By Ivor Thomas

The fantastic success 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; share and skill; 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 countless, the lever); Euclid. quantity II (Loeb Classical Library no. 362) includes: Aristarchus (distances of solar and moon); Archimedes (cylinder, sphere, cubic equations; conoids; spheroids; spiral; expression of enormous 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)**

**Example text**

8-11 ol yeco- rwa oe 7)€, €€[. 02. " €02 ^7, '' ^^ Plat. Lfg. vii. 817 , ] -820 d TOLVVV ^ iXev- . , . 8, eoTLV ev €—€ Ttva? , ^€, €' — , ' paSiov . . " Plato is thought to have redeenied this promise towards the end of the Laws, where he describes the composition of the Nocturnal Council, whose nieml)ers are required to have considerable knowledjre of mathematics. ^ The Greek word is derived from the same root as the 20 INTRODUCTORY Mathematics (6) ix Greek Education lamblichus, O71 the Pythagorean Life 18.

4 *•" V €7 " ', TToUeiv, It is 8- "^? € €* perhaps unnecessary to follow . this trifle to its end. Rhabdas proceeds to show how the tens from 20 to 90, and the hundreds from 200 to 900, can be represented in similar manner. M. ii. 552. { I have not found it possible to give a satisfactory rendering of Rhabdas's names for the fingers. ) can mean spasms or convulsions, and Mr. Colin Roberts tentatively suggests (to my mind convincingly) that the middle finger is so called because it is joined with the thumb in cracking the fingers.

The problem, stripped of its trimmings, is to find eight unknown ' the 16 number of INTRODUCTORY (e) Harmonics It would appear, I said, that just as our eyes were intended for astronomy, so our ears were intended for harmonious movements, and that these are in a mianner sister sciences," as the Pythagoreans assert and as we, Glaucon, agree. , it regards 3 as a triad and 10 as a decad, and applies the theorems of arithmetic to such cases. It is, then, logistic Avhich treats on the one hand the problem called by Archimedes the cattle-problem,^ and on the other hand melite and phialite numbers, the latter appertaining in other types of to bowls, the former to flocks ^ problem too it has regard to the number of sensible Its subjectbodies, treating them as absolute.