| Robert Simson - Trigonometry - 1762 - 488 pages
...PR OB. TO divide a given ftraight line into two parts, fo that the rectangle contained by the whole, **and one of the parts, fhall be 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... | |
| Euclid - Geometry - 1765 - 492 pages
...this, there being no number that can be divided into two others f«ch, that the product of the whole by **one of the parts, fhall be equal to the fquare of the other part.** PROP. XII. THE OR. In obtufe-axgicd triangles, the fquare of the fide eppofite to the obtufe angle,... | |
| Robert Simson - Trigonometry - 1775 - 534 pages
...ftraight line ; it is required to divide it into two parts, fo that the rectangle contained by the whole, **and one of the parts, fhall be equal to the fquare of the other part.** Upon AB deferibe * the fquare ABDC ; bifect b AC in E, and join BE ; produce CA to F, and makec EF... | |
| Euclid - 1781 - 552 pages
...PRO B. TO divide a given ftraight line into two parts, fo that the rectangle contained by the whole, **and one of the parts, fhall be 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... | |
| Richard Turner - Geometry - 1787 - 264 pages
...Right Line given into extreme and meati Proportion ; that is, to cut a Line fo that the Product of **the whole Line and one of the Parts fhall be equal to the** Square of the other Part. Let AB be the Right Line given to be fo divided. 11 «L AC Cbnftruflion.... | |
| Euclid - Euclid's Elements - 1789 - 296 pages
...AB be the given right line ; it is required to divide it into two parts, fo that the reŁtangle of **the whole line and one of the parts fhall be equal to the fquare of the other part.** Upon AB defcribe the fquare AC (II. i.), and bifeft the fide of it AD in E (I. 10.) Join the points... | |
| John Playfair - Euclid's Elements - 1795 - 462 pages
...the lines." PR O P. VIII. THEO R." TF a ftraight line be divided into any two parts, J. four times **the reftangle contained by the whole line, and one of the parts,** together with the fquare of the other part, is equal to the fquare of the ftraight line which is made... | |
| Alexander Ingram - Trigonometry - 1799 - 374 pages
...it is required to divide CoIK II. it into two parts, fo that the rectangle contained by the whole, **and one of the parts, fhall be equal to the fquare of the other part.** Upon AB defcribe » the fquare ABDC ; bifea b AC in E, and join BE ; produce CA to F, and make c EF... | |
| John Bonnycastle - Euclid's Elements - 1803 - 470 pages
...PROP. XXII. PROBLEM. • • - y To divide a given right line into two parts, fo that the re&angle **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 line ; it is required to divide it into two parts, fo that the reftangle... | |
| Robert Simson - Trigonometry - 1804 - 528 pages
...ftraight line; it is required to divide it into two parts, fo that the rectangle contained by the whole, **and one of the parts, fhall be equal to the fquare of the other part.** Upon AB defcribe » the fquare ABDC, bifect b AC in E, and join BE; produce CA to F, and make c EF... | |
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