A Manual of Greek MathematicsDover Publications, 1963 - 552 pagina's |
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Pagina 251
... radius of the circle ) to saying that ( r + d ) d = r2 , whence d = { r ( √ / 5—1 ) . Proposition 10 proves that p2 = h2 + d2 or r2 + d2 , whence we can deduce pr√ ( 10-2 / 5 ) . Euclid does not find p , the side of the pentagon , in ...
... radius of the circle ) to saying that ( r + d ) d = r2 , whence d = { r ( √ / 5—1 ) . Proposition 10 proves that p2 = h2 + d2 or r2 + d2 , whence we can deduce pr√ ( 10-2 / 5 ) . Euclid does not find p , the side of the pentagon , in ...
Pagina 295
... radius of the base . That is , if s be a generator and r the radius of the base , the curved surface of the cone is ( as we should say ) πrs and that of the cylinder 2πrs . We will illustrate Archimedes ' working of the method of ...
... radius of the base . That is , if s be a generator and r the radius of the base , the curved surface of the cone is ( as we should say ) πrs and that of the cylinder 2πrs . We will illustrate Archimedes ' working of the method of ...
Pagina 444
... radius vector OB to a point B on the first turn is one - third of the area of the sector of the circle described with centre O and radius OB which is cut off between the initial line and the radius OB . In the next propositions he ...
... radius vector OB to a point B on the first turn is one - third of the area of the sector of the circle described with centre O and radius OB which is cut off between the initial line and the radius OB . In the next propositions he ...
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