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 18
... greater than , equal to , or less than another , according as the side opposite to the former is greater than , equal to , or less than the side opposite to the latter . Corollary 2. - All the angles of a scalene triangle are unequal ...
... greater than , equal to , or less than another , according as the side opposite to the former is greater than , equal to , or less than the side opposite to the latter . Corollary 2. - All the angles of a scalene triangle are unequal ...
Σελίδα 109
... greater than the other . Let A be the greater . As in the preceding proposition , take D and E , equimultiples of A and B , and Fa multiple of C , such that D may be greater than F , but E not greater than F. B Because A is to C as B ...
... greater than the other . Let A be the greater . As in the preceding proposition , take D and E , equimultiples of A and B , and Fa multiple of C , such that D may be greater than F , but E not greater than F. B Because A is to C as B ...
Σελίδα 116
... greater than C , D is greater than F ; if equal , equal ; and if less , less . First , let A be greater than C. D is greater than F. Because A is greater than C , and A- D B- C F E- B is any other magnitude ; and , of unequal magnitudes , ...
... greater than C , D is greater than F ; if equal , equal ; and if less , less . First , let A be greater than C. D is greater than F. Because A is greater than C , and A- D B- C F E- B is any other magnitude ; and , of unequal magnitudes , ...
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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