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By P. K. Jain, Ahmed Khalid

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For the other case see note 116. The solution of the problems here stated is equivalent to the solution of a quadratic equation. By means of 11. 5 and 6 we can solve the equations ax±x2=b2, x2 — ax=b2, but in VI. 28, 29 Euclid gives the equivalent of the solution of the general equations ax ±px2 = A. VI. ieal figure and deficient by a fiarallelograinmic figure similar to a given one: PROPOSITIONS 17-18 39] 51 "After having done what was required, if some one ask, How is it possible to apply to the line AB a rectangle such A ^ c z.

By Hultsch, Vol. 2, Berlin, 1877, pp. 917-919. J'm'= v, the line mni! " Les trots livres de Porismes d'Euclide, Paris, i860, p. 284. See also the restoration by R. Simson, pp. 527-530 of " D e porismatibus tractatus," Opera quaedam reliqua... LXXVI. III. " PROPOSITION 1. 22. " To divide™ a given triangle into equal parts by a line parallel to its base" [Leonardo 5, p. 119, 11. ] Let abg be the given triangle which it is required to bisect by a line parallel to bg. Produce ba to d till ba = 2ad.

Wiss. X. Heft, Leipzig, 1900), p. 202, No. 517. 19] ARABIAN WRITERS ON DIVISIONS OF FIGURES 25 of the Dee book On Divisions was Muh. b. Muh. el-Bagdadi who wrote at Cairo a table of sines for every minute. A little later75, however, Suter discovered facts which led him to believe that the true author was Abu Muhammed b. 'Abdelbaqi el-Bagdadi (d. 1141 at the age of over 70 years) to whom an excellent commentary on Book x of the Elements has been ascribed. Of a MS. by this author Gherard of Cremona (1114-1187) may well have been a translator.

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A Textbook Of Analytical Geometry Of Two Dimensions by P. K. Jain, Ahmed Khalid

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