A Manual of Greek MathematicsDover Publications, 1963 - 552 pagina's |
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Pagina 83
... Eucl . I , Def . 17 ) ; ( 2 ) that the angles at the base of an isosceles triangle are equal ( = Eucl . I. 5 ) ; ( 3 ) that , if two straight lines cut one another , the ver- tically opposite angles are equal ( = Eucl . I. 15 ) ; ( 4 ) ...
... Eucl . I , Def . 17 ) ; ( 2 ) that the angles at the base of an isosceles triangle are equal ( = Eucl . I. 5 ) ; ( 3 ) that , if two straight lines cut one another , the ver- tically opposite angles are equal ( = Eucl . I. 15 ) ; ( 4 ) ...
Pagina 137
... Eucl . VIII . 8 ; the particular inference is a consequence of Eucl . VII . 20 , to the effect that the least numbers of those which have the same ratio with them measure the latter the same number of times , the greater the greater and ...
... Eucl . VIII . 8 ; the particular inference is a consequence of Eucl . VII . 20 , to the effect that the least numbers of those which have the same ratio with them measure the latter the same number of times , the greater the greater and ...
Pagina 184
... Eucl . II . 5 , and of the more general case corresponding to Eucl . VI . 27 , 28 , while the condition of the possibility of constructing a triangle out of three given straight lines ( = Eucl . I. 22 ) must have been common knowledge ...
... Eucl . II . 5 , and of the more general case corresponding to Eucl . VI . 27 , 28 , while the condition of the possibility of constructing a triangle out of three given straight lines ( = Eucl . I. 22 ) must have been common knowledge ...
Inhoudsopgave
INTRODUCTORY 157 | 5 |
NUMERICAL NOTATION AND PRACTICAL CAL | 11 |
PYTHAGOREAN ARITHMETIC | 36 |
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algebra Apollonius Archimedes Archytas arithmetic assumes astronomy axis base bisects Book centre of gravity chord circle circumscribed commentary cone conics contained cube curve cylinder definition diameter Diophantus divided edition equal equation equivalent Eratosthenes Eucl Euclid Eudemus Eudoxus Eutocius figure geometry given ratio given straight line gives Greek height Heron Hipparchus hyperbola inscribed lemmas length loci mathematics mean proportionals method method of exhaustion moon multiplied namely Pappus parabola parallel parallelogram pentagon perpendicular plane Plato polygonal number Porisms Posidonius problem Proclus proof Prop propositions proved Ptolemy pyramid Pythagoras Pythagoreans quadratic quadratic equations radius rectangle respectively right angles right-angled triangle segment semicircle sexagesimal sides similar solid solution solved sphere square number surface tangent Theon Theon of Alexandria theorem theory tion translation treatise triangular number volume whence