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My question is based on the information that appears in several websites, according to which i found three examples of a kind of instrument that was probably an analog computer. The first one mentioned, which is from the great soviet encyclopedia (so i suspect it might not be true), is a kind a integrator, i.e a machine that can solve differential equations. The second instrument is from wikipedia article here: https://en.wikipedia.org/wiki/Tractrix, and it's supposedly a drawing machine. The third one is reported by Couturat and was a kind of an algebraic calculator. i.e a calculator that can perform algebraic operations. And i have to mention another source: http://web.mit.edu/STS.035/www/PDFs/Newell.pdf, which states: " Many other elementary analog devices were described before the modern period: Differential gears (Figure 1). used for adding or subtracting two variables. arc usually ascribed to Leonardo da Vinci: and Leibniz is credited for the idea late in the seventeenth century of a similar-triangles device for equation solving or root solving"

So can anyone offer explanation of the underlying principle of this instruments? and mayby even offer explanation of their inner-workings?

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Yes, Leibniz did design a famous computing machine called the stepped-reckoner. It was a (digital) computer, but not an analog computer. Don't confuse digital with electronic. The difference is only that digital computers use discrete values for computation, whereas analog computers use continuous values, for example real numbers in case of Tractrix.

I think you're mixing up different definitions, and also the question doesn't match the description. I'll try to explain the rest below.

A computer can be defined (in an extremely generalized way) as a machine that performs certain logical (or arithmetical) operations automatically (usually on a given input). Guess what, the foundational proves of Euclidean Geometry, and a lot of geometrical algorithms were written by Euclid for a computer that requires only a ruler and a compass.

All the machines that you've mentioned can be described with the above definition, except that the details of their implementation will vary from case to case. Also, this is where the line between computer science and engineering starts arising. A computer scientist may just assume that there is some computer which can perform arithmetical operations. Now he/she might go on to write an algorithm, say to find square roots of a natural number. An engineer on the other hand, will put in his or her expertise to build a machine that can support the requirements for that machine.

What is the underlying principle behind all the computers you've mentioned? It is the definition of computers itself- perform certain logical or arithmetical operations (on an input).

Explanation of inner workings? Those are specific to different machines and you will have to look into each of them. But if you know what they are doing, it's not that difficult to figure out. For example, try figuring out how one can build a Leibniz's stepped-reckoner for simple addition and subtraction. Watch this animation https://www.youtube.com/watch?v=klLB5k3LkwU and see if you can explain its inner workings completely.

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  • $\begingroup$ Hey!! i don't confuse digital with analog computers - my question is purposedly not concerned with the stepped reckoner (which i know is a digital computer). Actually i know the inner workings of the stepped reckoner (i wrote a wikipedia article at a certain lanuague about the stepped reckoner). My question is concerned with some of the other mechanisms of leibniz, wich i suspect were analog. $\endgroup$ – user2554 Jul 9 '17 at 11:58
  • $\begingroup$ So you didnt answer my question - my question at least asks for good articles about these mechanisms, and maybe for explanation. $\endgroup$ – user2554 Jul 9 '17 at 12:26
  • $\begingroup$ The one that I know of is actually what you mentioned- the tractrix curve. Though it was originally studied by Huygens, it was Leibniz who motivation the public interest in this curve (they both were contemporaries). Sadly, this is the only one I know of. But again, Leibniz was more interested in the general idea of computation rather than the design. $\endgroup$ – DaveIdito Jul 9 '17 at 12:38
  • $\begingroup$ (Here's)[phaser.com/modules/historic/leibniz/] a one page reading which actually starts with the tractrix curve. Check out the reference section of the page as well. (This page)[publicdomainreview.org/2016/11/10/… too (a bit general towards end). The reference section is quite rich though. Good luck! $\endgroup$ – DaveIdito Jul 9 '17 at 12:44

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