 | Euclides - 1874 - 342 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...F be proportionals, viz., as AB to CD, so E to F. Then the rectangle contained by AB, F, shall be equal to the rectangle contained by CD, E. Construction.... | |
 | William Alexander Myers - Circle-squaring - 1874 - 207 pages
...6 therefore the rectangle contained by A and G is equal to the rectangle contained by B and D ; but if the rectangle contained by the extremes be equal...means, the four straight lines are proportionals; [FI. 16.] therefore A is to B as D is to (7. But B is equal to D] [Construction.'] Therefore A is to... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...rectangle contained fy the extremes is equal to the rectangle contained by the means: and conversely, if the rectangle contained by the extremes be equal...proportionals. Let the four straight lines AB, CD, E, /"be proportionals, viz. as AB to CD, so E to F. The rectangle contained by AB, F, shall be equal to... | |
 | Euclides, James Hamblin SMITH - 1876 - 382 pages
...in D, and the circle in C, prove that the square on CE is equal to twice the AEBC. And Conversely, If the rectangle contained by the extremes be equal...means, the four straight lines are proportionals. Let rect. AB, GH"=rect. CD, EF. Then must AB be to CD as EF is to GH. For, the same construction being... | |
 | Richard Wormell - 1876 - 268 pages
...rectangle contained by the extremes is equal to the rectangle contained by the means. Сonversely, if the rectangle contained by the extremes be equal...means, the four straight lines are proportionals. Since rectangles are equiangular parallelograms, the proof in this case is identical with that of the... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...the rectangle contained by the means; and, conversely, if the rectangle contained by the extremes is equal to the rectangle contained by the means the four straight lines are proportional. COR. If three straight lines are proportional the rectangle contained by the extremes... | |
 | James Maurice Wilson - 1878 - 450 pages
...the rectangle contained by the means; and, conversely, if the rectangle contained by the extremes is equal to the rectangle contained by the means the four straight lines are proportional. BC D I Let A be to B as C to D ; then will the rectangle contained by A and D be equal... | |
 | University of Oxford - Greek language - 1879 - 414 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. II. Elements of Geometry. II. 1. Define secant and tangent of an angle, and prove that (1) sin2 A =... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...Theorem.—If four straight lines be proportional, the redangle of the extremes is equal to the rectangle of the means ; and if the rectangle contained by the...contained by the means, the four straight lines are proportional. Let A, B, C, D be four straight lines, so that A : B :: C: D; then the rectangle contained... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 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, B,... | |
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If four straight 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 extremes be equal to the rectangle contained by the means, the four straight lines... 
