 | Euclides - 1816 - 588 pagina’s
...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 square of half the line bisected, is equal to the square of the straight line which... | |
 | Daniel Cresswell - 1817 - 454 pagina’s
...cut off from the two given tangents, also subtend equal angles, at the center of the circle. (LXVII.) To produce a given straight line, so that the rectangle...of it produced, shall be equal to a given square. (LXVII i.) If, from the bisection of any given arch of a circle, a straight line be drawn cutting the... | |
 | Sir John Leslie - 1817 - 456 pagina’s
...of another problem of the same nature ; in which it is required to produce a straight line AB, such that the rectangle contained by the whole line thus produced and the part produced, shall be equivalent to the square of the line AB itself. Divide AB, by this proposition,... | |
 | John Playfair - 1819 - 354 pagina’s
...following pYoblem, more simple, and, as was observed in the former instance very little less general . " To produce a given straight line, so that the rectangle '• contained by the segments, between the extremities of the given. " line, and the point to which it is produced, may... | |
 | Peter Nicholson - 1825 - 1046 pagina’s
...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 square of half the line bisected, is equal to the square of the straight line which... | |
 | Euclides - 1826 - 226 pagina’s
...PROPOSITION X. THEOREM. If a right line be cut into two equal parts, and produced to any point, the square of the whole line thus produced, and the part of it produced, shall be together double to the square of the half line, and of the line made up of the half and the part produced.... | |
 | Euclid - 1826 - 234 pagina’s
...PROPOSITION X. THEOREM. If a right line be cut into two equal parts, and produced to any point, the square of the whole line thus produced, and the part of it produced, shall be together double to the square of the half line, and of' the line made up of the half and the part produced.... | |
 | Hirsch - 1827 - 690 pagina’s
...of this construction is founded on Eue. VI. 13, 17. SECTION LXXIII. Рвов. То produce a given line, so that the rectangle contained by the whole line thus produced, and the part produced, may be equal to the square of a given line. SOLUT. Let the line AB be given (ßg. 86) : lengthen... | |
 | Robert Simson - 1827 - 546 pagina’s
...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 square of half the line bisected, is equal to the square of the straight line which... | |
 | Meyer Hirsch - 1827 - 288 pagina’s
...proof of this construction is founded on Eue. VI. 13, 17. SECTION LXXIII. PROB. To produce a given line, so that the rectangle contained by the whole line thus produced, and the part produced, may be equal to the square of a given line. SOLUT. Let the line AB be given (ßg. 86) : lengthen... | |
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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... 
