Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books 1 - 10 of 14 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... "
Books 10-13 and appendix - Page 372
by Euclid, Sir Thomas Little Heath, 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 it to...
Full view - About this book

The Historical Development of the Calculus

C.H.Jr. Edwards - Mathematics - 1994 - 368 pages
...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 lesser magnitude set out. . This result, which we will call "Eudoxus' principle," may be phrased as follows. Let A/o and e be...
Limited preview - About this book

Jurisculture: Greece and Rome

Gray L. Dorsey - Law - 1988 - 87 pages
...and from the greater a magnitude greater than its half is subtracted, and this process is repeated continually, there will be left some magnitude which will be less than the lesser magnitude set out. This means that any magnitude is infinitely divisible; that there is no smallest magnitude, because...
Limited preview - About this book

Mathematical Thought from Ancient to Modern Times:

Morris Kline - Mathematics - 1990 - 428 pages
...which is left a magnitude greater than its 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 conclusion of the proof Euclid says the theorem can be proven if the parts subtracted be halves....
Limited preview - About this book

Excursions in Calculus: An Interplay of the Continuous and the ..., Volume 13

Robert M. Young - Mathematics - 1992 - 417 pages
...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 lesser magnitude set out. Application of this principle shows that, for any e > 0, we obtain after a finite number of steps an...
Limited preview - About this book

Berkeley's Philosophy of Mathematics

Douglas M. Jesseph - Mathematics - 1993 - 322 pages
...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 lesser magnitude set out. (Elements X, 1) The general procedure for an exhaustion proof is to begin with upper and lower bounds...
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
...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 lesser magnitude set out. As an example of proof by exhaustion we will consider proposition 10 of book XII of the Elements. PROPOSITION...
Limited preview - About this book

Lebesgue Measure and Integration: An Introduction

Frank Burk - Mathematics - 1998 - 292 pages
...that which is left a magnitude 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. In modem terminology, let A/ and e > 0 be given with 0 < e < M. Then form: M , M - rM = (l -r)A/,(l...
Limited preview - About this book

Plato's Parmenides

Plato - Philosophy - 1998 - 351 pages
...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 lesser magnitude." This theorem, which later came to be called the Postulate of Archimedes, is the foundation of much...
Limited preview - About this book

The Cambridge Companion to Galileo

Peter Machamer - Philosophy - 1998 - 462 pages
...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 lesser magnitude set out." V, 3: "a ratio is a sort of relation in respect of size between two magnitudes of the same kind" (My...
Limited preview - About this book




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