If three straight lines be proportionals, the rectangle contained by the extremes is equal to the square on the mean ; and conversely, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals. SYLLABUS OF PLANE GEOMETRY - Side 561876Uten tilgangsbegrensning - Om denne boken
| John Playfair - 1806 - 311 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 - 186 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
...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
...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
...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 - 361 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
...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
...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
...(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.... | |
| Euclid, Isaac Todhunter - 1867 - 400 sider
...if four straight lines &c. QED PROPOSITION 17. 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... | |
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