A Manual of Greek MathematicsClarendon Press, 1931 - 552 pagina's |
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Pagina 193
... magnitudes of the same kind as the original magnitudes . This lemma , now known as the Axiom of Archimedes , is really equiva- lent to the definition of magnitudes having a ratio to one another ( Eucl . V , Def . 4 ) . ' Magnitudes are ...
... magnitudes of the same kind as the original magnitudes . This lemma , now known as the Axiom of Archimedes , is really equiva- lent to the definition of magnitudes having a ratio to one another ( Eucl . V , Def . 4 ) . ' Magnitudes are ...
Pagina 224
... magnitudes , and to magnitudes of every kind ( straight lines , angles , areas , volumes , numbers , times , & c . ) . Greek mathematics can boast of no finer discovery than this theory , due to Eudoxus , which first put on a sound ...
... magnitudes , and to magnitudes of every kind ( straight lines , angles , areas , volumes , numbers , times , & c . ) . Greek mathematics can boast of no finer discovery than this theory , due to Eudoxus , which first put on a sound ...
Pagina 242
... magnitude there be subtracted more than its half ( or its half ) , from the remainder again more than its half ( or its half ) , and so on continually , there will at length remain a ... magnitudes , just as VII . 2 , 3 do 242 EUCLID.
... magnitude there be subtracted more than its half ( or its half ) , from the remainder again more than its half ( or its half ) , and so on continually , there will at length remain a ... magnitudes , just as VII . 2 , 3 do 242 EUCLID.
Inhoudsopgave
INTRODUCTORY 1 157 | 1 |
NUMERICAL NOTATION AND PRACTICAL CAL | 11 |
PYTHAGOREAN ARITHMETIC | 36 |
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according added algebra Apollonius appears Archimedes assumes base begins Book called centre circle cone conics construction contained corresponding cube curve cylinder definition described diameter Diophantus divided draw drawn earth edition Elements equal equation equivalent Euclid expression fact figure five follows four geometry given gives greater Greek height Heron included inscribed Join known latter lemmas length less mathematics means measure meet mentioned method moon multiplied namely observations obtained original Pappus parallel particular perpendicular plane polygon position problem produced proof Prop proportion propositions proved Ptolemy pyramid Pythagoreans radius ratio rectangle reference regarded regular relation represented respectively result right angles segment shows sides similar solid solution solved sphere square straight line Suppose surface theorem theory tion translation treatise triangle volume whole