Apollonius of Perga (English Wikipedia)

Mackenzie, Dana. "A Tisket, a Tasket, an Apollonian Gasket". American Scientist. 98, January–February 2010 (1): 10–14. Archived from the original on 10 April 2017. Retrieved 5 February 2015.

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Many of the commentators and translators, as well, no doubt, as copyists, have been explicitly less than enthusiastic about their use, especially after analytic geometry, which can do most of the problems by algebra without any stock of constructions. Taliaferro stops at Book III. Heath attempts a digest of the book to make it more palatable to the reader (Heath 1896, Intersecting Conics) Fried is more true to Apollonius, supplying an extensive critical apparatus instead (Fried 2013, Footnotes). Heath, Thomas Little, ed. (1896). Treatise on conic sections, edited in modern notation. Cambridge University Press. Fried, Michael N., ed. (2013). Apollonius of Perga Conics: Books I-IV. Translated by Taliaferro, R. Catesby; Fried, Michael N. Santa Fe, NM: Green Lion Press. ISBN 978-1-888009-41-5. Retrieved 1 May 2025.
A summary of the question can be found at Heath 1896, p. lxx. Toomer 1990, pp. lxix–lxx: "we may regard the establishment of limits of solution as its main purpose" Heath, Thomas Little, ed. (1896). Treatise on conic sections, edited in modern notation. Cambridge University Press. Toomer, Gerald J., ed. (1990). Apollonius Conics: books V to VII. Sources in the History of Mathematics and Physical Sciences. Vol. 9. New York: Springer. doi:10.1007/978-1-4613-8985-9. ISBN 978-1-4613-8987-3. Retrieved 1 May 2025.
Ball 1960, p. 52. Ball, W.W. Rouse (1960) [1908]. A Short Account of the History of Mathematics (4th ed.). Mineola: Dover. ISBN 978-0-486-20630-1.
Eutocius, Commentary on Conica, Book I, Lines 5-10, to be found translated in Thomas 1953, p. 277 Thomas, Ivor (1953). Selections illustrating the history of greek mathematics. Loeb Classical Library. Vol. II From Aristarchus to Pappus. Cambridge, MA: Harvard University Press.
Fried & Unguru 2001, Introduction Fried, Michael N.; Unguru, Sabetai (2001). Apollonius of Perga's Conica: text, context, subtext. Leiden: Brill. ISBN 978-90-04-11977-2. Retrieved 1 May 2025.
Thomas Little Heath (1908). "The thirteen books of Euclid's Elements". Cambridge University Press.
Heath 1896, p. c Heath, Thomas Little, ed. (1896). Treatise on conic sections, edited in modern notation. Cambridge University Press.
Fried & Unguru 2001, p. 146 Fried, Michael N.; Unguru, Sabetai (2001). Apollonius of Perga's Conica: text, context, subtext. Leiden: Brill. ISBN 978-90-04-11977-2. Retrieved 1 May 2025.
Fried & Unguru 2001, p. 189 Fried, Michael N.; Unguru, Sabetai (2001). Apollonius of Perga's Conica: text, context, subtext. Leiden: Brill. ISBN 978-90-04-11977-2. Retrieved 1 May 2025.
Heath 1896, Propositions Leading Immediately to the Determination of the Evolute Heath, Thomas Little, ed. (1896). Treatise on conic sections, edited in modern notation. Cambridge University Press.
Fried & Unguru 2001, p. 182 Fried, Michael N.; Unguru, Sabetai (2001). Apollonius of Perga's Conica: text, context, subtext. Leiden: Brill. ISBN 978-90-04-11977-2. Retrieved 1 May 2025.
Boyer 1991, p. 142, "The Apollonian treatise On Determinate Section dealt with what might be called an analytic geometry of one dimension. It considered the following general problem, using the typical Greek algebraic analysis in geometric form: Given four points A, B, C, D on a straight line, determine a fifth point P on it such that the rectangle on AP and CP is in a given ratio to the rectangle on BP and DP. Here, too, the problem reduces easily to the solution of a quadratic; and, as in other cases, Apollonius treated the question exhaustively, including the limits of possibility and the number of solutions". Boyer, Carl B. (1991). "Apollonius of Perga". A History of Mathematics (Second ed.). Wiley. ISBN 0-471-54397-7.
Heath 1896, p. ci Heath, Thomas Little, ed. (1896). Treatise on conic sections, edited in modern notation. Cambridge University Press.
Heath 1896, p. cxv Heath, Thomas Little, ed. (1896). Treatise on conic sections, edited in modern notation. Cambridge University Press.
Apollonius, Conics, Book I, Definition 4. Refer also to Heath 1896, p. clxi Heath, Thomas Little, ed. (1896). Treatise on conic sections, edited in modern notation. Cambridge University Press.
Boyer 1991, pp. 156–157. Boyer, Carl B. (1991). "Apollonius of Perga". A History of Mathematics (Second ed.). Wiley. ISBN 0-471-54397-7.
Heath 1896, pp. ci–cii Heath, Thomas Little, ed. (1896). Treatise on conic sections, edited in modern notation. Cambridge University Press.
Cajori, Florian (1993). A history of mathematical notations. New York: Dover Publications. p. 295. ISBN 9780486677668.
Heath 1896, pp. clvii–clxx Heath, Thomas Little, ed. (1896). Treatise on conic sections, edited in modern notation. Cambridge University Press.

