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
... square of CB is equal ( II . 5 ) to the square of CD . And it has been proved that A D is equal to N B. Therefore the rectangle A D.D B , and the square of CB is equal to the square of CD . N C B D PROP . VII . THEOREM . If a straight ...
... square of CB is equal ( II . 5 ) to the square of CD . And it has been proved that A D is equal to N B. Therefore the rectangle A D.D B , and the square of CB is equal to the square of CD . N C B D PROP . VII . THEOREM . If a straight ...
Σελίδα 48
... square of CD is equal ( II . 4 Cor . 2 ) to four times the square of CB ; and twice the rectangle A C. CD is equal ( II . Ax . 2 ) to four times the rectangle A C. C B. Therefore , adding these equals , the square of C D and twice the ...
... square of CD is equal ( II . 4 Cor . 2 ) to four times the square of CB ; and twice the rectangle A C. CD is equal ( II . Ax . 2 ) to four times the rectangle A C. C B. Therefore , adding these equals , the square of C D and twice the ...
Σελίδα 50
... square of E C is equal to the square of CA. Therefore the squares of EC and CA are double of the square of CA. But the square of E A is equal ( I. 47 ) to the squares of E C and CA. Therefore the square of E A is double of the square of ...
... square of E C is equal to the square of CA. Therefore the squares of EC and CA are double of the square of CA. But the square of E A is equal ( I. 47 ) to the squares of E C and CA. Therefore the square of E A is double of the square of ...
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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