 | Euclides - 1837 - 112 σελίδες
...that 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 σελίδες
...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...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 σελίδες
...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 - 1841 - 378 σελίδες
...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 σελίδες
...is 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...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 - 1842 - 332 σελίδες
...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 - 1845 - 382 σελίδες
...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 σελίδες
...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... | |
 | Euclides - 1846 - 292 σελίδες
...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...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, John Playfair - 1846 - 334 σελίδες
...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... 
