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 49
... double of the square of CD . But it has been proved that the square of AE is double of the square of A C. Therefore the squares of A E and EF are double of the squares of A C and CD . But the square of A F is equal ( I. 47 ) to the ...
... double of the square of CD . But it has been proved that the square of AE is double of the square of A C. Therefore the squares of A E and EF are double of the squares of A C and CD . But the square of A F is equal ( I. 47 ) to the ...
Σελίδα 50
... 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 A C. Again , because G F is equal to E F , the square of G F is equal to the ...
... 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 A C. Again , because G F is equal to E F , the square of G F is equal to the ...
Σελίδα 69
... double of the angle at the circumference standing upon the same arc , that is , upon the same part of the cir- cumference . Let A B C be a circle , BEC an angle at the centre , and BAC an angle at the circumference , standing upon the ...
... double of the angle at the circumference standing upon the same arc , that is , upon the same part of the cir- cumference . Let A B C be a circle , BEC an angle at the centre , and BAC an angle at the circumference , standing upon the ...
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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