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==The 17th century== ===Overview=== The 17th century marked the beginning of the history of mechanical calculators, as it saw the invention of its first machines, including [[Pascal's calculator]], in 1642.<ref name="INVENT"/><ref>Please see [[Pascaline#Pascal versus Schickard]]</ref> [[Blaise Pascal]] had invented a machine which he presented as being able to perform computations that were previously thought to be only humanly possible.<ref>"The arithmetical machine produces effects which approach nearer to thought than all the actions of animals. But it does nothing which would enable us to attribute will to it, as to the animals.", Pascal, Pensées [//www.bartleby.com/48/1/6.html Bartleby.com, Great Books online, Blaise Pasdcal, Thoughts]</ref> {{quote |In a sense, Pascal's invention was premature, in that the mechanical arts in his time were not sufficiently advanced to enable his machine to be made at an economic price, with the accuracy and strength needed for reasonably long use. This difficulty was not overcome until well on into the nineteenth century, by which time also a renewed stimulus to invention was given by the need for many kinds of calculation more intricate than those considered by Pascal.|S. Chapman|Pascal tercentenary celebration, London, (1942)<ref name="tercent">[[#NAT_CHAP|Magazine Nature]], (1942)</ref>}} The 17th century also saw the invention of some very powerful tools to aid arithmetic calculations like [[Napier's bones]], [[Mathematical table#Tables of logarithms|logarithmic tables]] and the [[slide rule]] which, for their ease of use by scientists in multiplying and dividing, ruled over and impeded the use and development of mechanical calculators<ref>[[#SCRI|Scripta Mathematica]], p. 128 (1932)</ref> until the production release of the [[arithmometer]] in the mid 19th century. [[File:17th-century-mechanical-calculators -Detail.jpg|thumb|center|upright=3.0|Four of Pascal's calculators and one machine built by Lépine in 1725,<ref>[[#350YEARS|From the calculating machine of Pascal to the computer]], p. 43 (1990)</ref> [[Musée des Arts et Métiers]]]] ===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> ===Other calculating machines=== Schickard, Pascal and Leibniz were inevitably inspired by the role of clockwork which was highly celebrated in the seventeenth century.<ref>See [http://metastudies.net/pmwiki/pmwiki.php?n=Site.TheModernEpochAndTheEmergenceOfTheModernCalculator#schickard http://things-that-count.net]</ref> However, simple-minded application of interlinked gears was insufficient for any of their purposes. Schickard introduced the use of a single toothed "mutilated gear" to enable the carry to take place. Pascal improved on that with his famous weighted sautoir. Leibniz went even further in relation to the ability to use a moveable carriage to perform multiplication more efficiently, albeit at the expense of a fully working carry mechanism. {{quote|...I devised a third which works by springs and which has a very simple design. This is the one, as I have already stated, that I used many times, hidden in the plain sight of an infinity of persons and which is still in operating order. Nevertheless, while always improving on it, I found reasons to change its design...|Pascal|Advertisement Necessary to those who have curiosity to see the Arithmetic Machine, and to operate it (1645)<ref>Translated from "j'en composai une troisième qui va par ressorts et qui est très simple en sa construction. C'est celle de laquelle, comme j'ai déjà dit, je me suis servi plusieurs fois, au vu et su d'une infinité de personnes, et qui est encore en état de servir autant que jamais. Toutefois, en la perfectionnant toujours, je trouvai des raisons de la changer" [[s:fr:La Machine d’arithmétique#Avis nécessaire à ceux qui auront curiosité de voir la Machine d'Arithmétique et de s'en servir|Avis nécessaire à ceux qui auront curiosité de voir la Machine d'Arithmétique et de s'en servir]] Wikisource: La Machine d’arithmétique, Blaise Pascal</ref>}} {{quote|When, several years ago, I saw for the first time an instrument which, when carried, automatically records the numbers of steps by a pedestrian, it occurred to me at once that the entire arithmetic could be subjected to a similar kind of machinery so that not only counting but also addition and subtraction, multiplication and division could be accomplished by a suitably arranged machine easily, promptly, and with sure results.|Leibniz|on his calculating machine (1685)<ref>Quoted in [[#SMITH|David Smith]], p. 173, (1929)</ref>}} The principle of the clock (input wheels and display wheels added to a clock-like mechanism) for a direct-entry calculating machine couldn't be implemented to create a fully effective calculating machine without additional innovation with the technological capabilities of the 17th century,<ref>[[#WILLIAMS|Michael Williams]], p. 124, 128 (1997) for Schikard's machine and the fact that the machines built by Burattini, Morland and Grillet were calculating clocks without a completely effective carry mechanism.</ref> because their gears would jam when a carry had to be moved several places along the accumulator. The only 17th-century calculating clocks that have survived to this day do not have a machine-wide carry mechanism and therefore cannot be called fully effective mechanical calculators. A much more successful calculating clock was built by the Italian [[Giovanni Poleni]] in the 18th century and was a two-motion calculating clock (the numbers are inscribed first and then they are processed). * In 1623, [[Wilhelm Schickard]], a German professor of Hebrew and Astronomy, designed a calculating clock which he drew on two letters that he wrote to [[Johannes Kepler]]. The first machine to be built by a professional was destroyed during its construction and Schickard abandoned his project in 1624. These drawings had appeared in various publications over the centuries, starting in 1718 with a book of Kepler's letters by [[Michael Gottlieb Hansch|Michael Hansch]],<ref>[http://history-computer.com/MechanicalCalculators/Pioneers/Schickard.html History of computer] (retrieved on 1 February 2012)</ref> but in 1957 it was presented for the first time as a long-lost mechanical calculator by Dr. Franz Hammer. The building of the first replica in the 1960s showed that Schickard's machine had an unfinished design and therefore wheels and springs were added to make it work.