| Euclid - 1835 - 540 pages
...AD, DB are double the squares of AC, CD. Wherefore, " if a straight line," &c. QED PROP. XI. PROB. **To divide a given straight line into two parts, so...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 to divide it into two parts, so... | |
| Robert Simson - Trigonometry - 1835 - 513 pages
...CD. Wherefore, " if a straiglit line," &.c. QED PROP. XI. PROB. To divide a given straight line info **two parts, so that the rectangle contained by the...and one of the parts, shall be equal to the square** of the other part. Let AB be the given straight Hue; it is required to divide it into two part", so... | |
| John Playfair - Geometry - 1836 - 114 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...and one of the parts shall be equal to the square** of the other part. Upon AB describe (16. 2.) the square ABDC; bisect (8. 1.) AC in E, and join BE ;... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...AG"; and that this = AC* + CE* + EF! + FG", and that these = 2 AC* + 2 CD!. H PROPOSITION XI. E ._ **Problem. To divide a given straight line into two...and one of the parts shall be equal to the square** of c KT~i the other part. Steps of the Demonstration. 1. Prove that CF x FA + AE* = EF*, and that this... | |
| Euclid - Geometry - 1837 - 410 pages
...HB, AD are equal. Then c B (II. 9.) HB2 + BD*, or AD2 + BD2= 5-a ' — 2CD2+2AC2.* PROP. XI. PROB. **To divide a given straight line into two parts, so...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... | |
| Euclides - 1838 - 264 pages
...AD, DB are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. PROS. **To divide a given straight line into two parts, so...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 to divide it into two parts, so... | |
| Euclides - 1841 - 378 pages
...AD, DB are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. PROB. 1 **To divide a given straight line into two parts, so...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 to divide it into two parts, so... | |
| Euclides - 1842 - 320 pages
...are equivalent to double the squares of AC, CD. If therefore a straight line, &c. QED PROP. XI. PROB. **To divide a given straight line into two parts, so...contained by the whole, and one of the parts, shall be** equivalent to the square of the other part. Let AB be the given straight line : it is required to divide... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...(2a-f*)2+*2=2a2+2(a+i)2, and the proposition is evident from this algebraical equality. PROP. XI. PROB. **To divide a given straight line into two parts, so...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... | |
| Scotland free church, gen. assembly - 1847 - 552 pages
...the squares described on the other two sides, these sides contain a right angle. 3. Divide a given **line into two parts, so that the rectangle contained by the whole** line and one of the parts may be equal to the square of the other part. 4. The angle in a semicircle... | |
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