 | Euclides - Euclid's Elements - 1837 - 112 pages
...that these = 2 AC* + 2 CD!. H PROPOSITION XI. E ._ Problem. 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 c KT~i the other part. Steps of the Demonstration. 1. Prove that CF... | |
 | John Hind - Algebra - 1837 - 584 pages
...which answer the symbolical condition. • Ex. 3. Divide 20 into two parts, so that the product of the whole and one of the parts, may be equal to the square of the other part. Let a? = one part : .-. 20 - as = the other : whence, 20a? = (20 - off = 400 - 40a?... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...the given lines are equal. PROP. XXIII. PROB. To divide a given straight line into two parts, such. that the rectangle contained by the whole and one of the parts may have a given ratio to the square of the other. Let AB (see the last figure) be the given line; it is... | |
 | Euclides - 1838 - 264 pages
...CD. Wherefore, if a straight line, &c. QED PROP. XI. PROS. 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. Let AB be the given straight line: it is required to... | |
 | Euclides - 1840 - 192 pages
...To divide a given straight line (AB) in such a manner that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. Upon AB construct the square ACDB ; bisect AC in E ; join EB, and produce CA towards... | |
 | Euclides - 1840 - 82 pages
...PROB. To divide a given straight line in such a manner that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. rtl PROP. XII. THEOR. In an obtuse-angled triangle, the square of the side subtending... | |
 | Euclides - Geometry - 1841 - 378 pages
...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 the whole and one of the parts, shall be equal to the square of the other part. Upon AB describe* the square ABDC; bisect* AC * 46.... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...is evident from this algebraical equality. PROP. XI. PROB. To divide a given straight line into two parts, so that the 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 divide it into two parts, so... | |
 | Euclides - 1842 - 316 pages
...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 the whole, and one of the parts, shall be equivalent to the square of the other part. Upon AB describe (46. 1.) the square ABDC ; bisect... | |
 | Scotland free church, gen. assembly - 1847 - 554 pages
...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 is a right angle. 5. Of unequal chords in a circle the... | |
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AB be the given straight line ; it is required to divide it 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. 