<ref name="UNFINISHED">[[#WILLIAMS|Michael Williams]], p. 122 (1997)</ref> The use of these replicas showed that the single-tooth wheel, when used within a calculating clock, was an inadequate carry mechanism.<ref name=NOTDO>[[#WILLIAMS|Michael Williams]], p. 124, 128 (1997)</ref> ([[Pascal's Calculator#Pascal versus Schickard|see Pascal versus Schickard]]). This did not mean that such a machine could not be used in practice, but the operator when faced with the mechanism resisting rotation, in the unusual circumstances of a carry being required beyond (say) 3 dials, would need to "help" the subsequent carry to propagate. * Around 1643, a French clockmaker from Rouen, after hearing of Pascal's work, built what he claimed to be a calculating clock of his own design. Pascal fired all his employees and stopped developing his calculator as soon as he heard of the news.<ref>"The appearance of this small ''avorton'' disturbed me to the utmost and it dampened the enthusiasm with which I was developing my calculator so much that I immediately let go all of my employees..." translated from the French: "L'aspect de ce petit avorton me déplut au dernier point et refroidit tellement l'ardeur avec laquelle je faisais lors travailler à l'accomplissement de mon modèle qu'à l'instant même je donnai congé à tous les ouvriers..."</ref> It is only after being assured that his invention would be protected by a royal privilege that he restarted his activity.<ref>"But, later on, Lord Chancellor of France [...] granted me a royal privilege which is not usual, and which will suffocate before their birth all these illegitimate ''avortons'' which, by the way, could only be born of the legitimate and necessary alliance of theory and art." translated from the French: "Mais, quelque temps après, Monseigneur le Chancelier [...] par la grâce qu'il me fit de m'accorder un privilège qui n'est pas ordinaire, et qui étouffe avant leur naissance tous ces avortons illégitimes qui pourraient être engendrés d'ailleurs que de la légitime et nécessaire alliance de la théorie avec l'art"</ref> A careful examination of this calculating clock showed that it didn't work properly and Pascal called it an ''avorton'' (aborted fetus).<ref>"...a useless piece, perfectly clean, polished and well filed on the outside but so imperfect inside that it is of no use whatsoever." translated from the French: "...qu'une pièce inutile, propre véritablement, polie et très bien limée par le dehors, mais tellement imparfaite au dedans qu'elle n'est d'aucun usage"</ref><ref>All the quotes in this paragraph are found in (fr) [[s:fr:La Machine d’arithmétique#Avis nécessaire à ceux qui auront curiosité de voir la Machine d'Arithmétique et de s'en servir|Wikisource: Avis nécessaire à ceux qui auront curiosité de voir la Machine d'Arithmétique et de s'en servir]].</ref> * In 1659, the Italian [[Tito Livio Burattini]] built a machine with nine independent wheels, each one of these wheels was paired with a smaller carry wheel.<ref>[http://brunelleschi.imss.fi.it/mediciscienze/emed.asp?c=35423 Picture of Burattini's machine] {{webarchive|url=https://web.archive.org/web/20100609022832/http://brunelleschi.imss.fi.it/mediciscienze/emed.asp?c=35423 |date=9 June 2010 }} Florence, Istituto e Museo di Storia della Scienza, inv. 3179 (accessed on January, 09 2012)</ref> At the end of an operation the user had to either manually add each carry to the next digit or mentally add these numbers to create the final result. * In 1666, [[Samuel Morland]] invented a machine designed to add sums of money,<ref name="Chronicle, p. 12">[[#CHRONICLE|A calculator Chronicle, ''300 years of counting and reckoning tools'']], p. 12, IBM</ref> but it was not a true adding machine since the carry was added to a small carry wheel situated above each digit and not directly to the next digit. It was very similar to Burattini's machine. Morland created also a multiplying machines with interchangeable disks based on Napier's bones.<ref>[[#WILLIAMS|Michael Williams]], p.140 (1997)</ref><ref>[http://brunelleschi.imss.fi.it/mediciscienze/emed.asp?c=35418 Picture of Morland multiplying machine] Florence, Istituto e Museo di Storia della Scienza, inv. 679 (retrieved on January, 09 2012)</ref> Taken together these two machines provided a capacity similar to that of the invention of Schickard, although it is doubtful that Morland ever encountered Schickard's calculating clock. * In 1673, the French clockmaker [[René Grillet de Roven|René Grillet]] described in ''Curiositez mathématiques de l'invention du Sr Grillet, horlogeur à Paris'' a calculating machine that would be more compact than Pascal's calculator and reversible for subtraction. The only two Grillet machines known<ref>They belong to the [[Musée des Arts et Métiers]] in Paris.</ref> have no carry mechanism, displaying three lines of nine independent dials they also have nine rotating napier's rod for multiplication and division. Contrary to Grillet's claim, it was not a mechanical calculator after all.<ref>"Grillet's machine doesn't even deserve the name of machine" translated from the French "La machine de Grillet ne mérite donc pas même le nom de machine", [[#MARG|Jean Marguin, p.76 (1994)]]</ref>
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