 | Euclides - 1852
...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 contained by...parts, shall be equal to the square of the other part. Upon AB describe* the square ABDC; • x hi. i. bisect* AC in E, " x . i. and join BE; produce CA to... | |
 | Charles Astor Bristed - 1852
...every triangle are equal to two right angles. 3. Divide a given straight line into two such parts, that the rectangle contained by the whole and one...parts shall be equal to the square of the other part. 4. The angle at the centre of a circle is double of the angle at the circumference, upon the same base,... | |
 | 1852
...general one ? 2. To divide a given straight line into two parts, so that the rectangle contained hy the whole and one of the parts, shall be equal to the square of the other part. Can this be solved arithmetically ? if so, find approximately into how many parts the given line must... | |
 | Royal Military Academy, Woolwich - 1853
...of AC, CD. Wherefore, if a straight line, etc. QED PROPOSITION XI. PROB. To divide a given straight line into two parts, so that the rectangle contained...parts, shall be equal to the square of the other part. Upon AB describe (46. i.) the square ABDC ; bisect (10. i.) AC in E, and join BE ; produce CA to F,... | |
 | Euclides - 1853
...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 contained by...parts, shall be equal to the square of the other part. Upon AB describe (1. 46.) the square ABDC ; bisect (I. 10.) AC in E, and join BE; produce CA to F,... | |
 | Royal Military Academy, Woolwich - 1853
...divide a line of 20 inches in length into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Let x = the greater part ; then 20 — x = the less part, and hence by the question we have x8 = 20 (20... | |
 | Euclides - 1853
...line. It is required to divide it into two such parts, that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. On AB describe (i. 46) the square ACDB ; and supposing A to be that extremity of AB adjacent to which... | |
 | Cambridge univ, exam. papers - 1854
...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... | |
 | William Somerville Orr - 1854
...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... | |
 | William Walton, Charles Frederick Mackenzie - 1854 - 225 σελίδες
...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... | |
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To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part. 
