| Euclides - 1816 - 588 pages
...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... | |
| Sir John Leslie - Geometry - 1817 - 456 pages
...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,... | |
| Daniel Cresswell - Geometry - 1819 - 446 pages
...ofL. 94. COR. By the help of this proposition and (E. 14. 2.), a given straight line may be produced, so that the rectangle contained by the whole line...the part of it produced, shall . be equal to a given rectilineal figure. PROP. LXXIV. 95. THEOREM. IJ\ from the bisection of any given arch of a circle,... | |
| Daniel Cresswell - Geometry - 1819 - 486 pages
...and which is equal to the tangent, itself also touches the circle. " --> PROP. LXXIII. 93. PROBLEM. To produce a given straight line, so that the rectangle contained by the whole lint? thus produced, and the part of it produced, shall be equal to a given square. Let AB be a given... | |
| John Playfair - 1819 - 354 pages
...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 - Mathematics - 1825 - 1046 pages
...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... | |
| Euclid - 1826 - 234 pages
...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.... | |
| Euclides - 1826 - 226 pages
...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.... | |
| Robert Simson - Trigonometry - 1827 - 546 pages
...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 - Geometry - 1827 - 288 pages
...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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