| Sir John Leslie - Geometry, Analytic - 1809 - 493 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, Olinthus Gilbert Gregory - 1813
...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... | |
| Charles Butler - Mathematics - 1814
...<•! a + xx + aa=(aa + %ax+xx=) a+xf; that is, the rectangle contained by the line produced and part **produced, together with the square of half the line bisected, is equal to the square of the** line made up of the half, and part produced. QKD Cor. Hence, if three lines ,r, a 4 ,r, and 2rt + ,r... | |
| Euclides - Euclid's Elements - 1816 - 528 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 - 436 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 - Circle-squaring - 1819 - 333 pages
...rectangle " contained by their sum and difference, or that AC2 - CD2 = (AC+ CD)(AC_CD)." PROP. VI. THEOR. **if a straight line be bisected, and produced to any...the part of it produced, together with the square** nf half the. line bisected, is equal to the square of the straight line which is made up of the half... | |
| Daniel Cresswell - Geometry - 1819 - 410 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 - 372 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 - 513 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... | |
| Hirsh - 1827 - 304 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... | |
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