A Manual of Greek MathematicsDover Publications, 1963 - 552 pagina's |
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Pagina 296
... ( surface of pyramid exclud- ing base ) . Therefore ( surface of pyramid ) = ( polygon about B ) . But ( polygon about B ) : ( polygon in B ) < S : B ; therefore ( surface of pyramid ) : ( polygon in B ) < 8 : B. This is impossible ...
... ( surface of pyramid exclud- ing base ) . Therefore ( surface of pyramid ) = ( polygon about B ) . But ( polygon about B ) : ( polygon in B ) < S : B ; therefore ( surface of pyramid ) : ( polygon in B ) < 8 : B. This is impossible ...
Pagina 298
... surface made up of the surfaces of cones and frusta of cones ; and Archimedes has proved ( Prop . 14 ) that the surface of the cone ABB ' is what we should write as π . AB . BF , and ( Prop . 16 ) that the surface of the frustum BC ' is ...
... surface made up of the surfaces of cones and frusta of cones ; and Archimedes has proved ( Prop . 14 ) that the surface of the cone ABB ' is what we should write as π . AB . BF , and ( Prop . 16 ) that the surface of the frustum BC ' is ...
Pagina 335
... surface is downwards and the base entirely outside the fluid , or ( 2 ) the curved surface is upwards and the base is entirely submerged . Archimedes proves that , in either case , ' if the figure be forced into such a position that the ...
... surface is downwards and the base entirely outside the fluid , or ( 2 ) the curved surface is upwards and the base is entirely submerged . Archimedes proves that , in either case , ' if the figure be forced into such a position that the ...
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