Two prototypes of the Leibniz machine were built. Today, only one of them is in the Lower Saxony National Library (Dutch Landesbibliothek) in Hanover, Germany. Somewhat later examples are exhibited, for example, at the German Museum in Munich. Despite the mechanical shortcomings of the step counter, he presented opportunities for future builders of calculators. The current mechanism, invented by Leibniz, called a stepped cylinder or Leibniz wheel, has been used on many computers for 200 years, and in the 1970s it was replaced by Kurt's handheld calculator. The year Leibniz was created is the 1673rd.
Leibniz Wheel
A wheel or a step drum is a cylinder with a set of incremental length teeth, which, when connected to a counting wheel, can be used in a computing engine of the class of mechanical calculators. Invented by Leibniz in 1673, it was used for three centuries before the advent of an electronic calculator in the mid-1970s.
Leibniz built a machine called a step-type reconstructor (or Leibniz machine), based on the construction of a step-type drum in 1694. He was widely celebrated by Thomas de Colmar when he used it a century and a half later in his arithmometer, the first production computer. It was also used in Kurt's calculator, a very popular portable calculator introduced in the second half of the 20th century.
If you connect the Leibniz wheel to a counting wheel that is free to move up and down along its length, the counting wheel can engage with any number of teeth. You can see the photo of Leibniz car in this article. Many enthusiasts are trying to recreate this 17th-century miracle at home, using improvised materials.
Leibniz machine: principle of operation
This primitive calculator had nine prongs connected to a red counting wheel.
The computing device of the arithmometer has a set of coupled wheels connected to the crank handle. Each turn of the crank handle rotates all the wheels by one full revolution. Input sliders move the counting wheels up and down the wheels, which themselves are connected by a transfer mechanism.
Since the end of the nineteenth century, Leibniz's drums, extracted from this mechanism and used in all proto-calculators, were partially replaced by pins, which in their function are similar, but had a more compact appearance. Step drums remained the main technology for electromechanical calculators until the development of purely electronic counterparts in the last century.
The calculating machine was created on the basis of the mechanism that Leibniz invented and which is now called the Leibniz machine. It is not clear how many different copies of this world's first calculator were made. Some sources claim that there were 12. This article describes the surviving 16-digit prototype stored in Hanover.
Description
The machine has a length of about 67 cm (26 inches), made of polished brass and steel, mounted in an oak casing. It consists of two attached parallel parts. The battery section was located at the rear, the keyboard contained 16 decimal digits and an 8-bit input section at the front.
The input section has 8 sets with buttons for setting the operand number, a telephone dial on the right to set the digit of the multiplier, and a crank on the front panel for calculating. The result of the calculation appeared in the 16-digit window on the back of the battery.
The input section is mounted on rails and can be moved along the battery section using a crank on the left end that rotates the worm gear to change the alignment of the operand numbers with the battery numbers.
There is also a carry indicator with dozens and a control for setting zeros in calculations.
Addition and Subtraction
Addition or subtraction is performed in one step with the rotation of the handle. Multiplication and division are performed using the keys of the multiplier or divider in a procedure equivalent to the familiar long-term multiplication and long-division methods taught at school. The sequence of these operations can be performed by the number in the battery: for example, it can calculate the roots using a series of sections and additions. For its time, the Leibniz counting machine was a very progressive mechanism. Its components, as already mentioned above, have been used in mechanical calculators for the whole 300 years, which seems completely unbelievable.
History
Leibniz developed the idea of a computer in 1672 in Paris thanks to a pedometer. He later found out about Blaise Pascal's machine when he read his Pensees treatise. He focused on expanding Pascal's mechanism so that it could multiply and divide. On February 1, 1673, he introduced the wooden model to the Royal Society of London and received great support. In a letter dated March 26, 1673 to Johann Friedrich, where he mentioned the performance in London, Leibniz described the purpose of the "arithmetic machine" as making calculations for leicht, geschwind, gewiß, that is, easily, quickly and accurately. Leibniz also added that theoretically calculated numbers could be even larger if the size of the machine was properly adjusted. Gottfried Leibniz's first preliminary brass machine was built between 1674 and 1685. His so-called old machine was built between 1686 and 1694. The “younger machine”, preserved to our days and exhibited in Hanover, was built from 1690 to 1720.
In 1775, the "youngest car" was sent to the University of Gottingen for repair and forgotten. In 1876, workers found her in the attic of a university building in Göttingen. She was returned to Hanover in 1880. From 1894 to 1896, Arthur Burkhardt, the founder of a large German calculating company, restored it.
Functional
The machine performs multiplication by repeated addition and division by repeated subtraction. The main operation performed is to add (or subtract) the operand number to the drive register as many times as necessary (to subtract, the working crank rotates in the opposite direction). The number of additions (or subtractions) is controlled by a multiplier. It works like a telephone disk, with ten holes in a circle with numbers from 0 to 9. To multiply by one number, a pen-shaped stylus is inserted into the corresponding hole on the dial, and the crank is rotated. The multiplier dial rotates clockwise, the machine performs one addition for each hole until the stylus stops at the top of the dial. The result appears in the drive windows.
Repeated subtractions are performed in the same way, except that the multiplier dial rotates in the opposite direction, so the second set of digits highlighted in red is used. To do one addition or subtraction, the multiplier is simply set to one. As you can understand, Leibniz's computer was extremely convenient for its time.
Complex multiplication
- The multiplier is set in the operand loops.
- The first (least significant) digit of the multiplier is set to the multiplier dial, as described above, and the crank rotates, multiplying the operand by this digit and placing the result in the drive window.
- The input section is shifted one digit to the left using the end crank.
- The next digit of the multiplier is set to the dial of the multiplier, and the crank is rotated again, multiplying the operand by this digit and adding the result to the window.
- The above 2 steps are repeated for each digit of the multiplier. At the end, the result appears in the windows.
- Thus, the operand can be multiplied by any large number that a person needs, although the result is limited by the capacity of the drive windows.
Division
The division operation on the Leibniz machine is carried out in a slightly different way:
- The dividend is set in the drive, and the divider is set in the operand cycles.
- The input section is moved with the end crank until the left and right digits of these two numbers are lined up.
- The operation crank rotates, and the divider is subtracted from the battery several times until the left (most significant) digit of the result is zero.
- The number displayed on the dial of the multiplier is the first digit of the desired result.
- The input section shifts one digit.
- The above two steps are repeated to get each digit of the desired result until the input carriage reaches the right end of the battery.
- It can be seen that these procedures are simply mechanized versions of the long division and multiplication.
Pascal calculator
Pascal's calculator (also known as the arithmetic machine or Pascalina) is a mechanical calculator invented by Blaise Pascal in the early 17th century. Pascal was asked to develop a calculator for the laborious arithmetic calculations necessary to work as the head of the tax service in Rouen. He developed a machine for adding and subtracting two numbers directly and for performing multiplication and division by repeated addition or subtraction.
Pascal's calculator has been particularly successful in terms of the transfer mechanism, which adds 1 to 9 on one watch face, and when it changes from 9 to 0, it transfers 1 to the next table next to it. Pascal was the first scientist who redesigned and adapted for his purpose the lantern mechanism used in tower clocks and water wheels. To a certain extent, the Leibniz arithmetic machine was a continuation of Pascal's idea, and his experience was studied and used by German scientists to create his own mechanical masterpiece.