 | Euclid - 1835 - 540 pages
...PROP. X. PROB. To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line ; it is required to divide it into two equal parts. al. 1. Describe a upon it an equilateral triangle ABC, and bisect b9. i. bthe angle ACB... | |
 | Robert Simson - 1835 - 544 pages
...info 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 Hue; it is required to divide it into two part", so that the rectangle contained by the whole, and... | |
 | John Playfair - 1836 - 148 pages
...PROP. XXIV. PROB. ff To divide a given straight line into two partx, so that the rectangle con tained 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 divide it into two parts, so that the rectangle... | |
 | Robert Mudie - 1836 - 524 pages
...are now in a condition for showing how the same result may be arrived at geometrically. Let AB be any line, it is required to divide it into two parts, so that the square of one part shall be equal to the rectangle of the whole and the other part. At the point B,... | |
 | Robert Mudie - 1836 - 542 pages
...are now in a condition for showing how the same result may be arrived at geometrically. Let AB be any line, it is required to divide it into two parts, so that the square of one part shall be equal to the rectangle of the whole and the other part. At the point B,... | |
 | Euclides - 1837 - 112 pages
...FG", and 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...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 pages
...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 * The ten foregoing proposition)! may all be proved very easily by means of algebra, in connexion with... | |
 | Andrew Bell - 1837 - 290 pages
...and of the mean distance. PROPOSITION XI. PROBLEM. To divide a given straight line in medial section. Let AB be the given straight line ; it is required to divide it in medial section. Upon AB describe the square ABDC (I. 46) ; bisect AC in E (1. 10), and join BE ;... | |
 | Euclides - 1838 - 264 pages
...done. PROP. X. PROB. Tobiseet a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line ; it is required to divide it into two equal parts. «. . Describe* upon AB an equilateral triangle ABC, „,',' and bisect* the angle ACB... | |
 | Robert Simson - 1838 - 434 pages
...PROP. X. PROB. To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts. Describe (1. 1.) upon it an equilateral triangle ABC, and bisect (9. 1.) the angle... | |
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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. 
