 | John Playfair - Mathematics - 1806 - 320 pages
...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 - Geometry - 1829 - 210 pages
...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 pages
...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 pages
...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 pages
...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 - Geometry, Plane - 1860 - 380 pages
...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 pages
...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 pages
...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 pages
...(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 pages
...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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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. 
