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 46
... twice the rectangle A B.B C , is double of A K , for BK is equal ( II . 4 Cor . ) to BC . Therefore the gnomon A KF and the square CK , are together equal to twice the rectangle A B.B C. To each of these equals , add HF , which is equal ...
... twice the rectangle A B.B C , is double of A K , for BK is equal ( II . 4 Cor . ) to BC . Therefore the gnomon A KF and the square CK , are together equal to twice the rectangle A B.B C. To each of these equals , add HF , which is equal ...
Σελίδα 49
... twice the rectangle AC.CD are together equal to the squares of AC and CD . But the square of AD is equal ( II . 4 ) to the squares of AC and CD , and twice the rectangle AC.CD. Therefore adding these equals , the squares of A D and B D ...
... twice the rectangle AC.CD are together equal to the squares of AC and CD . But the square of AD is equal ( II . 4 ) to the squares of AC and CD , and twice the rectangle AC.CD. Therefore adding these equals , the squares of A D and B D ...
Σελίδα 52
... twice the rectangle C B. D B. A Because the straight line C B or BD , is B divided into two parts at D or at C , the А squares of C B and B D are equal ( II . 7 ) to twice the rectangle CB.BD , and the square of D C. To each of these ...
... twice the rectangle C B. D B. A Because the straight line C B or BD , is B divided into two parts at D or at C , the А squares of C B and B D are equal ( II . 7 ) to twice the rectangle CB.BD , and the square of D C. To each of these ...
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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