 | Euclides - 1834
...PROBLEM. — To divide a given straight line into two parts, to that the rectangle contained by the wholc 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... | |
 | Euclid - 1835 - 513 páginas
...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...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 that... | |
 | Robert Simson - 1835 - 513 páginas
...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...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 that... | |
 | John Playfair - 1836 - 114 páginas
...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 ; produce... | |
 | Euclid, James Thomson - 1837 - 390 páginas
...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
...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...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 that... | |
 | John D. Williams - 1840 - 605 páginas
...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?,... | |
 | Euclides - 1841 - 351 páginas
...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...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 that... | |
 | Euclides - 1842
...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 - 317 páginas
...(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. 
