| Euclid, John Keill - Geometry - 1723 - 442 pages
...PROPOSITION XVII. THEOREM. If three Right Linet be proportional, the Re&tingle contained under the **Extremes, is equal to the Square of the Mean ; and...the Extremes, be equal to the Square of the Mean,** then the three Right Lines are proportional, - • T ET there be three Right Lines A, B, C, propor-.... | |
| Euclid, John Keill - Geometry - 1733 - 448 pages
...demonftrated. PROPOSITION XVII. THEOREM. If three Right Lines be proportional, the RfRangle contained under the **Extremes, is equal to the Square of the Mean ; and if the** Rett angle under the Extremes be equal to the Square of the Mean, then the three Right Lines are proportional... | |
| John Keill - Geometry - 1782 - 399 pages
...PROPOSITION XVII. THEOREM. If three Right Lines be proportional, the Reflatgle contained1 under the **Extremes is equal to the Square of the Mean ; and if the** Rettangle under the Extremes be equal to the Square of the Mean, then the three Right Lines are proportional.... | |
| Robert Simson - Trigonometry - 1806 - 518 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.... | |
| John Playfair - Euclid's Elements - 1806 - 320 pages
...lines, &c. 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 be equal to the square of the mean, the three straight lines are proportional.... | |
| Charles Hutton - Mathematics - 1811
...rectangle of the two extremes is equal to the 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,... | |
| Charles Hutton - Mathematics - 1812
...rectangle of the two extremes is equal to the 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. Carol. 2. Since it appears, by the rules of proportion in Arithmetic and Algebra,... | |
| Euclides - 1816 - 528 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 - Circle-squaring - 1819 - 348 pages
...ED S i PROP. XVII. THEOR. If three straight hues 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 Mason Good - 1819 - 740 pages
...proportionals. 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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