 | Edinburgh Mathematical Society - Electronic journals - 1899 - 340 pages
...rectangle contained by the extremes is equal to the rectangle contained by the means. Conversely : If the rectangle contained by the extremes be equal...contained by the means, the four straight lines are proportional. (1) Let the four straight t lines AB, AC, AD, AE be proportional, so that AB : AC = AD... | |
 | Eldred John Brooksmith - Mathematics - 1901 - 368 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. x 12. The diameter BCA of the circle APQB whose centre is C, a produced through A to O, and from O... | |
 | Euclid - Euclid's Elements - 1904 - 488 pages
...to the rectangle contained by the means. Conversely, if the, rectangle contained by the extremes is equal to the rectangle contained by the means, the four straight lines are proportional. EG Let the st. lines AB, CD, EF, GH be proportional, so that AB : CD :: EF : GH. Then... | |
 | Euclid - Mathematics, Greek - 1908 - 456 pages
...lines be proportional, 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 -will be proportional. Let the three straight lines A,... | |
 | Edward Grant - History - 1974 - 890 pages
...lines be proportional, the rectangle contained by the extremes is equal to the rectangle contained by the means ; and if the rectangle contained by the...rectangle contained by the means, the four straight lines will be proportional" (Heath, II, 221). 38. See note 35. 39. See note 36. 40. See note 37. 41. See... | |
 | Chris Pritchard - Mathematics - 2003 - 572 pages
...lines be proportional, 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 will be proportional. Prop. 25: To construct one and the... | |
 | Oxford univ, exam. papers, 2nd publ. exam - 1884 - 594 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. 8. Inscribe an equilateral and equiangular hexagon in a given circle. 9. If four magnitudes of the... | |
 | Edinburgh Mathematical Society - Electronic journals - 1900 - 410 pages
...rectangle contained by the extremes is equal to the rectangle contained by the means. Conversely : If the rectangle contained by the extremes be equal...contained by the means, the four straight lines are proportional. (1) Let the four straight £ lines AB, AC, AD, AE be proportional, so that AB:AC = AD:AE:... | |
 | Euclid - 452 pages
...lines be proportional, 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 will be proportional. Let the three straight lines A,... | |
 | Peter M. Engelfriet - Mathematics - 1998 - 516 pages
...lines be proportional, 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 straight lines will be proportional. ± a ft # mmmm » ft if £ ft a ft m &... | |
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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... 
