tax collector and spent a long time sitting behind tedious calculations. The design itself took a long time and required a large physical, mental and material investment from the scientist. In the latter case, Blaise Pascal was assisted by his own father, who quickly realized the benefits of developing his son.
Competitors
Naturally, while the application of any electronic means calculations and speech did not go. Everything was carried out only due to the mechanics. Using the rotation of the wheels to carry out the addition operation was proposed long before Pascal. For example, a device created in 1623 was no less popular at one time. However, certain technical innovations were proposed in Pascal's machine that significantly simplified the addition process. For example, a French inventor developed a scheme for automatically transferring a unit when a number moves to the highest digit. This made it possible to add multi-digit figures without human intervention in the counting process, which practically eliminated the risk of errors and inaccuracies.
Appearance and principle of operation
Visually, Pascal's first adding machine looked like an ordinary metal box in which gears connected to each other were located. The user, through the rotation of the dial wheels, set the values \u200b\u200bnecessary for him. Each of them was marked with numbers from 0 to 9. When a complete revolution was made, the gear shifted the adjacent one (corresponding to a higher category) by one unit.
The very first model had only five gears. Subsequently, Blaise Pascal's calculating machine underwent some changes regarding the increase in the number of gears. There were 6 of them, then this number increased to 8. This innovation made it possible to carry out calculations up to 9,999,999. The answer appeared at the top of the device.
Operations
The wheels in Pascal's calculating machine could only rotate in one direction. As a result, the user was only able to perform addition operations. With some skill, the devices were also adapted for multiplication, but in this case it was noticeably more difficult to perform calculations. There was a need to add the same numbers several times in a row, which was extremely inconvenient. The inability to rotate the wheel in the opposite direction did not allow calculations with negative numbers.
Spreading
Since the creation of the prototype, the scientist has made about 50 devices. Pascal's mechanical machine aroused unprecedented interest in France. Unfortunately, the product was never able to win wide distribution, despite the resonance among the general public and in scientific circles.
The main problem of the products was their high cost. The production was costly, naturally, this had a negative effect on the final price of the entire device. It was the difficulties with the release that led to the fact that the scientist was able to sell no more than 16 models in his entire life. People appreciated all the advantages of automatic calculation, but they did not want to take devices.
Banks
The main emphasis in the implementation of Blaise Pascal put it on the banks. But financial institutions, for the most part, refused to buy a machine for automatic settlements. The problems arose because of the complex monetary policy of France. In the country at that time there were livres, denier and sous. One livre consisted of 20 sous, and a sous of 12 denier. That is, the decimal system was absent as such. That is why it was almost impossible to use the Pascal machine in the banking sector in reality. France switched to the system of calculation adopted in other countries only in 1799. However, even after this time, the use of an automated device was noticeably complicated. This has already addressed the previously mentioned difficulties in production. Labor was mostly manual, so each machine required painstaking work. As a result, they simply stopped making them in principle.
Government support
Blaise Pascal presented one of the first automatic calculating machines to Chancellor Séguier. It is this statesman provided support to a novice scientist in the early stages of creating an automatic device. At the same time, the chancellor managed to obtain from the king privileges for the production of this unit specifically for Pascal. Although the invention of the machine was wholly owned by the scientist himself, patent law was not developed in France at that time. The privilege from the monarch was received in 1649.
Sales
As mentioned above, Pascal's machine did not gain wide distribution. The scientist himself was engaged only in the manufacture of devices, his friend Roberval was responsible for the sale.
Development
The principle of rotation of mechanical gears, implemented in Pascal's computer, was taken as the basis for the development of other similar devices. The first successful improvement is attributed to the German mathematics professor Leibniz. The creation of the adding machine is dated 1673. Number additions were also performed in the decimal system, but the device itself was distinguished by great functionality. The fact is that with its help it was possible not only to carry out addition, but also to multiply, subtract, divide and even extract Square root. The scientist added a special wheel to the design, which made it possible to speed up repetitive addition operations.
Leibniz presented his product in France and England. One of the cars even got to the Russian Emperor Peter the Great, who presented it to the Chinese monarch. The product was far from perfect. The wheel that Leibniz invented to carry out subtraction later became used in other adding machines.
The first commercial success of the mechanical dates back to 1820. The calculator was created by the French inventor Charles Xavier Thomas de Colmar. The principle of operation is in many ways similar to Pascal's machine, but the device itself is smaller, it is a little easier to manufacture and cheaper. This is what predetermined the success of the businessmen.
The fate of creation
Throughout his life, the scientist created about 50 machines, only a few have "survived" to this day. Now it is reliably possible to trace the fate of only 6 devices. Four models are in permanent storage at the Paris Museum of Arts and Crafts, two more in the museum in Clermont. The remaining computing devices found their home in private collections. It is not known for sure who owns them now. The serviceability of the units is also a big question.
Opinions
Some biographers associate the development and creation of Pascal's adding machine with the failing health of the inventor himself. As mentioned above, the first works scientist started still in his youth. They demanded from the author a colossal effort of mental and physical strength. The work was carried out for almost 5 years. As a result of this, Blaise Pascal began to be haunted by severe headaches, which then accompanied him for the rest of his life.
