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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... "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Pągina 133
per John Playfair - 1846 - 317 pągines
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

Eldred John Brooksmith - 1901
...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...
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A Text-book of Euclid's Elements for the Use of Schools, Llibre 1

Euclid - 1904 - 456 pągines
...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...
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Books 3-9

Euclid - 1908
...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,...
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A Source Book in Medieval Science

Edward Grant - 1974 - 864 pągines
...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...
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The Changing Shape of Geometry: Celebrating a Century of Geometry and ...

Mathematical Association, Mathematical Association of America - 2003 - 541 pągines
...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...
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Pass school, group A (-D).

Oxford univ, exam. papers, 2nd publ. exam
...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...
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Proceedings of the Edinburgh Mathematical Society, Volums 18-20

Edinburgh Mathematical Society - 1900
...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:...
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The Thirteen Books of Euclid's Elements

Euclid
...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,...
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Euclid in China: The Genesis of the First Chinese Translation of Euclid's ...

Peter M. Engelfriet - 1998 - 488 pągines
...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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The Bombay University Calendar

University of Bombay - 1902
...lines be proportionals, the rectangle contained by the 13 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. Prove that the straight line bisecting...
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