A Manual of Greek MathematicsDover Publications, 1963 - 552 pagina's |
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Pagina 349
... hyperbola used by Menaechmus is a rect- angular hyperbola , and it is remarkable that the property used is the fundamental asymptote - property . This suggests a deeper study of the curve than would be necessary in the case of the ...
... hyperbola used by Menaechmus is a rect- angular hyperbola , and it is remarkable that the property used is the fundamental asymptote - property . This suggests a deeper study of the curve than would be necessary in the case of the ...
Pagina 351
... hyperbola only a single branch was considered . The hyperbola , therefore , was not regarded as having a centre ; what we call the centre was the point of intersection of the asymp- totes , which Archimedes called ' the nearest lines to ...
... hyperbola only a single branch was considered . The hyperbola , therefore , was not regarded as having a centre ; what we call the centre was the point of intersection of the asymp- totes , which Archimedes called ' the nearest lines to ...
Pagina 447
... hyperbola ( Props . 34 , 35 ) . The veûous itself is solved by means of the intersection of a hyperbola and a circle ( cf. pp . 148-50 above ) . In one of the direct solu- tions by means of a hyperbola the focus - directrix property is ...
... hyperbola ( Props . 34 , 35 ) . The veûous itself is solved by means of the intersection of a hyperbola and a circle ( cf. pp . 148-50 above ) . In one of the direct solu- tions by means of a hyperbola the focus - directrix property is ...
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