| Robert Simson - Trigonometry - 1781 - 534 pages
...&c. Book II. *. 46. i. b. 3i. i. v. 3<. i. i 43- i. PROP. VI. THEO R. TF a ftraight line be bifecled, **and produced to any point ; the rectangle contained...whole line thus produced, and the part of it produced,** togc ther with the fquare of half of the line bifefted, is equal to the fquare of the ftraight line... | |
| John Playfair - Mathematics - 1806 - 320 pages
...away the equal rectangles 2BC.CD and 2AC.CD, " there remains AD2+DB2=2AC2+2CD2. QED" PROP. X. THEOR. **IF a straight line be bisected, and produced to any point, the** square of the whole line thus produced, and the square of the part of it produced, are together double... | |
| Robert Simson - Trigonometry - 1806 - 546 pages
...of AD, DB are double of the squares of AC, CD. If therefore a straight line, &c. QED PROP. X. THEOR. **IF a straight line be bisected, and produced to any point, the** square of the whole line thus produced, and the square of the part of it produced, are together double... | |
| 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
...square of half the line, and of the square of the line between the points of section. Prop. X. Theor. **If a straight line be bisected, and produced to any point, the** square of tht; whole line thus produced, and the square of the part of it produced, are together double... | |
| Euclides - 1816 - 588 pages
...of AD, DB are double of the squares of AC, CD. If therefore a straight line, &c. QED PROP. X. THEOR. **IF a straight line be bisected, and produced to any point, the** square of the whole line thus produced, and the square of the part of it produced, are together double... | |
| 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,... | |
| 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
...AC, CD, is equal to the rectangle contained by their sum and difference. 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... | |
| Robert Simson - Trigonometry - 1827 - 546 pages
...AD, DB, are double of the squares of AC, CD. If therefore a straight line, &c. QED PROP. X. THEOR. **If a, straight line be bisected, and produced to any point, the** square of the whole line thus produced, and the square of the part of it produced, are together double... | |
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