| Andrew Bell, Robert Simson - 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 - 1838 - 264 pages
...unequal lines AC, CD, is equal to the rectangle contained by their sum and difference. PROP. VI. THEOR. **If a straight line be bisected, and produced to any...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... | |
| 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... | |
| 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... | |
| 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... | |
| 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, 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, John Playfair - Euclid's Elements - 1846 - 334 pages
...CD2=(AC+CD) (AC — " CD)." SCHOLIUM. X £ / it M r"3> ' '•• * PROP. VI THEOR. Ifastraightlinebe **bisected, and produced to any point ; the rectangle...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... | |
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