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" SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Página 165
por Euclides - 1814
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 324 páginas
...: 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 - 1829 - 186 páginas
...CoB. 1. In like manner it may be proved that similar figures of four sides, or of any number of sides, are to one another in the duplicate ratio of their homologous sides; and it has been proved in triangles. Therefore, universally, similar rectilineal figures are to one...
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University of Cambridge - 1830
...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 - 1830 - 272 páginas
...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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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 333 páginas
...proportionals, they are similar to one another: and in the same manner a rectilineal figure of six, or more, sides may be described upon a given straight line similar to one given, and so an. Which was to be dona. PROP. XIX. THEOR, Similar triangles are to one another in the duplicate ratio...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1833 - 333 páginas
...proportionals, they are similar to one another ; and in the same manner a rectilineal figure of six, or more, sides may be described upon a given straight line...triangles are to one another in the duplicate ratio of the homologous sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1835 - 316 páginas
...proportionals, they are similar to one another ; and in the same manner a recD tilineal figure of six, or more, sides may be described upon a given straight line similar to one given, and so on. PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of the homologous sides....
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...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 - 513 páginas
...the same has already been proved of triangles. Therefore, universally, «'milar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COR. 2. And if to AB, FG, two of the homologous sides, h lO.def. 5. a third proportional M be taken,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1836 - 311 páginas
...proportionals, they are similar to one another ~. and in the same manner a rectilineal figure of six, or more, sides may be described upon a given straight line...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 A DEtoEF,sothat...
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