 | John Playfair - Euclid's Elements - 1832 - 358 pages
...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...by AB, F is equal to the rectangle contained by CD, L. From the points A, C draw (11. 1.) AG, CH at right angles to AB, CD; and make AG equal to F, and... | |
 | John Playfair - Euclid's Elements - 1833 - 346 pages
...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 contain* ed by the means, the four straight lines are proportionals. Let the four straight lines, AB,... | |
 | Euclides - 1834 - 518 pages
...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...CD, so E to F : the rectangle contained by AB, F, shall be equal to the rectangle contained by CD, E. From the points A, C, draw * AG, CH at right angles... | |
 | Euclid - 1835 - 540 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,... | |
 | Mathematics - 1836 - 488 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. XIX. Similar triangles are to one another... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...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...E to F ; the rectangle contained by AB, F is equal to»the rectangle contained by CD, E. From the points A, C draw (6. 1.) AG, CH at right angles to AB,... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 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,... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...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...AB, CD, E, F, be proportionals, viz. as AB to CD, so is E to F ; the rectangle contained by AB, F is equal to the rectangle contained by CD, E. t From the... | |
 | Euclides - 1838 - 264 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 proportiona Is . Let the three straight lines A, B,... | |
 | Euclides - 1840 - 82 pages
...lines be proportional, the rectangle contained by the extremes is equal to the rectangle contained by the means: and, if the rectangle contained by the...contained by the means, the four straight lines are proportional. PROP. XVII. THEOR. If three straight lines be proportional, the rectangle contained by... | |
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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... 
