| Euclid - 1835 - 540 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.** e 47. 1. Upon AB describe » the square ABDC ; bisect5 AC in E, Book ir. and join BE ; produce CA to... | |
| Robert Simson - Trigonometry - 1835 - 544 pages
...square of the other part. Let AB be the given straight Hue; it is required to divide it into two part", **so that the rectangle contained by the whole, and...parts, shall be equal to the square of the other part.** c 3. ']. ' e 47. 1. Upon AB describe * the square ABDC ; bisect b AC in E, Book II and join BE ; produce... | |
| John Playfair - Geometry - 1836 - 148 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 (16. 2.) the square ABDC; bisect (8. 1.) AC in E, and join BE ; produce CA to F, and... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...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 parts, so...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, James Thomson - 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... | |
| John D. Williams - Algebra - 1840 - 634 pages
...required to divide a line of 20 inches in length, into two such parts that the rectangle of the whple **and one- of the parts shall be equal to the square of the other.** Let one part — x ; then the other will be 20 — x. And by the question 20(20 — х)=з?, or ^+20^=400... | |
| Euclides - Geometry - 1841 - 378 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* the square ABDC; bisect* AC * 46. 1. in E, and join BE; produce CA to F, making*... | |
| Euclides - 1842 - 316 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 - 554 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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