| Euclides - 1837
...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... | |
| Euclides - 1840
...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 - 1841
...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
...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 - 317 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... | |
| Robert Potts - 1845
...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... | |
| Robert Simson - Geometry - 1845 - 199 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... | |
| James Thomson - Geometry - 1845 - 358 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 - 1846
...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
...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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