A Manual of Greek MathematicsClarendon Press, 1931 - 552 pagina's |
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Pagina 54
... irrational of any sort could only be denoted by a straight line or a combination of lines . This is illustrated by Euclid's Book X on irra- tionals ... irrationality of √2 was discovered before 54 PYTHAGOREAN ARITHMETIC The irrational.
... irrational of any sort could only be denoted by a straight line or a combination of lines . This is illustrated by Euclid's Book X on irra- tionals ... irrationality of √2 was discovered before 54 PYTHAGOREAN ARITHMETIC The irrational.
Pagina 241
... irrational magnitudes , setting out a number of orders of irrational magnitudes and exhibiting their whole extent . To begin with the definitions . ' Commensurable ' magni- tudes can be measured by one and the same measure ...
... irrational magnitudes , setting out a number of orders of irrational magnitudes and exhibiting their whole extent . To begin with the definitions . ' Commensurable ' magni- tudes can be measured by one and the same measure ...
Pagina 242
... irrational ( 3 ) . On the other hand , while the square on the straight line assumed as rational is rational , any area incommensurable with it is irrational ( 4 ) . Thus , if p is a straight line assumed as rational , not only is kp ...
... irrational ( 3 ) . On the other hand , while the square on the straight line assumed as rational is rational , any area incommensurable with it is irrational ( 4 ) . Thus , if p is a straight line assumed as rational , not only is kp ...
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