| 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
...which contain the right angle. Is this proposition included in any more 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... | |
| Royal Military Academy, Woolwich - 1853
...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 the...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 - 147 sider
...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 (i. 46) the square abdС; bisect (i. 10) a С in e, and join be, produce С a 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
...therefore the difference of the parallelograms GF, EH is equal to twice the triangle KBD. 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 Walton, Charles Frederick Mackenzie - 1854 - 225 sider
...therefore the difference of the parallelograms GF, EH is equal to twice the triangle KBD. 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... | |
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