Rabdological abacus Claude Perrot
French scientist and architect Claude Perrot, brother of the famous storyteller Charles Perrault, invented an original counting device - a rabdological abacus. The summing machine became a valuable addition to the XVII – XVVth centuries, a period rich enough for the invention of counting devices.
Claude Perrot (1613-1688)
Perrault gave his invention the name in the spirit of ancient times, when a small board on which numbers were written was called the abacus. And since the machine carried out arithmetic operations with the help of small rods with numbers, it was considered a rabdological one.
')
roman abacus
For the first time the device was mentioned in the book “Collection of a large number of machines of his own composition” (1700) by Claude Perrot, published posthumously. The collection contained descriptions of almost all the inventions of the author ("pendulum clock", "machine for lifting weights", "machine for increasing the effect of firearms", etc.). Rabdological abacus was listed at number ten.
It was a compact and simple computer, noted in history due to a significant difference from other devices invented in its field. Instead of the usual gear wheels of Pascal, gear racks (cremallets) were used in the rhabdological abacus.
The counting machine was in the form of a plate with a finger thickness, its height reached about 30 cm, and its width was 14 cm. Two windows were cut out on the front side of the device, where the results were displayed. The result of the subtraction was shown in the upper window, and the addition in the lower window. The multiplication table was engraved in the lower part of the front side.
In addition, seven slots were cut on the front side, along which scales with divisions 1, 2, 3, 4, 5, 6, 7, 8, 9 were placed. In the slots there were rulers. With the help of a pin with a pointed tip, they moved up and down to the bottom of the device.
Deep risks divided each line into 26 parts. The tips of the pin were inserted into the risks, which made it possible to move the rulers with ease and necessary precision. In the upper eleven divisions of the ruler there was an increasing sequence (0,1,2,3,4,5,6,7,8,9,0) for subtraction. In the lower eleven divisions the sequence was placed, which decreased (0,9,8,7,6,5,3,3,2,1,0). Accordingly, it was used for addition. The numbers of these sequences were shown in the result windows. In the lower window, they were the desired value of addition, and in the upper window - the desired value of subtraction.
The sequences printed on the rulers were separated from each other by four empty divisions.
In the bag, the device used seven rulers, which were separated from each other by thin plates. The rulers kept sequence ascending. The extreme right symbolized the discharge of units, the ruler following it represented the discharge of tens, then hundreds and so on until the discharge of millions.
Each plate separating the rulers from each other, there was a hole. It was used to transfer the overflow from the low-order to the senior and was at the base of the ruler, which was pushed to the very top of the device. The size of the hole reached three divisions of the ruler.
Each ruler had 11 teeth near the base of the right side - one per division. On the other side of the ruler (if we take it from below - under the 11 and 12 divisions) there was a spring-loaded hook. The tines and hook were used to transfer the overflow from low to high.
The transfer from the junior to the senior occurred as follows. When the low-order slat was at the top of the device (that is, there were zeros in the windows of the result of addition and subtraction), the spring-loaded hook was hidden in the body of the ruler, resting on the plate to the left of it. As the ruler moves down, the spring-loaded hook approaches the hole in the plate. When the figure 7 belonging to the ruler being moved appeared in the addition result window, the spring-loaded hook began to slide out into the hole of the bar, and at the moment when the number 9 appeared in the result window, it entered into the teeth of the high-level ruler. Subsequently, the movement of the low-order ruler moved the high-order rulers. As a result, when the number 0 of the low-order ruler appeared in the window of the addition results, following the number 9, the high-order ruler moved exactly one division down due to the hook-to-tooth coupling.
Example of the addition operation 127 + 65
Step 1. First, all the digits of the working abacus are set to 0. To do this, the ruler moves to the highest position.
Step 2. The pin is placed in the groove at the risk of the low-order ruler, which is opposite the number 7. The ruler moves until the pin rests on the lower end of the groove. At the same time, the input number 7 will be displayed in the addition result window in the low-order digit. An important point is that the number needed to complement the seven to ten, that is, the number 3, will be displayed in the subtraction result window.
