 | Euclid - 1835 - 540 σελίδες
...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...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 that the rectangle... | |
 | Robert Simson - 1835 - 544 σελίδες
...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...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 that the rectangle... | |
 | John Playfair - 1836 - 148 σελίδες
...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 - 1837 - 112 σελίδες
...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 - 1837 - 410 σελίδες
...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 σελίδες
...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...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 that the rectangle... | |
 | John D. Williams - 1840 - 634 σελίδες
...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 - 1841 - 378 σελίδες
...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...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 that the rectangle... | |
 | Euclides - 1842 - 316 σελίδες
...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 - 1842 - 332 σελίδες
...(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... | |
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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, shall be equal to the square of the other part. 
