 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 372by Euclid - 1908Full view - About this book
 | Chris Pritchard - Mathematics - 2003 - 572 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... | |
 | Hans Niels Jahnke - Mathematics - 436 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... | |
 | Avicenna Study Group. Conference - Philosophy - 2004 - 281 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... | |
 | Gert Schubring - Mathematics - 2005 - 700 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 (quoted from Edwards 1979, 16). This proposition fmds its typical application in the inscribing polygons... | |
 | Ernest William Hobson - Mathematics - 2021 - 76 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 principle is deduced by Euclid from the axiom that, if there are two magnitudes of the same kind,... | |
 | Peter M. Engelfriet - Mathematics - 1998 - 516 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. Unfortunately, Clavius does not give a motivation for his choice. Although he devoted an extensive... | |
 | Arhimēdēs - 2004 - 522 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... | |
 | 562 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 magnitude C. For C if multiplied will sometime be greater than AB. [cf. v. Def. 4] Let it be multiplied,... | |
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