Step 3. A similar operation is extended with the discharge of a dozen, only in this case, the groove is installed opposite the number 2.
Step 4. To discharge hundreds, the groove is installed opposite the number 1. Next, the groove moves down to the stop, that is, one division. The number 127 will be displayed in the addition result box.
Step 5. The next step is to enter the second term. The pin is installed in the groove at the risk of a low-level ruler, opposite the number 5, the ruler moves down to the stop. In this case, the pin will stop in front of the number 2, since the ruler will rest on the bottom wall of the device before the pin reaches the bottom end of the groove. At the same time, the dozen discharge line will go down one division, due to the operation of the overflow transfer mechanism. The number 130 appears in the addition result window.
Step 6. In order to get the correct digit in the discharge unit - 2, without removing the pin from the slot, move the ruler upward until the pin rests against the end of the slot. Thus, the figure 132 will be displayed in the result result window.
Step 7. The final stage - the tens of the second term is entered. To do this, the pin is installed in the groove at the risk of a tens ruler, opposite the number 6, the ruler moves down to the stop. This is where the calculations end, and the desired value is displayed in the result result window: 192.
Example of the subtraction operation 68-23
Step 1. All digits of the working abacus are set to 0. To do this, with the help of a pin, the rulers move to the highest position.
Step 2. The lower order of the decrement is entered. The low-order ruler moves in such a way that the figure 8 is displayed in the subtraction result window in the low-order position. To achieve this, you need to put the pin in the notch at risk opposite the number 2 and move the ruler down until the pin rests against the end groove.
Step 3. Next, you enter the discharge of ten declining, for which the corresponding ruler moves so that in the subtraction result window the number 6 is displayed in the second position. To do this, put the pin in the notch at risk opposite the number 4, and the ruler moves down until the pin rests on the end of the groove. As a result, the subtraction result window will display the number 68.
Step 4. The deductible is entered in the same way as the addition term. To enter the subtracted low-order bit, the pin is inserted into the groove at the risk of the low-order ruler, opposite the number 3. The ruler moves downward until the pin abuts the end of the groove. Next, the most significant bit of the deductible is entered, for which the pin is placed in the groove at risk of the second ruler to the left, opposite the number 2. The ruler moves down until the pin rests on the end of the groove. The difference between the two numbers is found, the desired result is displayed in the subtraction result window: 45.
When subtracting with the help of a workbook abacus, a supplement of up to ten was used, similar to the method used in Pascalin.
As an example, the solution of the equation: Y = 68-23 = 45. Using the method of addition, the number 68 is represented as the difference of the numbers 100 and 32 (68 = 10-32). As a result, the equation reduces to the following form: Y = 68-23 = 100-32-23 = 100- (32 + 23) = 27. Such a transformation replaces subtraction with addition and subtraction of the result of addition from 100, which is the inverse of addition. Consequently, it remains to solve the problem of automatic addition to ten, for which two lines of numbers are plotted on all rulers, and on the cover of a workbook abacus - two windows of output, arranged so that the sums of two numbers displayed in the windows and located under each other ten.
In his design, Perrault used the elements that were first used by the Scottish mathematician John Napier in the simplest replicating device. It was intended to multiply, divide, extract the square root and was described in detail by Napier in the last publication during his lifetime (Rabdologia seu Numerationis, 1617).
Naper's sticks
A description of the rhabdological abacus shows its difference from the computers existing at that time. And, importantly, the device was pretty easy to use. However, the rhabdological abacus did not receive due recognition. Perhaps because of the unreliability of the device of a spring-loaded hook (it was used not only for carrying, but also for fixing the slats in positions corresponding to the input numbers), which, during continuous operation, often failed. But if the realized invention did not become widely used in practice, then the ideas of Perrault, later found application in other simple and reliable counting devices (“Kummer numerator”, “Hans Zabelny Comptator”, etc.).
