 | 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...to the 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;... | |
 | 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...to the rectangle contained by the means, the four straight lines are proportionals. Let the four straight lines AB, CD, E, F be proportionals, viz.,... | |
 | 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...to the rectangle contained by the 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]... | |
 | 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...to the rectangle contained by the means, the four straight lines are proportionals. Let rect. AB, GH"=rect. CD, EF. Then must AB be to CD as EF 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...to the rectangle contained by the means, the four straight lines are proportionals. Let the four straight lines AB, CD, E, /"be proportionals, viz. as... | |
 | 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...to the rectangle contained by the means, the four straight lines are proportionals. Since rectangles are equiangular parallelograms, the proof in this... | |
 | University of Oxford - Greek language - 1879 - 414 pages
...antecedents is to its consequent, so shall all the antecedents be to all the consequents. 7. If four straight lines be proportionals, the rectangle contained by...to the rectangle contained by the means, the four straight lines are proportionals. 8. Inscribe an equilateral and equiangular hexagon in . a given circle.... | |
 | 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...to the rectangle 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... | |
 | 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... 
