| John Playfair - 1806 - 320 sider
...CD : : E : F. Wherefore, if four straight 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... | |
| John Playfair - 1829 - 210 sider
...equal the rectangle contained by the means ; and conversely. ED. Cor. 4. If three straight lines be proportional the rectangle contained by the extremes is equal to the square of the mean ; and conversely. ED. Cor. 5. Equal triangles, or equal parallelograms, have their bases... | |
| Euclides - 1840 - 192 sider
...Prop. IB). But since D = B, the rectangle B'D is the same as B'B, or the square of B ; and therefore, if three straight lines are proportional, the rectangle contained by the extremes is equal to the square of the mean. And conversely, if three straight lines be such that the rectangle contained by the extremes... | |
| Euclides - 1840 - 82 sider
...the means, the four straight lines are 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... | |
| Scottish school-book assoc - 1845 - 444 sider
...the means of the proportion be equal, the rectangle formed by them will be a square. Hence, " when three straight lines are proportional, the rectangle...contained by the extremes is equal to the square on tie mean ;" and conversely. PROPOSITION LXV — THEOREM. If two chords, AB, CD, cut one another in... | |
| Robert Potts - 1860 - 380 sider
...7.) Wherefore, if four, &c. QED PROPOSITION XVH. THEOREM. If three straight lines be proportionals, the rectangle contained by the extremes is equal to...conversely, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals. r Let the three straight... | |
| Euclides - 1860 - 288 sider
...therefore AB is to CD as E toF. PROPOSITION XVII. THEOREM. If three straight lines be proportionals, the rectangle contained by the extremes is equal to the square on the mean ; and if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines... | |
| Euclides - 1864 - 448 sider
...7.) Wherefore, if four, &c. QED PROPOSITION XVII. THEOREM. If three straight lines be proportionals, the rectangle contained by the extremes is equal to...conversely, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals. Let the three straight... | |
| Euclides - 1865 - 402 sider
...(v. 7.) Wherefore, if four, &c. QED PROP. XVH.— THEOREM. //" Him', straight lines be proportionals, the rectangle contained by the extremes is equal to...conversely, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals. (References— Prop.... | |
| Robert Potts - 1865 - 528 sider
...QED PROPOSITION XVII. .THEOREM. lf (hree straight lines be proportionals, the rectangle contained Jy the extremes is equal to the square on the mean ;...conversely, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals. Let the three straight... | |
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