 | John Playfair - Euclid's Elements - 1832 - 333 pages
..."(AC+CD)(AC-CD)" PROP. VI. THEOR. If a straight line be bisected, and produced to any point; therect angle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half... | |
 | John Playfair - Euclid's Elements - 1833 - 333 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... | |
 | Euclides - 1834 - 518 pages
...difference. PROPOSITION VI. THEOR. — If a straight line be bisected, and produced to any point, lke rectangle contained by the whole line thus produced,...the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half... | |
 | 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... | |
 | John Playfair - Geometry - 1836 - 114 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... | |
 | 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... | |
 | Mathematics - 1836 - 472 pages
...double of the square of half the line, and of the square of the line between the points of section. X. 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... | |
 | 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... | |
 | Euclid - 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... | |
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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 of half the line bisected, is equal to the square of the straight line which is made... 
