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" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
The Solutions of the Geometrical Problems: Consisting Chiefly of Examples in ... - Page 117
by Thomas Gaskin - 1847 - 263 pages
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...: and it has already been proved in triangles : therefore, universally, similar rectilinear figures are to one another in the duplicate ratio of their homologous sides. (629) COR. 2. — And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...other as the rectangles contained by the sides about the equal angles. .• PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be two similar triangles, having the angles at A and D equal; and let AC : AB : : DF :...
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New Series of The Mathematical Repository, Volume 5

Thomas Leybourn - Mathematics - 1830 - 630 pages
...square of the distance. SATURDAY MORNING, 9 o'clock to 1 1 . First, Second, Third, and Fourth Classes. 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. 2. If a straight line be at right angles to a plane, every plane passing through that straight line is...
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Calendar

University of Cambridge - 1830 - 554 pages
...differing in origin and intensity. SATURDAY MORNING .... 9 to 11. First, Second, Third and Fourth Classes. 1. SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. 2. If two straight lines meeting one another, be parallel to two straight lines which meet one another,...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...with the homologous sides of the figures, are to one another, each to eich, in the same ratio. But similar triangles are to one another in the duplicate ratio of their homologous sides. Therefore the triangles into which the figure А В С DEF is divided, are to the similar triangles...
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New Series of The Mathematical Repository, Volume 6

Thomas Leybourn - Mathematics - 1835 - 682 pages
...in origin and intensity. SATURDAY MORNING 9 o'clock to 11. First, Second, Third, and Fourth Classes. 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. s. It two straight lines meeting one another, be parallel lu two straight lines which meet one another,...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...reciprocally proportional; ЗУ. being citc'd instead of 35. Therefore, &c. • PROP. 42. (Eue. vi. 10.) Similar triangles are to one another in the duplicate ratio of their homologous sides. LetABC.DEF be similar triangles, and let the sides В С, EF be homologous ; the triangle ABC shall...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...upon a given straight line similar to one given, and so on. Which was to be done. PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as...
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The Element of Geometry

John Playfair - Geometry - 1836 - 148 pages
...upon a given straight line similar to one given, and so on. Which was to be done. PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles having the angle B equal to the angle E, and let AB be to BC, as...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...by the extremes be equal to the square of the mean, the three straight lines are proportionals. XIX. Similar triangles are to one another in the duplicate ratio of their homologous sides. Сок. From this it is manifest, that if three straight lines be proportionals, as the first is to...
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