"Kummer Reader" (1846)
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Claude Perrot (1613-1688)
Perrault gave his invention the name in the spirit of ancient times, when a small board on which numbers were written was called the abacus. And since the machine carried out arithmetic operations with the help of small rods with numbers, it was considered a rabdological one.
')
roman abacus
For the first time the device was mentioned in the book “Collection of a large number of machines of his own composition” (1700) by Claude Perrot, published posthumously. The collection contained descriptions of almost all the inventions of the author ("pendulum clock", "machine for lifting weights", "machine for increasing the effect of firearms", etc.). Rabdological abacus was listed at number ten.
It was a compact and simple computer, noted in history due to a significant difference from other devices invented in its field. Instead of the usual gear wheels of Pascal, gear racks (cremallets) were used in the rhabdological abacus.
The counting machine was in the form of a plate with a finger thickness, its height reached about 30 cm, and its width was 14 cm. Two windows were cut out on the front side of the device, where the results were displayed. The result of the subtraction was shown in the upper window, and the addition in the lower window. The multiplication table was engraved in the lower part of the front side.
In addition, seven slots were cut on the front side, along which scales with divisions 1, 2, 3, 4, 5, 6, 7, 8, 9 were placed. In the slots there were rulers. With the help of a pin with a pointed tip, they moved up and down to the bottom of the device.
Deep risks divided each line into 26 parts. The tips of the pin were inserted into the risks, which made it possible to move the rulers with ease and necessary precision. In the upper eleven divisions of the ruler there was an increasing sequence (0,1,2,3,4,5,6,7,8,9,0) for subtraction. In the lower eleven divisions the sequence was placed, which decreased (0,9,8,7,6,5,3,3,2,1,0). Accordingly, it was used for addition. The numbers of these sequences were shown in the result windows. In the lower window, they were the desired value of addition, and in the upper window - the desired value of subtraction.
The sequences printed on the rulers were separated from each other by four empty divisions.
In the bag, the device used seven rulers, which were separated from each other by thin plates. The rulers kept sequence ascending. The extreme right symbolized the discharge of units, the ruler following it represented the discharge of tens, then hundreds and so on until the discharge of millions.
Each plate separating the rulers from each other, there was a hole. It was used to transfer the overflow from the low-order to the senior and was at the base of the ruler, which was pushed to the very top of the device. The size of the hole reached three divisions of the ruler.
Each ruler had 11 teeth near the base of the right side - one per division. On the other side of the ruler (if we take it from below - under the 11 and 12 divisions) there was a spring-loaded hook. The tines and hook were used to transfer the overflow from low to high.
The transfer from the junior to the senior occurred as follows. When the low-order slat was at the top of the device (that is, there were zeros in the windows of the result of addition and subtraction), the spring-loaded hook was hidden in the body of the ruler, resting on the plate to the left of it. As the ruler moves down, the spring-loaded hook approaches the hole in the plate. When the figure 7 belonging to the ruler being moved appeared in the addition result window, the spring-loaded hook began to slide out into the hole of the bar, and at the moment when the number 9 appeared in the result window, it entered into the teeth of the high-level ruler. Subsequently, the movement of the low-order ruler moved the high-order rulers. As a result, when the number 0 of the low-order ruler appeared in the window of the addition results, following the number 9, the high-order ruler moved exactly one division down due to the hook-to-tooth coupling.
Example of the addition operation 127 + 65
Step 1. First, all the digits of the working abacus are set to 0. To do this, the ruler moves to the highest position.
Step 2. The pin is placed in the groove at the risk of the low-order ruler, which is opposite the number 7. The ruler moves until the pin rests on the lower end of the groove. At the same time, the input number 7 will be displayed in the addition result window in the low-order digit. An important point is that the number needed to complement the seven to ten, that is, the number 3, will be displayed in the subtraction result window.
Step 3. A similar operation is extended with the discharge of a dozen, only in this case, the groove is installed opposite the number 2.
