| Euclides - 1864 - 448 pages
...: and converselg, if the rectangle contained bg the extremes be iqual to the rectangle contained bg the means, the four straight lines are proportionals. Let the four straight lines AB, CD, E, .Fbe proportionals, viz. as AB to CD, so E to F. The rectangle contained by AB, F, shall be equal to... | |
| Robert Potts - 1865 - 528 pages
...rectangle contained by the extremes is equal to the rectangle contained l»j the means : and conversely, if the rectangle contained by the extremes be equal...straight lines are proportionals. Let the four straight linos AB, CD, E, .Fbe proportionals, viz. as AB to CD, so E to F. The rectangle contained by AB, F,... | |
| Euclides - 1865 - 402 pages
...rectangle contained by the extremes is equal to the rectangle contained by the means : and conversely, if the rectangle contained by the extremes be equal...means, the four straight lines are proportionals. Prop. 1 7. If three straight lines be proportionals, the rectangle contained by the extremes is equal... | |
| John Playfair - Geometry - 1855 - 360 pages
...proportionals, the rectangle contained by the extremes it equal to the rectangle conla.ine.dlty themeans; And if the rectangle contained by the extremes be...; the rectangle contained by AB, F is equal to the rect angle contained by CD, E. From the points A, C draw (11. l.)AG, CH at right angles to AB, CD ;... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...[Construction. therefore the rectangle contained by A and 6' is equal to the rectangle contained by B and D. But if the rectangle contained by the extremes be equal...the means, the four straight lines are proportionals ; [VI. 16. therefore A is to B as D is to (7. But B is equal to D ; [CorutnicHon. Therefore A is to... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...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 are proportionals. Let the three straight lines A, 13,... | |
| Robert Potts - 1868 - 434 pages
...rectangle contained bit the extremes is equal to the rectangle contained by the meant: and conversely, if the rectangle contained by the extremes be equal...proportionals. Let the four straight lines AB, CD, E, .Fbe proportionals, viz. as AB to CD, so E to F. The rectangle contained by AB, F, shall be equal to... | |
| Cambridge univ, exam. papers - 1870 - 272 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...means, the four straight lines are proportionals. Two chords AB, CD of a circle intersect in 0, prove that AO is to CO as DO is to BO. 5. Prove that... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...circle in C, prove that the square on CE is equal to twice the quadrilateral AEBC. And Conversely, If the rectangle contained by the extremes be equal to the rectangle contained by the means, the jywr straight lines are proportionals. Let rect. AB, GH=rect. CD, EF. Then must AB be to CD as EF is... | |
| William Alexander Myers - Circle-squaring - 1873 - 238 pages
...[Hypothesis.] therefore the 'rectangle contained by A and C is equal to the rectangle contained by B and D; but if the rectangle contained by the extremes be equal...rectangle contained by the means, the four straight lines ate proportionals; [FT. 16.] therefore A is to B as D is to C. But B is equal to D; [Construction.]... | |
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