 | Euclides - 1848 - 52 pages
...by the extremes is equal to the square of the mean : and conversely, if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals. PROP. XVIII. PROBLEM. Upon a given straight line to describe a rectilineal... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...XVIIi. PROPOSITION XVII. THEOR. If three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean; and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals.... | |
 | Euclides - Geometry - 1853 - 176 pages
...XVII. — THEOREM. If three straight lines be proportionals, tlie rectangle contained by the extreme» is equal to the square of the mean; and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals.... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...PROPOSITION XVII.— THEOREM. . . If three straight lines be proportionals, the rectangles contained by the extremes is equal to the square of the mean ; and if the rectangle contained by the extremes is equal to the square of the mean, the three straight lines are proportionals.... | |
 | Euclides - 1855 - 270 pages
...by the extremes is equal to the square of the mean ; and conversely, if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals. First, let the three straight lines A, B, and С be proportionals,... | |
 | W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...straight lines are proportionals. If three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean, and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals.... | |
 | Euclides - 1861 - 464 pages
...by the extremes is equal to the square of the mean ; and conversely, if the rectangle contained by the extremes be equal to the square of the mean, the three st. lines are proportionals. Coi'. 3, I. DEM. 7, V. 16, VI. E. 1 c. E 1. D. l Hyp. Cone. 3,I. H & 7,... | |
 | Euclides - 1863 - 122 pages
...the extremes is equal to the square of (13) the mean; and, conversela, if tbc rectangle contained bg the extremes be equal to the square of the mean, the three straight lines ureprcporlionals. Take the straight line D equal to the straight line B. Because A is... | |
 | Euclides - 1865 - 402 pages
...by the extremes is equal to the square of the mean ; and conversely, if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals. Prop. 18. Upon a given straight line to describe a rectilineal figure... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...rectangle of the two extremes is equal to the square of the mean ; and, conversely, if the rectangle of the extremes be equal to the square of the mean, the three lines are proportionals. Corol. 2. Since it appears by the rules of proportion in arithmetic and algebra... | |
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IF three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean ; and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals. 
