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 digit. Having made a complete revolution, the excess over the number 9 was transferred to the next digit, shifting the neighboring wheel by 1 position. The first versions of the Pascalina had five gears, later their number increased to six or even eight, which made it possible to work with large 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. Nevertheless, the Pascal machine allowed not only addition, but also other operations, but at the same time it required the use of a rather inconvenient procedure for repeated additions. Subtraction was performed using additions up to nine, which, to help the counter, appeared in a window placed 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 French monetary system was difficult. Calculations were carried out in livres, suidene In livre, there were 20 sous, in su - 12 deniers. It is clear that the use of the decimal system 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 (German. Wilhelm Schickard), created in 1623.

In 1799, the transition of France to the metric system also affected its monetary system, which finally became decimal. However, almost until the beginning of the 19th century, the creation and use of counting machines remained unprofitable. It wasn't until 1820 that Charles Xavier Thomas de Colmar (b. Charles Xavier Thomas de Colmar) patented the first commercially successful mechanical calculator.

Leibniz calculator History of creation

The idea of ​​creating a machine that performs calculations came from the outstanding German mathematician and philosopher Gottfried Wilhelm Leibniz after he met the Dutch mathematician and astronomer Christian Guynian. The huge amount of calculations that an astronomer had to do led Leibniz to the idea of ​​\u200b\u200bcreating a mechanical device that could facilitate such calculations (“Since it is unworthy of such wonderful people, like slaves, to waste time on computational work that could be entrusted to anyone with using the machine).

The mechanical calculator was created by Leibniz in 1673. The addition of numbers was carried out using wheels connected to each other, just like on the computer of another outstanding scientist and inventor Blaise Pascal - Pascaline. The moving part added to the design (a prototype of the movable carriage of future desktop calculators) and a special handle that allowed turning the stepped wheel (in subsequent versions of the machine - cylinders) made it possible to speed up repetitive addition operations, which were used to divide and multiply numbers. The required number of repeated additions was performed automatically.

The machine was demonstrated by Leibniz at the French Academy of Sciences and the Royal Society of London. One copy of the calculator came to Peter the Great, who presented it to the Chinese emperor, wanting to surprise the latter with European technical achievements.

Two prototypes were built, to this day only one has been preserved in the National Library of Lower Saxony (in German. Niedersächsische Landesbibliothek) in Hannover, Germany. Several later copies are in museums in Germany, such as one in the Deutsches Museum in Munich.

Blaise Pascal's counting adding machine is an invention that surprised contemporaries, but never found its circle of customers. The mechanism, which is based on gear wheels, is considered one of the progenitors of the calculator.

The history of the development of summing devices began in the 17th century. "Pascaline" is an invention of the French scientist Blaise Pascal, which is attributed to one of the stages in the formation of computer technology. Pascal, already at the age of 19, began to develop his own calculating machine, which can now be read on the pages of textbooks. This invention is considered one of the prototypes of the calculator.

"Pascalina": the history of occurrence

The creation of one of the earliest models of adding machines belongs to the French physicist and mathematician Blaise Pascal. Pascal's father was a tax collector, so already at the age of 19, the future scientist saw how various counting operations were carried out. Already during this period, the first drawings of Pascalina were created. In total, the final development of the device took 5 years.

In theory, Pascal's mechanism was quite simple to use, but due to the poor development of the technical side, the implementation of the scientist's plan became a difficult task, for which many difficulties had to be overcome.

Blaise wanted his adding machine to simplify the performance of any complex calculations, both for an educated person and for someone who understood little about arithmetic. Pascal touched upon an important problem concerning not only his family, but also the development of science in the 17th century.

Over the course of 10 years, the researcher created more than 50 calculating machines, but he was able to sell only a small fraction of his inventions. Pascal gave one of the first ready-made devices to Chancellor Sergier as gratitude for his help in the scientific work of the young Blaise.

What is Blaise Pascal's calculating machine?

"Pascalina" is a small box in which there are many cogwheels (gears) interconnected. Each wheel was marked from zero to nine. In order to perform the addition operation, it was necessary to dial the summed numbers using the required number of revolutions of the gears. The wheels moved until the right number appeared. With a full turn of the remaining balance (more than 9), the gear shifted to another digit, moving the adjacent wheel by one division.

The use of wheel revolutions for the addition process was not an innovation in the scientific activity of Pascal, since this idea was voiced back in 1623 by Wilhelm Schickard. Indeed, the invention of Blaise is considered to be the transfer of the remainder to the next discharge with the full rotation of the gear.

In the first "pascalines" there were five gear wheels, and with further modernization of the technology in the mechanism, their number reached eight pieces, which made it possible to work with large numbers (up to 9999999).

This mechanism was actively used in various technical devices until the 20th century. Its advantage was the ability to automatically add multi-digit numbers by the device itself.

Researchers of the history of the emergence of counting mechanisms believe that Pascal created his adding machine practically from scratch, since he was not familiar with Schikkard's project.

The device surprised modern science, but due to the high cost and complexity of operation, it could not find its audience. Nevertheless, the invention of Pascal made a huge contribution to the history of the development of computer technology.

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 rantiers 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 in this way: “I did not save either time, or 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, ebony wood, 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 measuring 36x13x8 cm, 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). This transmitted the rotation of the type wheel (A) 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 around 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 number 9 to 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 dials in the opposite direction, as was done in Schickard's Computing 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 models of Pascalina to Chancellor Seguier, 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 it did not receive practical application, although a lot was said and written about them. Perhaps because the clerks to whom the car was intended to help were afraid of losing their jobs because of it, and employers were stingy to buy expensive device preferring cheap labor.

Nevertheless, the ideas underlying the construction of Pascalina became the basis for the development of computer technology. 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 series of improvements that turned out to be more perfect.

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.

Pay attention!

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 a short life, he went down in history forever 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 numbers - 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 to the 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.

| 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. For ten years, Pascal managed to collect more than 50 different versions of the device. 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. The answer to arithmetic operations was visible in the upper part of the metal case of the device. The rotation of the wheels was only possible in one direction, thus eliminating 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.