| 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...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 - Geometry - 1853 - 176 pages
...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 - 146 pages
...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 - Mathematics - 1853 - 474 pages
...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 - Geometry - 1853 - 334 pages
...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 - 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... | |
| 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... | |
| 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... | |
| Robert Potts - 1855 - 1050 pages
...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 that...parts, shall be equal to the square of the other part** Solve the same problem algebraically, and give the geometrical interpretation of the result. 4. The... | |
| 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...parts shall be equal to the square of the other part.** Section 3. 1. The angles in the same segment of a circle are equal. 2. If from a point without a circle... | |
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