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 102
... multiple any one of them is of its part , the same multiple is all the first magnitudes of all the others . Q.E. D. PROP . II . THEOREM . If the first magnitude be the same multiple of the second that the third is of the fourth , and ...
... multiple any one of them is of its part , the same multiple is all the first magnitudes of all the others . Q.E. D. PROP . II . THEOREM . If the first magnitude be the same multiple of the second that the third is of the fourth , and ...
Σελίδα 105
... multiple of E , that K H is of F. But AB ( Hyp . ) is the same multiple of E , that CD is of F. Therefore K H is the same multiple of F , that CD is of F ; and K H is equal to C D ( V. Ax . 1 ) . From these equals , take the common ...
... multiple of E , that K H is of F. But AB ( Hyp . ) is the same multiple of E , that CD is of F. Therefore K H is the same multiple of F , that CD is of F ; and K H is equal to C D ( V. Ax . 1 ) . From these equals , take the common ...
Σελίδα 114
... multiple of BE . Therefore , NP , the multiple of DF , is also greater than N M , the multiple of the same D F ; if K O be equal to K H , N P is equal to N M ; and if less , less . First , if K O be not greater than KH ; NP is not ...
... multiple of BE . Therefore , NP , the multiple of DF , is also greater than N M , the multiple of the same D F ; if K O be equal to K H , N P is equal to N M ; and if less , less . First , if K O be not greater than KH ; NP is not ...
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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