The first mechanical calculators
The Schickard calculator :
The first automation of addition (substraction) is probably the work of Wilhem Schickard in 1623 (birth year of Blaise Pascal). Built in only one specimen, the machine was destroyed in a fire 5 months later. Schickard wrote to his friend Kepler:
"I would make you later a neater drawing of the arithmetic machine; in short : aaa are the knobs of the vertical cylinders marked with the figures of the multiplication table which appear at your convenience in the apertures of the slides bbb. The discs ddd are fixed at interior wheels of ten teeth gearing between them in such a way that, if the wheel of right-hand side makes ten turns, its neighbor of left revolves only by one turn; and that if the first makes one hundred of them, the third on the left does one revolution and so on... The figures marked on each wheel are read in the openings ccc in the middle. _ finally on the bottom, the knobs eee are used to register in the opening fff the figures that are necessary to note during operation... I have asked to J.Pfister (who lives here) to make a specimen of this machine for you, but three days ago, it was destroyed with some of my personal estates in a fire suddenly breaked out in the night."
The machine was composed of Naperian cylinders placed vertically on the top to facilitate the multiplications. On the bottom numeral wheels allow to register the numbers appearing in the apertures. The mechanism located just above, was similar to the old mileage odometers of the cars (with simultaneous passage of carry). Reproductions of this machine exist, you can see some of them on the Web.
The calculator made by Blaise Pascal (named pascaline) :
In 1640, Blaise Pascal conceives what one regards as the first arithmetic machine of the history. The construction of this adding machine was very difficult for this time. About twenty of these calculators (pascalines) were probably built, of which eights are known today. Pascalines were well adapted for the additions, on the other hand, the nonreversible mechanism constrains to use a special technique for the subtraction (the numeral wheels are graduated with two set of figures in opposite direction. According to the graduation used, the rotation of a wheel makes progress the figures in the increasing or in the decreasing way).
An old user's manual (from the 18th century) has been retrieved. the explanations given for the multiplication (division) show that it was not so difficult to make this operations (as one thought wrongly. See "The pascaline" - "was it useful ?").
The Leibniz calculator :
Thirty years after Pascal, Leibniz devises a calculator which allows to easily multiply and divide. His driving mechanism has been used in many calculators until the last ones. However the construction of this calculator is very delicate for the time and the machine only built in two specimens will never be marketed.
Nevertheless, this is the first calculator to materialize the definition of a product of two numbers. The multiplicand is registered once and for all at the beginning of the operation and can then be added to himself as many time as desired. The mechanism is composed for each order of units of a cylinder of 9 teeth of increasing lengths. This drum can slide along its axis. According to its position, a revolution of the cylinder makes turn a gear of a going number of teeth from zero to nine.
Leibniz is regarded as the true precursor of mechanical calculation.
The Thomas de Colmar arithmometer:
The calculating machine, just like other mechanical instruments, was not commercially successful until the second part of 19th century (high purchase price and unnecessary device for commercial and scientific work). On the second half of 19th century, the arrival of industrial methods of manufacture allows the production of precise mechanical parts. A mechanical calculator can be manufactured with a minimum of manual intervention to adjust the differents pieces. The interchangeability of the elements between the machines reduces the maintenance price.
The first easy to use calculator has been designed in 1820 by the french Thomas de Colmar. This machine has been produced and marketed industrially from 1850 until the beginning of the 20th century. The Thomas arithmometer makes use of the Leibniz cylinder, but instead of the cylinder, a gear wheel slides along the cylinder.