 | Mathematics - 1835 - 684 pages
...proportionals, the rectangle under the extremes shall be equal to the square of the mean ; and, conversely, if the rectangle under the extremes be equal to the square of the mean, the three straight lines shall be proportionals. Cor. 2. It appears from the proposition that rectangles which... | |
 | Euclid - 1835 - 540 pages
...&c. Q..ED PROP. 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.... | |
 | Mathematics - 1836 - 488 pages
...lines are proportionals. XVII. 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.... | |
 | John Playfair - Geometry - 1836 - 148 pages
...&c. QED PROP. 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 ertremes be equal to the square of the mean, thi three straight lines are proportionals.... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...PROPOSITION XVII. THEOREM. 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.... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...contained by the extremes is equal to the square of the mean : and (2.) if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals. Let the three straight lines A, B, C be proportionals, viz., A :... | |
 | Euclides - 1838 - 264 pages
...demonstrations. PROP. 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 proportiona... | |
 | Euclides - 1840 - 192 pages
...XVII. THEOR. If three straight lines be proportional (A : B : : B : c), the rectangle contained by the extremes is equal to the square of the mean : and, if the rectangle contained by the extremes (of three given straight lines) be equal to the square of the mean, the three... | |
 | Euclides - 1840 - 82 pages
...proportional. PROP. XVII. THEOR. If three straight lines be proportional, the rectangle contained by the extremes is equal to the square of the mean: and, if the rectangle contained by the extremes (of three given straight lines) be equal to the square of the mean, the three... | |
 | Euclides - Geometry - 1841 - 378 pages
...&c. QED PROP. 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.... | |
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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. 
