By Ivor Thomas
The fantastic fulfillment of Greek arithmetic is the following illustrated in volumes of chosen mathematical works. quantity I comprises: The divisions of arithmetic; arithmetic in Greek schooling; calculation; arithmetical notation and operations, together with sq. root and dice root; Pythagorean mathematics, together with homes of numbers; sq. root of two; percentage and capacity; algebraic equations; Proclus; Thales; Pythagorean geometry; Democritus; Hippocrates of Chios; duplicating the dice and squaring the circle; trisecting angles; Theaetetus; Plato; Eudoxus of Cnidus (pyramid, cone, etc.); Aristotle (the endless, the lever); Euclid. quantity II (Loeb Classical Library no. 362) includes: Aristarchus (distances of sunlight and moon); Archimedes (cylinder, sphere, cubic equations; conoids; spheroids; spiral; expression of huge numbers; mechanics; hydrostatics); Eratosthenes (measurement of the earth); Apollonius (conic sections and different works); later improvement of geometry; trigonometry (including Ptolemy's desk of sines); mensuration: Heron of Alexandria; algebra: Diophantus (determinate and indeterminate equations); the revival of geometry: Pappus.
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Additional resources for Greek Mathematical Works: Volume I, Thales to Euclid. (Loeb Classical Library No. 335)
Ath. And again by surface ? Clein. Certainly. Ath. And you know that these are tVo distinct and that volume is a third distinct from them ? things, Clein. Even so. Ath. Now does not it appear to you that they are all commensurable one with another ? Clein. Yes. Ath. I mean, that line is in its nature measurable by line, and surface by surface, and similarly with volume. Clein. Most assuredly. Ath. But suppose this cannot be said of some of them, neither with more assurance nor with less, but is in some cases true, in others not, and suppose you think it true in all cases >vhat you do think of your state of mind in this matter ?
2 if. M. i. " : 27 , GREEK MATHEMATICS €€ '€€ ? , €€ €€. *' € € elvaL ^ SeovTog, , , ^' ^ ^ '^^ . el aya^oi', he , , 6- he , ^, /Lia^rjjLiaat ? ) Enumeration by Fingers Aristot. Prob. xv. 3, 910 ", -; 28 8, , . . ; ?? b 23-911 a ,, . 1 , eVava- INTRODUCTORY — our own times I mean geometry, astronomy, and the so-called eristic dialogues, in which our young men delight more than they ought, though there is not one of the older men who would pronounce them tolerable. Nevertheless I urge those who are inclined to these work hard and apply disciplines to their mind to all of them, saying that even if these studies can do no other good, they at least keep the young out of many Indeed, for those other things that are harmful.
Ii. T. L. Heath, The Works of Archimedes, pp. 319pp. 202 fF. 326, and for a complete discussion, A. Anithor, Zeitschrift fur Math. u. -litt. Ahtheilung), xxv. (1880), pp. 153-171, supplementing an article by B. Krumbiegel (pp. 121136) on the authenticity of the problem. He should probably have said " apples ". ; ** 17 ,, GREEK MATHEMATICS - . ,. ) Later Classification Anatolius ap. Her. , ed. Heiberg 164. 9-18 , , , ,,. , , , 8 ; ** 8, ^^ , . " " '' 38. , that which deals with non-sensible objects.
Greek Mathematical Works: Volume I, Thales to Euclid. (Loeb Classical Library No. 335) by Ivor Thomas