Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books 11 - 20 of 24 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
Full view - About this book

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...
Limited preview - About this book

Plato's Parmenides

Plato - Philosophy - 1998 - 351 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...
Limited preview - About this book

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....
Limited preview - About this book

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...
Limited preview - About this book

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...
Limited preview - About this book

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...
Limited preview - About this book

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...
Limited preview - About this book

History in Mathematics Education: An ICMI Study

John Fauvel, Jan Maanen, J.A. van Maanen - Education - 2000 - 437 pages
1 . The political context ...
Limited preview - About this book

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...
Limited preview - About this book

Geometry: Our Cultural Heritage

Audun Holme - Mathematics - 2002 - 378 pages
...of Exhaustion is established. We find it already in Proposition 1, quoted here from [16]: Euclid X.1 Two unequal magnitudes being set out, if from the...some magnitude which will be less than the lesser of the magnitudes. This proposition is used to prove Proposition X1I.2, namely that the areas of two...
Limited preview - About this book




  1. My library
  2. Help
  3. Advanced Book Search
  4. Download PDF