| Euclides - 1838 - 264 pages
...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...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
...of section, is equal to the square of half the line. P E_ AD PROP. VI. THEOR. If a straight line be bisected and produced to any point, the rectangle contained by the whole line produced and the produced part, together with the square of half the line, is equal to the square of... | |
| Euclides - Geometry - 1841 - 378 pages
...rectangle, not exceeding the square upon half the given line. 44. To produce a given straight line, so that the rectangle contained by the whole line thus produced, and the part produced, shall be equal to a given rectangle. 45. In a given circle to inscribe three equal circles,... | |
| Euclides - 1842 - 316 pages
...equivalent 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...the part of it produced, together with the square of half the line bisected, is equivalent to the square of the straight line which is made up of the... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...equivalent to the difference of their squares PROP. VI THEOR. If a straight line be bisected, and producedto any point ; the rectangle contained by the whole line...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... | |
| Euclid, James Thomson - Geometry - 1845 - 382 pages
...difference of the hypotenuse and the other. PROP. VI. THEOR. — If a straight line be bisected, and be produced to any point; the rectangle contained by...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 - 1845 - 546 pages
...chord in the interior circle be produced either way to meet the circumference of the exterior circle, the rectangle contained by the whole line thus produced and the part produced, is a constant quantity. 103. If there be two concentric circles, and any chord of the greater... | |
| 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... | |
| Euclides - 1846 - 292 pages
...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...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... | |
| Great Britain. Admiralty - Geometry - 1846 - 128 pages
...be + (a — &)«=a 2 ; or be + (c—a)> = a e . 62 Prop. Prop. HypProp. Prop. Cor. Prop. GEOMETRY. any point; the rectangle contained by the whole line...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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