| 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... | |
| |