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 58
... Wherefore AB is bisected at F. Wherefore , if a straight line , & c . Q. E. D. Corollary . If there be any number of parallel chords in a circle , the diameter perpendicular to one of them bisects all of them . Exercise . If a straight ...
... Wherefore AB is bisected at F. Wherefore , if a straight line , & c . Q. E. D. Corollary . If there be any number of parallel chords in a circle , the diameter perpendicular to one of them bisects all of them . Exercise . If a straight ...
Σελίδα 153
... Wherefore the rectangle B A.A C is equal to the rectangle E A.AD ( VI . 16 ) . Therefore , if from any angle , & c . Q. E. D. PROP . D. THEOREM . The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle ...
... Wherefore the rectangle B A.A C is equal to the rectangle E A.AD ( VI . 16 ) . Therefore , if from any angle , & c . Q. E. D. PROP . D. THEOREM . The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle ...
Σελίδα 159
... Wherefore the base G F is equal ( I. 4 ) to the base FH . But it has been proved that G E is equal to EH , and E Fis common . Therefore G E and EF are equal to H E and E F , each to each ; and the base GF is equal to the base F H. Wherefore ...
... Wherefore the base G F is equal ( I. 4 ) to the base FH . But it has been proved that G E is equal to EH , and E Fis common . Therefore G E and EF are equal to H E and E F , each to each ; and the base GF is equal to the base F H. Wherefore ...
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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