 | Euclides - 1840 - 192 pages
...: F), the rectangle (AB'F) contained by the extremes, is equal to the rectangle (CD'E) contained by the means : and, if the rectangle contained by the...contained by the means, the four straight lines are proportional. From A and C, the extremities of AB and CD, draw the perpendiculars AG and CH, and make... | |
 | Euclides - Geometry - 1841 - 378 pages
...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. Let the three straight lines A, B,... | |
 | Euclides - 1842 - 316 pages
...the rectangle contained by the means : and if the rectangle contained by the extremes be equivalent to the rectangle contained by the means, the four...CD, so E to F : the rectangle contained by AB, F is equivalent to the rectangle contained by c D, E. EUC. B. VI. OF GEOMETRY. sides about equal angles... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...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. Let the three straight lines, A, B,... | |
 | Euclides - 1845 - 546 pages
...rectangle contained by the extremes is equal to the rectangle contained by the means : and conversely, if the rectangle contained by the extremes be equal...to CD, so E to F. The rectangle contained by AB, F, shall be equal to the rectangle contained by CD, E. H— From the points A, C draw AG, CH at right... | |
 | Euclid - Geometry - 1845 - 218 pages
...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. Let the three straight lines A, B,... | |
 | Euclides - 1846 - 292 pages
...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. First, let the three straight lines... | |
 | Euclides - 1848 - 52 pages
...rectangle contained by the extremes is equal to the rectangle contained by the means: and conversely, if the rectangle contained by the extremes be equal...means, the four straight lines are proportionals. PROP. XVII. THEOREM. If three straight lines be proportionals, the rectangle contained by the extremes... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...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. Let the three straight lines A, B,... | |
 | Euclides - Geometry - 1853 - 176 pages
...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. LET the three straight lines a, b,... | |
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If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means; And if the rectangle contained by the extremes be equal to the rectangle contained by the means, the four straight lines... 
