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Pagina 124
This lune had for its outer circumference the circumference of a semicircle. The
inner circumference was arrived at in this way. Joining the extremities of the
diameter to the middle point of the arc of the semicircle, we have an isosceles
triangle ...
This lune had for its outer circumference the circumference of a semicircle. The
inner circumference was arrived at in this way. Joining the extremities of the
diameter to the middle point of the arc of the semicircle, we have an isosceles
triangle ...
Pagina 126
Add to each the area between the straight lines BA, AC, CD and the
circumference of the segment on BD; therefore (trapezium BACD) = (the lune).
Hippocrates' third quadrature relates to a lune in which the outer circumference is
less than a ...
Add to each the area between the straight lines BA, AC, CD and the
circumference of the segment on BD; therefore (trapezium BACD) = (the lune).
Hippocrates' third quadrature relates to a lune in which the outer circumference is
less than a ...
Pagina 344
Syene) the inclination of the sun's SS rays to the vertical was 1/50th of a complete
circle, or of four right 5 angles, he calculated the circumference of the earth from
the known distance (5,000 stades) between Alexandria and Syene, making it ...
Syene) the inclination of the sun's SS rays to the vertical was 1/50th of a complete
circle, or of four right 5 angles, he calculated the circumference of the earth from
the known distance (5,000 stades) between Alexandria and Syene, making it ...
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Inhoudsopgave
INTRODUCTORY | 1 |
NUMERICAL INOTATION AND PRACTICAL CAL | 11 |
PYTHAGOREAN ARITHMETIC | 36 |
Copyright | |
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according added Apollonius appear applied Archimedes arithmetic assumed base beginning Book called centre circle cone conics construction contained corresponding cube curve cylinder definition described diameter Diophantus discovered divided draw drawn earth edition Elements equal equation equivalent Eucl Euclid expressed fact figure follows four geometry given gives greater Greek height Heron included inscribed Join known latter length less mathematics means measure meet mentioned method multiplied namely observations obtained original Pappus parallel parallelogram particular plane Plato polygon position problem Proclus produced proof Prop proportion propositions proved pyramid Pythagoreans radius ratio rectangle reference regular relation represented respectively result right angles says segment shows sides similar solid solution solved sphere square straight line Suppose surface theorem theory things third tion translation treatise triangle volume whole