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A mathematical explanation as well as precis of each proposition in the book can be found in Toomer 1990, pp. lxi–lxix Toomer, Gerald J., ed. (1990). Apollonius Conics: books V to VII. Sources in the History of Mathematics and Physical Sciences. Vol. 9. New York: Springer. doi:10.1007/978-1-4613-8985-9. ISBN 978-1-4613-8987-3. Retrieved 1 May 2025.
A summary of the question can be found at Heath 1896, p. lxx. Toomer 1990, pp. lxix–lxx: "we may regard the establishment of limits of solution as its main purpose" Heath, Thomas Little, ed. (1896). Treatise on conic sections, edited in modern notation. Cambridge University Press. Toomer, Gerald J., ed. (1990). Apollonius Conics: books V to VII. Sources in the History of Mathematics and Physical Sciences. Vol. 9. New York: Springer. doi:10.1007/978-1-4613-8985-9. ISBN 978-1-4613-8987-3. Retrieved 1 May 2025.
Toomer 1990, pp. lxi–lxix Toomer, Gerald J., ed. (1990). Apollonius Conics: books V to VII. Sources in the History of Mathematics and Physical Sciences. Vol. 9. New York: Springer. doi:10.1007/978-1-4613-8985-9. ISBN 978-1-4613-8987-3. Retrieved 1 May 2025.

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A mathematical explanation as well as precis of each proposition in the book can be found in Toomer 1990, pp. lxi–lxix Toomer, Gerald J., ed. (1990). Apollonius Conics: books V to VII. Sources in the History of Mathematics and Physical Sciences. Vol. 9. New York: Springer. doi:10.1007/978-1-4613-8985-9. ISBN 978-1-4613-8987-3. Retrieved 1 May 2025.
A summary of the question can be found at Heath 1896, p. lxx. Toomer 1990, pp. lxix–lxx: "we may regard the establishment of limits of solution as its main purpose" Heath, Thomas Little, ed. (1896). Treatise on conic sections, edited in modern notation. Cambridge University Press. Toomer, Gerald J., ed. (1990). Apollonius Conics: books V to VII. Sources in the History of Mathematics and Physical Sciences. Vol. 9. New York: Springer. doi:10.1007/978-1-4613-8985-9. ISBN 978-1-4613-8987-3. Retrieved 1 May 2025.
Toomer 1990, pp. lxi–lxix Toomer, Gerald J., ed. (1990). Apollonius Conics: books V to VII. Sources in the History of Mathematics and Physical Sciences. Vol. 9. New York: Springer. doi:10.1007/978-1-4613-8985-9. ISBN 978-1-4613-8987-3. Retrieved 1 May 2025.

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For a more precise version of the chain see Wakefield, Colin. "Arabic Manuscripts in the Bodleian Library" (PDF). pp. 136–137.

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Ji, Shanyu. "Apollonius and Conic Sections" (PDF). Archived from the original (PDF) on 2 December 2021. Retrieved 12 February 2021.

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Ji, Shanyu. "Apollonius and Conic Sections" (PDF). Archived from the original (PDF) on 2 December 2021. Retrieved 12 February 2021.
Mackenzie, Dana. "A Tisket, a Tasket, an Apollonian Gasket". American Scientist. 98, January–February 2010 (1): 10–14. Archived from the original on 10 April 2017. Retrieved 5 February 2015.

Apollonius of Perga (English Wikipedia)

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