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Question:

I am looking for good references on the early calculus papers. Optimally, I want emphasis on the mathematics itself and I want that mathematics to be translated into modern terminology and notation (not necessary, only if possible). I would prefer that extraneous commentaries were kept to a minimum. I am more interested in reading the works themselves than what people have to say about them. But I have to be able to comprehend the writing.


Other notes - TLDR

I am most interested in the works of Newton and Leibniz, although their contemporaries (I believe Barrow and Wallis would fall into this category) and predecessors (Descartes, and ancient Greek geometers who used the method of exhaustion) would also be relevant. And, for that matter, I would eventually like to move on to the later works on calculus - right now I am most interested in Lagrange and Euler, and also the formalizations provided by Cauchy, Weierstrass etc.

I realize that the literature on the above is massive, but the reason I am having trouble finding suitable material is because I have some very specific criteria:

  1. Optimally, I want emphasis on the mathematics itself and I want that mathematics to be translated into modern terminology and notation. I.e., I would prefer reading about integration with good illustrations, rather than fluids and fluxions with photographs of deteriorating 17th-century paper. All the historical literature I have found thus far maintains the use of older terms and notation, which makes it very hard for me to grasp the concepts. If this request is simply not possible, I would at least like a work with sufficient commentary and explanation to afford me a decent understanding of the material.

  2. I would prefer that extraneous commentaries were kept to a minimum. I am more interested in reading the works themselves than what people have to say about them. But as noted above, I have to be able to comprehend the writing.

  3. Please do not assume that I have any level of historical competence or requisite familiarity with "canonical" works. I have read very little on the subject, and basically need to start from scratch.

  4. As of writing I do not have immediate access behind pay-walls or to good libraries, but in the near future this should change. So recommend anything, but please note where I would find it.

  5. Please confine your recommendations to works that you have actually read. If possible, I would appreciate it if you would tell me how much is mathematics vs. prose, how good the explanations are, etc.

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    $\begingroup$ I posted a lot of references to "calculus historical material" in this 21 October 2006 AP-Calculus post at Math Forum. Specifically: 4 books, several internet sites, 8 papers from Amer. Math. Monthly, 1 paper from Math. Mag., 2 papers from College Math. J., 3 papers from Scripta Mathematica, 1 paper from Mathematical Gazette, 5 papers from Mathematics Teacher, 1 paper from The Pentagon, and 7 papers from other journals. $\endgroup$ – Dave L. Renfro May 16 '14 at 16:34
  • $\begingroup$ @DaveL.Renfro Thank you, that is very helpful! I finally get to the read "The Analyst", should be interesting :) $\endgroup$ – user142299 May 16 '14 at 17:36
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    $\begingroup$ I would like to add : Niccolò Guicciardini, Isaac Newton on Mathematical Certainty and Method (2011) and The Early Mathematical Manuscripts of Leibniz (Dover edition) $\endgroup$ – Mauro ALLEGRANZA May 16 '14 at 18:20
  • $\begingroup$ @MauroALLEGRANZA I happen to have both already! Excellent recommendations, cheers :) $\endgroup$ – user142299 May 16 '14 at 18:34
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    $\begingroup$ I happened to see a new book this weekend at a bookstore that you (and Mauro ALLEGRANZA) might be interested in: Amir R. Alexander, Infinitesimal. How a Dangerous Mathematical Theory Shaped the Modern World, April 2014. The book mainly discusses from the late 1500s to when Newton and Leibniz began to take over (1680s to early 1690s). $\endgroup$ – Dave L. Renfro May 27 '14 at 13:23
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What follows are the recommendations given in the comments, for easier later reference.

Dave L. Renfro: I posted a lot of references to "calculus historical material" in this 21 October 2006 AP-Calculus post at Math Forum. Specifically: 4 books, several internet sites, 8 papers from Amer. Math. Monthly, 1 paper from Math. Mag., 2 papers from College Math. J., 3 papers from Scripta Mathematica, 1 paper from Mathematical Gazette, 5 papers from Mathematics Teacher, 1 paper from The Pentagon, and 7 papers from other journals. Also, a just published book of possible interest is Amir R. Alexander, Infinitesimal. How a Dangerous Mathematical Theory Shaped the Modern World, April 2014. The book mainly discusses from the late 1500s to when Newton and Leibniz began to take over (1680s to early 1690s).

Niccolò Guicciardini: I would like to add : Niccolò Guicciardini, Isaac Newton on Mathematical Certainty and Method (2011); Leibniz (as translated by James Mark Child), The Early Mathematical Manuscripts of Leibniz (Dover edition).

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