 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...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 * The ten foregoing proposition)! may all be proved very easily by means of algebra, in connexion with... | |
 | Euclides - Euclid's Elements - 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 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 x FA + AE*... | |
 | Andrew Bell - Euclid's Elements - 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 - Geometry - 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... | |
 | Euclides - Geometry - 1841 - 378 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. * 1. 1. Describe* upon it an equilateral triangle ABC, and * 9. I- bisect* the angle ACB... | |
 | John Playfair - Euclid's Elements - 1842 - 332 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. Describe (1. 1.) upon it an equilateral triangle ABC, and bisect (9. 1.) the angle ACB... | |
 | John Playfair - Euclid's Elements - 1844 - 338 pages
...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...into two parts, so that the rectangle contained by Ji ^j. the whole, and one of the parts, shall be equal to the square of the other part. Upon AB describe... | |
 | Education - 1844 - 688 pages
...each of the parts are together equal to the square of the whole line. 7. 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. 8. If in a circle two straight lines cut one another, which... | |
 | Euclides - 1845 - 546 pages
...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 divide AB into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal... | |
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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. 
