 | John Playfair - Euclid's Elements - 1842 - 332 pages
...E : F. PROP. XVII. THEOR. If three straight lines lie 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 - Geometry - 1845 - 218 pages
...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.... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 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 : B... | |
 | Euclides - 1845 - 546 pages
...contained by the extremes is equal to the square of the mean; and conversely, if tke 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. as A... | |
 | Euclides - 1846 - 272 pages
...B as B to C), the rectangle under the extremes will be equal to the square which is constructed on the mean. And if the rectangle under the extremes be equal to the square constructed on the mean, the three right lines shall be proportional. PART 1. — Assume D equal to... | |
 | Dennis M'Curdy - Geometry - 1846 - 168 pages
...AG; that is, AB : CD :: E : F. 17 Th. If three straight lines be proportionals, the rectangle of the extremes is equal to the square of the mean: and if the rectangle of the extremes be equal to the square of the mean, the three straight lines are proportionals. The... | |
 | Euclides - 1846 - 292 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.... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...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. Let the three straight lines, A, B, C be proportionals, viz. as A... | |
 | Dennis M'Curdy - Geometry - 1846 - 166 pages
...proportionals, the rectangle of the extremes is equal to the square of the mean: and if the rectangle of the extremes be equal to the square of the mean, the three straight lines are proportionals. Given three straight lines A, B, C ; such, that AistoBasBistoC: then... | |
 | Charles William Hackley - Geometry - 1847 - 248 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. If the sides about the equal angles of parallelograms or triangles... | |
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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. 
