| Robert Simson - Trigonometry - 1775 - 520 pages
...ftraight line, &c. Q^ED t 47. r. PROP, Book IT. B4«. i. b lo. i. c 3. i. c. ». fi 47. PRO P. XI. PRO B. **•"TO divide a given ftraight line into two parts, fo that the** reftangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part.... | |
| Euclid - 1781 - 520 pages
...equal to the fquare of the other part. Let AB be the given ftraight line ; it is required to divide it **into two parts, fo that the rectangle contained by...parts, fhall be equal to the fquare of the other part.** Upon AB defcribe*the fquare ABDC ; bife&bAC in E, and join BE; produce CA to F, and make c EF equal... | |
| Euclid, James Williamson - Euclid's Elements - 1781 - 309 pages
...part produced, as upon one line. Which was to be demonftrated. PROP. XI. To cut a given ftraight line, **fo that the rectangle contained by the whole and one of the** fegments may be equal to the fquare of the remaining fegment. Let AB be the given ftraight line ; it... | |
| Euclid, John Playfair - Electronic book - 1795 - 400 pages
...fquares of AD, DB are double of the fquares of AC, CD i Wherefore, if a ftraight line, &c. Q^ ED PROP. **TO divide a given ftraight line into two parts, fo that the** redtangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part.... | |
| Alexander Ingram - Trigonometry - 1799 - 351 pages
...together double of the fquares of CD half their fum, and AC half their difference. PROP. XI. PROB. **TO divide a given ftraight line into two parts, fo that the** reel-angle contained by the whole, and one of the parts, lhall be equal to the fquare of the pther... | |
| John Bonnycastle - 1803 - 279 pages
...to the fum qf the fquareg of AS, Bg, CD and DA. Q..ED PROP. XXII, PROBLEM. To divide a given right **line into two parts, fo that the rectangle contained by the whole** line and one of the parts, fhall be equal to the fquare of the other part. Let AB be the given right... | |
| Robert Simson - Trigonometry - 1804
...ftraight line, &c. C^,E, D. h. 34. a. i. 47. i. i. 47. i. a. 46. t. b. 10. i. c. 3. l. <L 6. 3. e. 47. **PROP. XI. PR OB. TO divide a given ftraight line into...two parts, fo that the rectangle contained by the** whale, and one of the parts, fhall be equal to the fquare of the other part. Let AB be the given ftraight... | |
| Euclid, John Playfair - Circle-squaring - 1804 - 440 pages
...= AD2+DB% becaufe DGrrDB: Therefore, AD2+DB2=2AC2+2CD% Wherefore, if a ftraight line. Sec. D. PROP. **PROP. XI. PR OB. TO divide a given ftraight line into two parts, fo that** the.rectangle contained by the whole, and one of the parts, may be equal to the fquare of the other... | |
| John Playfair - Euclid's Elements - 1806 - 311 pages
...the other part. Let AB be the given straight line ; it is required to divide it into two parts, so **that the rectangle contained by the whole and one of the parts** shall be equal to the square of the other part, e 47. 1. Upon AB describe" the square ABDC ; bisectb... | |
| Euclides - 1816 - 528 pages
...straight line, £c. QED "46. 1 Ho. 1 PROP. XI. PROB. To divide a given straight line into two parts, so **that the rectangle contained by the whole, and one of the parts,** shall be equal to the square of the other part. Let AB be the given straight line; it is required to... | |
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