 | 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... | |
 | Euclides - 1840 - 82 pages
...squares of half the line, and of the part intermediate between the points of section. PROP. X. THEOR. If a straight line be bisected, and produced to any point, the squares of the whole produced line, and of the produced part, are together double of the squares of... | |
 | Euclides - Geometry - 1841 - 378 pages
...AD, DB are double of the squares of AC, CD. Therefore, if a straight line, &c. a ED 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 - 1842 - 332 pages
...algebraical expression, where a denotes AC, and b denotes CD ; hence, a+i =AD, a— i=DB. PROP. X. THEOR. b 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 - 1842 - 316 pages
...are equivalent to 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 equivalent... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...these equals together, and from the suras take 2 AC.CD : then '=2 A(J2-(-2 CD2. 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... | |
 | Euclides - 1845 - 546 pages
...of the squares of AC, CD. If therefore a straight line be divided, &c. QED 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... | |
 | Euclid - Geometry - 1845 - 218 pages
...are double of the squares of AC, CD. If therefore a straight line, &c. QED PROPOSITION X. THEOB. — 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 - 1846 - 292 pages
...are together double of the squares of AC, CD. Wherefore, If a straight line Ssc. QED 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 square... | |
 | Euclides - 1848 - 52 pages
...square of half the line, and of the square of the line between the points of section. PROP. 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... | |
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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 of the square of half the line bisected, and of the square of the line... 
