| Euclides - 1816 - 528 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 - 454 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 - 410 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 - 490 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 - 317 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 - 372 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 - 180 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 - 228 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 - 513 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 - 294 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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