Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books 1 - 10 of 17 on than its half, and from that which is left a magnitude greater than its half, and....  
" 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 which will be less than the magnitude C. For C if multiplied "
The Thirteen Books of Euclid's Elements - Page 14
by Euclid, Johan Ludvig Heiberg - 1908
Full view - About this book

The Works of Archimedes

Archimedes - Geometry - 1897 - 326 pages
...greater than the half, if from the remainder [a part] greater than the half be subtracted, and so on continually, there will be left some magnitude which will be less than the lesser given magnitude." This last lemma is frequently assumed by Archimedes, and the application of...
Full view - About this book

THE WORKS OF ARCHIMEDES

T. L. HEATH - 1897
...greater than the half, if from the remainder [a part] greater than the half be subtracted, and so on continually, there will be left some magnitude which will be less than the lesser given magnitude." This last lemma is frequently assumed by Archimedes, and the application of...
Full view - About this book

The Historical Development of the Calculus

C.H.Jr. Edwards - Mathematics - 1994 - 368 pages
...applied. 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...be left some magnitude which will be less than the lesser magnitude set out.. This result, which we will call “Eudoxus' principle,” may be phrased...
Limited preview - About this book

Mathematical Thought from Ancient to Modern Times:

Morris Kline - Mathematics - 1990 - 428 pages
...1. 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...half, and if this process be repeated continually, then there will be left some magnitude which will be less than the lesser magnitude set out. At the...
Limited preview - About this book

Berkeley's Philosophy of Mathematics

Douglas M. Jesseph - Mathematics - 1993 - 322 pages
...positive integers m and n such that ma > /3 and n/3 > a. from that which is left a magnitude greater than its half, and from that which is left a magnitude...be left some magnitude which will be less than the lesser magnitude set out. (Elements X, 1) The general procedure for an exhaustion proof is to begin...
Limited preview - About this book

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Paolo Mancosu Assistant Professor of Philosophy University of California at Berkeley - Mathematics - 1995 - 288 pages
...1. 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...be left some magnitude which will be less than the lesser magnitude set out. As an example of proof by exhaustion we will consider proposition 10 of book...
Limited preview - About this book

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Paolo Mancosu - Drama - 1999 - 275 pages
...1. 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...be left some magnitude which will be less than the lesser magnitude set out. As an example of proof by exhaustion we will consider proposition 10 of book...
Limited preview - About this book

Adversaries and Authorities: Investigations Into Ancient Greek and Chinese ...

Geoffrey Ernest Richard Lloyd - Philosophy - 1996 - 250 pages
...1. 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...be left some magnitude which will be less than the lesser magnitude set out."'' Used, as for example in Elements xt t 2, in the investigation of the ratios...
Limited preview - About this book

Chinese Studies in the History and Philosophy of Science and ..., Volume 179

Fan Dainian, Robert S. Cohen - History - 1996 - 471 pages
...Elements: 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...half, and if this process be repeated continually, then there will be left some magnitude which will be less than any known small magnitude. Because Archimedes...
Limited preview - About this book




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