 | Robert Mudie - Mathematics - 1836 - 542 pages
...PECULIAR RECTANGLE. 473 Geometrically, this last truth is usually enunciated : " If a straight line be bisected, and produced to any point ; the rectangle...half the line bisected is equal to the square of the straight line, which is made up of the half of the part produced." 10. Some very useful problems may... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...that AC2 — CD2=(AC+CD) (AC — " CD)." SCHOLIUM. X £ 7 / H A PROP. VI THEOR. If a straight line be bisected, and produced to any point ; the rectangle...half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...to the rectangle contained by their sum and difference. PROPOSITION VI. THEOREM. If a straight line be bisected, and produced to any point, the rectangle...half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...rectangle under the sum and difference of the hypotenuse and the other. PROP. VI. THEOR. IF a straight line be bisected, and produced to any point ; the rectangle...half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...these = figs. AH + LF ; and these = AD x DB + CD2. PROPOSITION VI. K Hi X Theorem. If a straight line be bisected and produced to any point, the rectangle contained by the whole line produced, and the part of it produced, together with the square of half the line bisected, is equal... | |
 | Euclides - 1838 - 264 pages
...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...half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected... | |
 | Euclides - 1840 - 82 pages
...points 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,... | |
 | 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...half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected... | |
 | 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...together with the square of half the line bisected, is equivalent to the square of the straight line which is made up of the half and the part produced. Let... | |
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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... 
