Suche Bilder Maps Play YouTube News Gmail Drive Mehr »
Anmelden
Books Bücher
" 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 - Seite 372
von Euclid - 1908
Vollansicht - Über dieses Buch

The Works of Archimedes

Archimedes - 1897 - 532 Seiten
...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...
Vollansicht - Über dieses Buch

Works

Archimedes - 1912 - 377 Seiten
...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...
Vollansicht - Über dieses Buch

"Squaring the Circle": A History of the Problem

Ernest William Hobson - 1913 - 57 Seiten
...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,...
Vollansicht - Über dieses Buch

A History of Greek Mathematics, Band 1

Sir Thomas Little Heath - 1921
...there be subtracted more than its half (or the half itself), from the remainder more than its half (or the half), and if this be done continually, there...some magnitude which will be less than the lesser of the given magnitudes. This last lemma is frequently used by Archimedes himself (notably in the second...
Vollansicht - Über dieses Buch

A History of Greek Mathematics, Band 1

Sir Thomas Little Heath - 1921
...there be subtracted more than its half (or the half itself), from the remainder more than its half (or the half), and if this be done continually, there will be left some niagmtude which will be less than the lesser of the given magnitudes. This last lemma is frequently...
Vollansicht - Über dieses Buch

The Historical Development of the Calculus

C.H.Jr. Edwards - 1994 - 368 Seiten
...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...
Eingeschränkte Leseprobe - Über dieses Buch

Jurisculture: Greece and Rome

Gray L. Dorsey - 1988 - 87 Seiten
...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...
Eingeschränkte Leseprobe - Über dieses Buch

Mathematical Thought from Ancient to Modern Times: Volume 1

Morris Kline - 1990 - 434 Seiten
...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....
Eingeschränkte Leseprobe - Über dieses Buch

Excursions in Calculus: An Interplay of the Continuous and the Discrete, Band 13

Robert M. Young - 1992 - 436 Seiten
...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...
Eingeschränkte Leseprobe - Über dieses Buch

Berkeley's Philosophy of Mathematics

Douglas M. Jesseph - 1993 - 335 Seiten
...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...
Eingeschränkte Leseprobe - Über dieses Buch




  1. Meine Mediathek
  2. Hilfe
  3. Erweiterte Buchsuche
  4. EPUB herunterladen
  5. PDF herunterladen