Step 4. To discharge hundreds, the groove is installed opposite the number 1. Next, the groove moves down to the stop, that is, one division. The number 127 will be displayed in the addition result box.
Step 5. The next step is to enter the second term. The pin is installed in the groove at the risk of a low-level ruler, opposite the number 5, the ruler moves down to the stop. In this case, the pin will stop in front of the number 2, since the ruler will rest on the bottom wall of the device before the pin reaches the bottom end of the groove. At the same time, the dozen discharge line will go down one division, due to the operation of the overflow transfer mechanism. The number 130 appears in the addition result window.
Step 6. In order to get the correct digit in the discharge unit - 2, without removing the pin from the slot, move the ruler upward until the pin rests against the end of the slot. Thus, the figure 132 will be displayed in the result result window.
Step 7. The final stage - the tens of the second term is entered. To do this, the pin is installed in the groove at the risk of a tens ruler, opposite the number 6, the ruler moves down to the stop. This is where the calculations end, and the desired value is displayed in the result result window: 192.
Example of the subtraction operation 68-23
Step 1. All digits of the working abacus are set to 0. To do this, with the help of a pin, the rulers move to the highest position.
Step 2. The lower order of the decrement is entered. The low-order ruler moves in such a way that the figure 8 is displayed in the subtraction result window in the low-order position. To achieve this, you need to put the pin in the notch at risk opposite the number 2 and move the ruler down until the pin rests against the end groove.
Step 3. Next, you enter the discharge of ten declining, for which the corresponding ruler moves so that in the subtraction result window the number 6 is displayed in the second position. To do this, put the pin in the notch at risk opposite the number 4, and the ruler moves down until the pin rests on the end of the groove. As a result, the subtraction result window will display the number 68.
Step 4. The deductible is entered in the same way as the addition term. To enter the subtracted low-order bit, the pin is inserted into the groove at the risk of the low-order ruler, opposite the number 3. The ruler moves downward until the pin abuts the end of the groove. Next, the most significant bit of the deductible is entered, for which the pin is placed in the groove at risk of the second ruler to the left, opposite the number 2. The ruler moves down until the pin rests on the end of the groove. The difference between the two numbers is found, the desired result is displayed in the subtraction result window: 45.
When subtracting with the help of a workbook abacus, a supplement of up to ten was used, similar to the method used in Pascalin.
As an example, the solution of the equation: Y = 68-23 = 45. Using the method of addition, the number 68 is represented as the difference of the numbers 100 and 32 (68 = 10-32). As a result, the equation reduces to the following form: Y = 68-23 = 100-32-23 = 100- (32 + 23) = 27. Such a transformation replaces subtraction with addition and subtraction of the result of addition from 100, which is the inverse of addition. Consequently, it remains to solve the problem of automatic addition to ten, for which two lines of numbers are plotted on all rulers, and on the cover of a workbook abacus - two windows of output, arranged so that the sums of two numbers displayed in the windows and located under each other ten.
In his design, Perrault used the elements that were first used by the Scottish mathematician John Napier in the simplest replicating device. It was intended to multiply, divide, extract the square root and was described in detail by Napier in the last publication during his lifetime (Rabdologia seu Numerationis, 1617).
Naper's sticks
A description of the rhabdological abacus shows its difference from the computers existing at that time. And, importantly, the device was pretty easy to use. However, the rhabdological abacus did not receive due recognition. Perhaps because of the unreliability of the device of a spring-loaded hook (it was used not only for carrying, but also for fixing the slats in positions corresponding to the input numbers), which, during continuous operation, often failed. But if the realized invention did not become widely used in practice, then the ideas of Perrault, later found application in other simple and reliable counting devices (“Kummer numerator”, “Hans Zabelny Comptator”, etc.).
"Kummer Reader" (1846)
PS We conduct a campaign specifically for Habr's readers. Post with the details here .
Source: https://habr.com/ru/post/271479/
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