The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth of EuclidCassell, Petter, and Galpin, 1859 - 212 σελίδες |
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Σελίδα 23
... equal angles in each triangle be equal to one another ; viz . , AB to DE . Then their other sides are equal ; viz . , AC to DF and BC to EF . And the third angle BAC is equal to the third angle EDF . For , if BC be not equal to EF , one ...
... equal angles in each triangle be equal to one another ; viz . , AB to DE . Then their other sides are equal ; viz . , AC to DF and BC to EF . And the third angle BAC is equal to the third angle EDF . For , if BC be not equal to EF , one ...
Σελίδα 73
... equal to each other . The are BK C is equal to the arc ELF . Join BC and E F. Because the circles A B C and DEF are equal , the straight lines drawn from their centres ( III . Def . 1 ) are equal ; therefore the two sides B G and G C ...
... equal to each other . The are BK C is equal to the arc ELF . Join BC and E F. Because the circles A B C and DEF are equal , the straight lines drawn from their centres ( III . Def . 1 ) are equal ; therefore the two sides B G and G C ...
Σελίδα 74
... equal circles , equal straight lines cut off equal arcs , the greater equal to the greater , and the less to the less . Let A B C and D E F be equal circles , and BC and E F equal straight lines in them , which cut off the two greater ...
... equal circles , equal straight lines cut off equal arcs , the greater equal to the greater , and the less to the less . Let A B C and D E F be equal circles , and BC and E F equal straight lines in them , which cut off the two greater ...
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A B and CD A B C D A B is equal adjacent angles altitude angle ABC angle B A C base B C bisected Cassell's centre circle A B C circle ABCD circumference cone cylinder D E F described diagonal diameter draw equal angles equal Ax equal Const equiangular equimultiples Euclid exterior angle given rectilineal given straight line gnomon greater homologous Illustrated inscribed join less Let A B C multiple opposite angles parallelopiped pentagon perpendicular polygon prism proposition pyramid Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle sphere squares of AC straight line drawn straight lines A B THEOREM three plane angles touches the circle triangle A B C triplicate ratio twice the rectangle vertex Wherefore