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Books Books 11 - 20 of 25 on Two unequal magnitudes being set out, if from the greater there be subtracted a magnitude....
" Two unequal magnitudes being set out, if from the greater there be subtracted a magnitude greater than its half, and from that which is left a magnitude greater than its half, and if this process be repeated continually, there will be left some magnitude... "
The Thirteen Books of Euclid's Elements - Page 14
by Euclid, Johan Ludvig Heiberg - 1908
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Euclid in China: The Genesis of the First Chinese Translation of Euclid's ...

Peter M. Engelfriet - Mathematics - 1998 - 488 pages
...The wording of the postulate here seems to be a combination of V.Def.4 with theorem I of Book X:┐ Two unequal magnitudes being set out, if from the...which will be less than the lesser magnitude set out. Unfortunately, Clavius does not give a motivation for his choice. Although he devoted an extensive...
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Plato's Parmenides

Plato, Reginald E. Allen - Philosophy - 1998 - 336 pages
...mathematics. Euclid, writing about ┐oo BC, is resolutely finitist. Elements X, Definition i states that “two unequal magnitudes being set out, if from the...magnitude which will be less than the lesser magnitude.” This theorem, which later came to be called the Postulate of Archimedes, is the foundation of much...
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Lebesgue Measure and Integration: An Introduction

Frank Burk - Mathematics - 1998 - 292 pages
...their diameters, an obvious result for regular polygons. “Truth” was to be based on Eudoxus' Axiom: Two unequal magnitudes being set out, if from the...greater than its half, and if this process be repeated continuously, there will be left some magnitude which will be less than the lesser magnitude set out....
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The Cambridge Companion to Galileo

Peter Machamer - Philosophy - 1998 - 462 pages
...act out, if from the greater chere be subacracced a magnitude greater than its half, and from chat which is left a magnitude greater than its half, and...magnitude which will be less than the lesser magnitude sec out.” V, ┐: “a ratio is a sort of relation in respect of size between two magnitudes of the...
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The Nine Chapters on the Mathematical Art: Companion and Commentary

Kangshen Shen, John N. Crossley, Anthony Wah-Cheung Lun, Hui Liu - Mathematics - 1999 - 596 pages
...such an n comes from the method of exhaustion, which appears in Proposition 10.1 of Euclid's Elements. “Two unequal magnitudes being set out, if from the...will be less than the lesser magnitude set out.” At the end of the Proposition Euclid added: “And the theorem can be similarly proved even if the...
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Squaring the Circle: The War Between Hobbes and Wallis

Douglas M. Jesseph - Mathematics - 2000 - 419 pages
...as proposition 1 of book 10 of the Elements in the form of the claim: OISPUTEO FOUNOATI ONS / 161 BD Two unequal magnitudes being set out, if from the...which will be less than the lesser magnitude set out. (Elements 10, prop. 1) The angle of contact appears to violate this condition, since no amount of division...
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Squaring the Circle: The War Between Hobbes and Wallis

Douglas M. Jesseph - Mathematics - 2000 - 419 pages
...as proposition 1 of book 10 of the Elements in the form of the claim: DISPUTED FOUNDATIONS 1161 BD Two unequal magnitudes being set out, if from the...which will be less than the lesser magnitude set out. (Elements 10, prop. 1) The angle of contact appears to violate this condition, since no amount of division...
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Mathematical Expeditions: Chronicles by the Explorers

Reinhard Laubenbacher, David Pengelley - Mathematics - 1999 - 275 pages
...Elements [51, Vol. 3, p. 14], as Proposition 1 in Book X: Two unequal magnitudes being set out, iffrom the greater there be subtracted a magnitude greater...which will be less than the lesser magnitude set out. Clearly, this is exactly what Archimedes uses to obtain his Corollary to Proposiiswhat makes it possible...
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History in Mathematics Education: An ICMI Study

John Fauvel, J.A. van Maanen - Education - 2000 - 437 pages
...10 of the Elements, which reads: Two unequal magnitudes being set out, if from the greater there he subtracted a magnitude greater than its half, and...magnitude which will be less than the lesser magnitude set oat. This approach concentrated on building up students' historical knowledge, at the expense of the...
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The World of Mathematics, Volume 1

James Roy Newman - Mathematics - 2000 - 768 pages
...it was proved in the first theorem of the tenth book that, if two unequal magnitudes be set out, and if from the greater there be subtracted a magnitude greater than its half, and from the remainder a magnitude greater than its half, and so on continually, there will be left some magnitude...
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