A Manual of Greek MathematicsDover Publications, 1963 - 552 pagina's |
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Pagina 53
... means . Plato speaks in the Timaeus of the geometric means between two squares and two cubes , observing that between two ' planes ' one such mean suffices , but to connect two ' solids ' two means are necessary . This is equivalent to ...
... means . Plato speaks in the Timaeus of the geometric means between two squares and two cubes , observing that between two ' planes ' one such mean suffices , but to connect two ' solids ' two means are necessary . This is equivalent to ...
Pagina 178
... means . In the Timaeus Plato , speaking of numbers ' whether solid or square ' , observes that between planes one mean suffices , but to connect two solids two means are necessary . The means are geometric means , and by ' planes ' and ...
... means . In the Timaeus Plato , speaking of numbers ' whether solid or square ' , observes that between planes one mean suffices , but to connect two solids two means are necessary . The means are geometric means , and by ' planes ' and ...
Pagina 238
... means between a and b , there are n geometric means between e and ƒ ( 8 ) . If an , an - 1b , an - 2b2 ... abn - 1 , bn is a G. P. of n + 1 terms , so that there are n - 1 geometric means between an and b " , there are the same number ...
... means between a and b , there are n geometric means between e and ƒ ( 8 ) . If an , an - 1b , an - 2b2 ... abn - 1 , bn is a G. P. of n + 1 terms , so that there are n - 1 geometric means between an and b " , there are the same number ...
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