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Pagina 136
In arithmetic (theory of numbers) we have a fragment of Archytas preserved by
Boëtius, consisting of a proof of the proposition that there can be no number
which is a (geometric) mean between two numbers in the ratio known as
émpuépuos ...
In arithmetic (theory of numbers) we have a fragment of Archytas preserved by
Boëtius, consisting of a proof of the proposition that there can be no number
which is a (geometric) mean between two numbers in the ratio known as
émpuépuos ...
Pagina 198
Euclid, by his more general proof, avoids the necessity for this. Aristotle is already
aware of the principle on which Eudoxus based the method of exhaustion: 'If I
continually add to a finite magnitude, I shall exceed every assigned magnitude, ...
Euclid, by his more general proof, avoids the necessity for this. Aristotle is already
aware of the principle on which Eudoxus based the method of exhaustion: 'If I
continually add to a finite magnitude, I shall exceed every assigned magnitude, ...
Pagina 214
A particular proposition may be without some of these parts (e.g. no construction
beyond the data may be necessary), but three parts are indispensable to all
propositions, the enunciation, proof, and conclusion. A special term was used in ...
A particular proposition may be without some of these parts (e.g. no construction
beyond the data may be necessary), but three parts are indispensable to all
propositions, the enunciation, proof, and conclusion. A special term was used in ...
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Inhoudsopgave
INTRODUCTORY | 1 |
NUMERICAL INOTATION AND PRACTICAL CAL | 11 |
PYTHAGOREAN ARITHMETIC | 36 |
Copyright | |
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according added Apollonius appear applied Archimedes arithmetic assumed base beginning Book called centre circle cone conics construction contained corresponding cube curve cylinder definition described diameter Diophantus discovered divided draw drawn earth edition Elements equal equation equivalent Eucl Euclid expressed fact figure follows four geometry given gives greater Greek height Heron included inscribed Join known latter length less mathematics means measure meet mentioned method multiplied namely observations obtained original Pappus parallel parallelogram particular plane Plato polygon position problem Proclus produced proof Prop proportion propositions proved pyramid Pythagoreans radius ratio rectangle reference regular relation represented respectively result right angles says segment shows sides similar solid solution solved sphere square straight line Suppose surface theorem theory things third tion translation treatise triangle volume whole