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Plane and solid geometry (1912)

Hart, C. A. (Clara Avis), b. 1863, Feldman, Daniel D., b. 1872 · New York, American Book Co · leaf 153

An illustration from Plane and solid geometry, 1912, leaf 153
I. li Z AOB and Z COE are commensurable. (b) Suppose that Z COE is not contained in Z ^05 an integralnumber of times. The proof is left as an exercise for thestudent. Hint. Some aliquot part of /.COE must be a measure of ZAOB(Why ?) Try i ACOE, \ /COE, etc. II, If Z ^0^ and Z COE are… … Argument 1. Let Z 1 be a measure of Z COE. Ap- ply Z 1 to Z AOB as many times aspossible. There will then be a re-mainder, Z.FOB, less than Zl. 2. Z AOF and Z COE are commensurable. 3. .-.the measure-number of Zaof, re- ferred to Z COE as a unit, equals themeasure-number of AFy referred toCE as a…

Geometry, Plane · Geometry, Solid

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