A Manual of Greek MathematicsDover Publications, 1963 - 552 pagina's |
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Pagina 120
... equal to one another . Now the figure shows that the pyramids , two and two , have equal bases and heights . It is , there- fore , only necessary to prove that triangular pyramids on equal bases and of the same height are equal . This ...
... equal to one another . Now the figure shows that the pyramids , two and two , have equal bases and heights . It is , there- fore , only necessary to prove that triangular pyramids on equal bases and of the same height are equal . This ...
Pagina 301
... equal to the first ' extinguisher ' is equal in area to the surface of the frustum described by the revolution of BC about AO ; and so on . Hence the volume of the whole inscribed solid of revolution is equal to that of a cone with ...
... equal to the first ' extinguisher ' is equal in area to the surface of the frustum described by the revolution of BC about AO ; and so on . Hence the volume of the whole inscribed solid of revolution is equal to that of a cone with ...
Pagina 424
... equal to R. Produce AC S T R to D , making CD equal to AC , and join BD . Then the angles ABC , DBC are both equal to R , so that the angle ABD is the angle of a regular pentagon . Now , says Heron , if AD be divided in extreme and mean ...
... equal to R. Produce AC S T R to D , making CD equal to AC , and join BD . Then the angles ABC , DBC are both equal to R , so that the angle ABD is the angle of a regular pentagon . Now , says Heron , if AD be divided in extreme and mean ...
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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