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 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 A B 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