A Manual of Greek MathematicsDover Publications, 1963 - 552 pagina's |
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Pagina 24
... equivalent to saying that 43 55 23 √3 = 1 + + + 60 602 603 ' " which again is equivalent to 1-7320509 ... : and is correct to the seventh decimal place . PRACTICAL CALCULATION ( a ) The abacus . The essence of the abacus is the ...
... equivalent to saying that 43 55 23 √3 = 1 + + + 60 602 603 ' " which again is equivalent to 1-7320509 ... : and is correct to the seventh decimal place . PRACTICAL CALCULATION ( a ) The abacus . The essence of the abacus is the ...
Pagina 104
... equivalent is this . Bisect AB at C and draw CQ at right angles to AB and of length equal to b . Then , with Q as centre and a as radius , draw a circle . If a > b , the circle will cut CB in some point D. By construction , CD2 = QD2 ...
... equivalent is this . Bisect AB at C and draw CQ at right angles to AB and of length equal to b . Then , with Q as centre and a as radius , draw a circle . If a > b , the circle will cut CB in some point D. By construction , CD2 = QD2 ...
Pagina 399
... equivalent to a table of sines of angles of 1 ° , 10 , 10 , and so on by quarters of a degree to 90 ° . Cos a is , of course , sin ( 90 ° —ɑ ) and therefore equivalent to ( crd . 180 ° —2a ) . One of Ptolemy's propositions proves the ...
... equivalent to a table of sines of angles of 1 ° , 10 , 10 , and so on by quarters of a degree to 90 ° . Cos a is , of course , sin ( 90 ° —ɑ ) and therefore equivalent to ( crd . 180 ° —2a ) . One of Ptolemy's propositions proves 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