 | 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 - 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... | |
 | 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 - 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 - 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, 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... | |
 | 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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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... 
