 | Meyer Hirsch - Geometry - 1827 - 288 pages
...construction is founded on Eue. VI. 13, 17. SECTION LXXIII. PROB. To produce a given line, so that the rectangle contained by the whole line thus produced, and the part produced, may be equal to the square of a given line. SOLUT. Let the line AB be given (ßg. 86) : lengthen... | |
 | John Playfair - Euclid's Elements - 1833 - 346 pages
...taking away the equal rectangles 2BC. CD and 2AC.CD, there re" mains AD2+DB2=2ACH2CD2." PROP. X. THEOR. If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...difference of two quantities, is equivalent ta the difference of their squares, B ID PROP. VI. THEOR. If a straight line be bisected, and produced to any...together with the square of half the line bisected, is equ2l to the square of the straight line which is made up of the half and the part produced. Let the... | |
 | Euclid - 1835 - 540 pages
...AD, DB are double the squares of AC, CD. " If, therefore, a straight " line," &c. QED PROP. X. THEOR. If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double... | |
 | Robert Mudie - Mathematics - 1836 - 524 pages
...geometrically, or as it applies to lines ; and for this purpose it is usually enunciated in these tcnns : " If a straight line be bisected, and produced to any point ; the square of the whole line thus produced, and the square of the part of it produced, are together double... | |
 | Robert Mudie - Mathematics - 1836 - 542 pages
...geometrically, or as it applies to lines ; and for this purpose it is usually enunciated in these terms : " If a straight line be bisected, and produced to any point ; the square of the whole line thus produced, and the square of the part of it produced, are together double... | |
 | John Playfair - Geometry - 1836 - 148 pages
...square of CB, is equal to the square of CD. Wherefore, if a straight line, &c. QED PROP. XXIII. THEOR. If a straight line be bisected, and produced to any point, the square of the whole line thus produced*, and the square of the part of it produced, are together double... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...AD*=AC8+CD2+2AC.CD. Add these equals together, and from the sums take 2AC.CD; then PROP. X. THEOR. IF a straight line be bisected, and produced to any point, the squares of the whole line thus produced, and of the part of it produced, are together double of the... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...DB ; therefore the squares of AD, DB, are double of the squares of AC, CD. PROPOSITION X. THEOREM. If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...and that this = AC* + CE* + EG* + GF*, and that these are = 2 ^cs + 2 CD*. PROPOSITION X. Theorem. If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are xf\' together... | |
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Prove it. 6.If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced together with the -square on half the line bisected, is equal to the square on the straight line... 
