Greek Mathematical Works: Volume I, Thales to Euclid. (Loeb by Ivor Thomas PDF

Ancient Classical

By Ivor Thomas

The fantastic fulfillment of Greek arithmetic is right here illustrated in volumes of chosen mathematical works. quantity I includes: The divisions of arithmetic; arithmetic in Greek schooling; calculation; arithmetical notation and operations, together with sq. root and dice root; Pythagorean mathematics, together with houses of numbers; sq. root of two; share and potential; 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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Extra info for Greek Mathematical Works: Volume I, Thales to Euclid. (Loeb Classical Library No. 335)

Example text

The numerator is written underneath the denominator, which is the reverse of our modern practice. , word = ||. There is no fixed order of preference for numerator and denominator. In . € ' Aristarchus of Samos we find /ze' for —^ and in Archimedes i oa for \\, where only the context will show that lOy^Y is not intended. " The following tables (2nd cent. ) show hoAV fractions can be represented as sums of submultiples. The Greek is set out in columns. Tlie " I am indebted to Mr. Colin Roberts for drawing my attention to them.

157, viii. 140 ; Thucydides iii. 96. d. lie is the author of two letters {Od. SO iv. " Nicolas Rhabdas,'' ed. Tannery, Notices et extracts des manuscrits de la Bibliotheque NationaUy vol. xxxii. pt. 1, pp. 146-132 Exposition of finger-notation * how numbers are represented on the hands hand is always used for the units and tens, and the right hand for the hundreds and thousands, while beyond that some form of characters must be This The is : left used, for the hands are not sufficient. '^ Again, closing this finger together Avith that next after it the second, called iiext the middle and epihate and keeping the remaining three fingers open, as we said, you have on the left hand 2 and on the — — hand 2000.

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. Geminus, according to Proclus in Eucl. i. (ed. Friedlein 8-12), gives the same classification, only in the order INTRODUCTORY tion and splitting up of fractions, whereby it explores the secrets lurking in the subject-matter of the problems by means of the theory of triangular and polygonal numbers.

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