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. Register - Page 310by University of Cambridge - 1849Full view - About this book
| Robert Simson - Trigonometry - 1762 - 466 pages
...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 the whole, and one of the parts,** fnall be equal to the fquare of the other part. Upon AB defcribc " the fquare ABDC, bifect b AC in... | |
| Robert Simson - Trigonometry - 1775 - 520 pages
...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 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... | |
| Euclid - 1781 - 520 pages
...look II, k 10 i. e SI 46.".. *47-IPRO P. XI. 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... | |
| Alexander Ingram - Trigonometry - 1799 - 351 pages
...*• 11 B Let AB be the given ftraight line ; 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... | |
| Robert Simson - Trigonometry - 1804
...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 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... | |
| Euclid, Robert Simson - Euclid's Elements - 1806 - 518 pages
...double of the squares of AC, CD. Wherefore, wr a straight line, &c. QED PROP. XI. PROB. TO clivjde **a given straight line into two parts, so that the...parts shall be equal to the square of the other part.** Let AB be the given straight line ; it is required to divide it into two parts, so that the rectangle... | |
| John Playfair - Euclid's Elements - 1806 - 311 pages
...because DG=DB; therefore AD2+DB2=2AC2+ 2CD2. Wherefore, if a straight line, &c, QE D, PROP. XI. PROB. TO **divide a given straight line into two parts, so that...rectangle contained by the whole and one of the parts** may be equal to the square of the other part. Let AB be the given straight line ; it is required to... | |
| Euclid - Geometry - 1810 - 518 pages
...DB are double of the squares of AC, CD. \Vherefore, if a straight line, &c. QED PR6P. XI. PROB. TO **divide a given straight line into two parts, so that...parts shall be equal to the square of the other part.** Let AB be the given straight line ; it is required to divide it into two parts, so that the rectangle... | |
| John Mason Good, Olinthus Gilbert Gregory - 1813
...and the part produced. Prop. XI. Prob. To divide a given straight line into two parts, so that thé **rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.** Prop. XII. Theor. In obtuse angled triangles, if a perpendicular be drawn from any of the acute angles... | |
| John Bonnycastle - Algebra - 1813
...It is required to divide a line, of 20 inches in length, into two such parts, that the rectangle of **the whole and one of the parts shall be equal to the square of the other.** Ans. 10/5 — 10 5. It is required to divide the number 60 into two such parts, that their product... | |
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