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... The Elements of Geometry - Page 104by George Bruce Halsted - 1885 - 366 pagesFull view - About this book
| Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...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 in C, so that the rectangle... | |
| John Mason Good - 1813 - 714 pages
...the points of section, is equal to the square of half the line. 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 «traight line which U made up of the half... | |
| Euclides - 1816 - 588 pages
...equal to the rectangle contained by their sum and difference. M ^5' 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... | |
| Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...subtend equal angles, at the center of the circle. (LXVII.) To produce a given straight line, so that the rectangle contained by the whole line thus produced, and the part of it produced, shall be equal to a given square. (LXVII i.) If, from the bisection of any given arch of a circle,... | |
| John Playfair - 1819 - 354 pages
...their sum and difference, or that AC3 — CD3 = (AC + CD) (AC-CD)." 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... | |
| Daniel Cresswell - Geometry - 1819 - 446 pages
...itself also touches the circle. PROP. LXXIII. 93. PROBLEM. To produce a given straight line, so that the rectangle contained by the whole line thus produced, and the part of it produced, shall be equal to a given square. Let AB be a given straight line, and L the side D EX of a given square... | |
| 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 is made up of the half... | |
| Robert Simson - Trigonometry - 1827 - 546 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...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... | |
| Hirsch - Algebra - 1827 - 690 pages
...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... | |
| Meyer Hirsch - Geometry - 1827 - 288 pages
...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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