Editing Mechanical calculator (section)

===Invention of the mechanical calculator===
[[Image:HNF-Schickard-Rechenmaschine.jpg|thumb|right|Replica of Schickard´s calculator]]
In 1623 and 1624 [[Wilhelm Schickard]], in two letters that he sent to [[Johannes Kepler]], reported his design and construction of what he referred to as an “arithmeticum organum” (“arithmetical instrument”), which would later be described as a Rechenuhr (calculating clock). The machine was designed to assist in all the four basic functions of arithmetic (addition, subtraction, multiplication and division). Amongst its uses, Schickard suggested it would help in the laborious task of calculating astronomical tables. The machine could add and subtract six-digit numbers, and indicated an overflow of this capacity by ringing a bell. The adding machine in the base was primarily provided to assist in the difficult task of adding or multiplying two multi-digit numbers. To this end an ingenious arrangement of rotatable Napier's bones were mounted on it. It even had an additional "memory register" to record intermediate calculations. Whilst Schickard noted that the adding machine was working, his letters mention that he had asked a professional, a clockmaker named Johann Pfister, to build a finished machine. Regrettably it was destroyed in a fire either whilst still incomplete, or in any case before delivery. Schickard abandoned his project soon after. He and his entire family were wiped out in 1635 by bubonic plague during the Thirty Years' War.

Schickard's machine used clock wheels which were made stronger and were therefore heavier, to prevent them from being damaged by the force of an operator input. Each digit used a display wheel, an input wheel and an intermediate wheel. During a carry transfer all these wheels meshed with the wheels of the digit receiving the carry.

[[Blaise Pascal]] invented a mechanical calculator with a sophisticated carry mechanism in 1642. After three years of effort and 50 prototypes<ref>[http://fr.wikisource.org/wiki/La_Machine_d%E2%80%99arithm%C3%A9tique (fr) La Machine d’arithmétique, Blaise Pascal], Wikisource</ref> he introduced [[Pascal's calculator|his calculator]] to the public. He built twenty of these machines in the following ten years.<ref>[[#MOUR|Guy Mourlevat, p. 12 (1988)]]</ref> This machine could add and subtract two numbers directly and multiply and divide by repetition. Since, unlike Schickard's machine, the Pascaline dials could only rotate in one direction zeroing it after each calculation required the operator to dial in all 9s and then ([[Pascal's calculator#Resetting the machine|method of {{nowrap|re-zeroing}}]]) propagate a carry right through the machine.<ref name="CR_RESET">[[#COURRIER|Courrier du CIBP]], N°8, p. 9, (1986)</ref> This suggests that the carry mechanism would have proved itself in practice many times over. This is a testament to the quality of the Pascaline because none of the 17th and 18th century criticisms of the machine mentioned a problem with the carry mechanism and yet it was fully tested on all the machines, by their resets, all the time.<ref name="NO_BLOC">"...''et si blocage il y avait, la machine était pratiquement inutilisable, ce qui ne fut jamais signalé dans les textes du XVIIIe siecle parmi ses défaults''" [[#MOUR|Guy Mourlevat]], p. 30 (1988)</ref>

{{quote | Pascal's invention of the calculating machine, just three hundred years ago, was made while he was a youth of nineteen. He was spurred to it by seeing the burden of arithmetical labour involved in his father's official work as supervisor of taxes at Rouen. He conceived the idea of doing the work mechanically, and developed a design appropriate for this purpose; showing herein the same combination of pure science and mechanical genius that characterized his whole life. But it was one thing to conceive and design the machine, and another to get it made and put into use. Here were needed those practical gifts that he displayed later in his inventions...|S. Chapman|Pascal tercentenary celebration, London, (1942)<ref name="tercent"/>}}

[[File:Cylindre de Leibniz animé.gif|right|thumb|In the position shown, the counting wheel meshes with three of the nine teeth of the Leibniz wheel.]]
In 1672, [[Gottfried Leibniz]] started working on adding direct multiplication to what he understood was the working of Pascal's calculator. However, it is doubtful that he had ever fully seen the mechanism and the method could not have worked because of the lack of reversible rotation in the mechanism. Accordingly, he eventually designed an entirely new machine called the [[Stepped Reckoner]]; it used his [[Leibniz wheel]]s, was the first two-motion calculator, the first to use cursors (creating a memory of the first operand) and the first to have a movable carriage. Leibniz built two Stepped Reckoners, one in 1694 and one in 1706.<ref name="LEIB" /> Only the machine built in 1694 is known to exist; it was rediscovered at the end of the 19th century having been forgotten in an attic in the [[University of Göttingen]].<ref name="LEIB" />
{{quote |In 1893, the German calculating machine inventor Arthur Burkhardt was asked to put Leibniz's machine in operating condition if possible. His report was favorable except for the sequence in the carry.<ref>[[#SCRI|Scripta Mathematica]], p. 149 (1932)</ref>}}
Leibniz had invented his namesake wheel and the principle of a two-motion calculator, but after forty years of development he wasn't able to produce a machine that was fully operational;<ref>{{Cite journal|last=Morar|first=Florin-Stefan|date=March 2015|title=Reinventing machines: the transmission history of the Leibniz calculator|journal=The British Journal for the History of Science|volume=48|issue=1|pages=123–146|doi=10.1017/S0007087414000429|pmid=25833800|s2cid=38193192|issn=0007-0874}}</ref> this makes Pascal's calculator the only working mechanical calculator in the 17th century. Leibniz was also the first person to describe a [[pinwheel calculator]].<ref name="PINWHEEL">[[#SMITH|David Smith]], p. 173-181 (1929)</ref> He once said "It is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be relegated to anyone else if machines were used."<ref>As quoted in {{harvnb|Smith|1929|pp=180–181|ref=SMITH}}</ref>