| John Playfair - Mathematics - 1806 - 320 pages
...away the equal rectangles 2BC.CD and 2AC.CD, " there remains AD2+DB2=2AC2+2CD2. 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... | |
| Robert Simson - Trigonometry - 1806 - 546 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 point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the... | |
| John Mason Good - 1813 - 714 pages
...square of half the line, and of the square of the line between the points of section. Prop. X. Theor. If a straight line be bisected, and produced to any point, the square of tht; whole line thus produced, and the square of the part of it produced, are together double... | |
| Euclides - 1816 - 588 pages
...lines AC, CD, is equal to the rectangle contained by their sum and difference. M ^5' PROP. VI. THEOR. 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... | |
| John Playfair - 1819 - 354 pages
..." contained by their sum and difference, or that AC3 — CD3 = (AC + CD) (AC-CD)." PROP. VI. THEOR. 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... | |
| Peter Nicholson - Mathematics - 1825 - 1046 pages
...AC, CD, is equal to the rectangle contained by their sum and difference. Proposition VI. Theoretn. If a straight line be bisected, and produced .to any point : the recangle contained by the whole line thus produced, and the part of it produced, together with the... | |
| Robert Simson - Trigonometry - 1827 - 546 pages
...AD, DB, are double of 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... | |
| 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 - 148 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
...is the same thing) c + b, as above stated. Geometrically, this last truth is usually enunciated : " 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... | |
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