Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books 11 - 20 of 23 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

Mathematical Expeditions: Chronicles by the Explorers

Reinhard Laubenbacher, David Pengelley - Mathematics - 1999 - 275 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. is what makes it possible to eventually undershoot it, since it does not recede as the halving process...
Limited preview - About this book

Using History to Teach Mathematics: An International Perspective

Victor J. Katz - Mathematics - 2000 - 261 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. About proposition II, in proving it we observe that it depends on the result of proposition III. As...
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

Pappus of Alexandria and the Mathematics of Late Antiquity

Serafina Cuomo - Mathematics - 2000 - 234 pages
...the greater there be subtracted more than its half, from the remainder more than its half and so on, there will be left some magnitude which will be less than the lesser of the first two"). and the "Eudoxus-Archimedes" one, based on ratios ("Of unequal magnitudes the greater...
Limited preview - About this book

From Discrete to Continuous: The Broadening of Number Concepts in Early ...

K. Neal - Education - 2002 - 174 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 proposition utilises Book V definition four, and it therefore links ratios to commensurability....
Limited preview - About this book

Geometry: Our Cultural Heritage

Audun Holme - Mathematics - 2002 - 378 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 of the magnitudes. This proposition is used to prove Proposition XII.2, namely that the areas of two...
Limited preview - About this book

A Smoother Pebble : Mathematical Explorations: Mathematical Explorations

Davis (Emeritus) Donald C. Benson Professor of Mathematics University of California - Mathematics - 2003 - 280 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. Proposition 2. If, when the less of rivo unequal magnitudes is continually subtracted in turn from...
Limited preview - About this book

The Changing Shape of Geometry: Celebrating a Century of Geometry and ...

Chris Pritchard, Mathematical Association of America - Mathematics - 2003 - 541 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. Prop. 9: The squares on straight lines commensurable in length have to one another the ratio which...
Limited preview - About this book

A History of Analysis

Hans Niels Jahnke - Mathematics - 422 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); or whether one considers this theorem to be another, a so-called dieisive form of...
Limited preview - About this book

Interpreting Avicenna: Science And Philosophy In Medieval Islam-Proceedings ...

Avicenna Study Group. Conference - Philosophy - 2004 - 262 pages
...half, and from that which is oo 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. 12 10 Euclid, Elements (1956), 2:114. 11 Usul al-handasa, 153. Ibn Siha's version of this statement...
Limited preview - About this book




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