 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...are double of the squares of AC, CD. Wherefore, if a straight line, etc. QED PROPOSITION XI. PROB. To divide a given straight line into two parts, so that...rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Upon AB describe (46. i.) the square ABDC ; bisect... | |
 | Euclides - 1853 - 146 pages
...are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. — PROBLEM. To divide a given straight line into two parts, so that...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... | |
 | Euclides - Geometry - 1853 - 176 pages
...С d. Wherefore, if a straight line, &c. QED PROPOSITION XI. — PROBLEM. To divide a given straigM 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... | |
 | William Walton, Charles Frederick Mackenzie - Education - 1854 - 266 pages
...BD the other diameter, the difference of the parallelograms is equal to twice the triangle BSD. 2. Divide a given straight line into two parts so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Produce a given straight... | |
 | Cambridge univ, exam. papers - 1854 - 284 pages
...BD the other diameter, the difference of the parallelograms is equal to twice the triangle BKD. 2. Divide a given straight line into two parts so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Produce a given straight... | |
 | G. Ainsworth - 1854 - 216 pages
...— - = -- (-4, and solving, x=lo. 3. Divide the number 20 into two such parts, that the product of the whole and one of the parts may be equal to the square of the other part. Let 2ж=; the difference of the two parts. Now, 20 being the sum, 10 + ж= the greater... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...the remarks at the end of this book. PROPOSITION XI.— PROBLEM. To divide a given straight line (AB) into two parts, so that the rectangle contained by the whole, and от of the parts, shall be equal to the square of the other part. From A draw AC perpendicular and... | |
 | John Playfair - Geometry - 1855 - 334 pages
..., and the proposition is evident from this algebraical equality. PROP. XI. PROB. To divide a givrn straight line into two parts, so that the rectangle...whole, and one of the parts, may be equal to the square of the other part. I Let AB be the given straight line; it is required to divide it into two parts,... | |
 | Robert Potts - 1855 - 1050 pages
...them, that iSj divides them into two equal parts. Prove also that the two diameters bisect each other. 3. Divide a given straight line into two parts, so...rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part Solve the same problem algebraically, and give the geometrical... | |
 | Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...upon the other two sides of it, the angle contained by those two sides is a right angle. 3. Divide a 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. Section 3. 1. The angles in the same segment of a circle... | |
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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. 
