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Similar triangles are to one another in the duplicate ratio of their homologous sides.
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Seite 167
von Robert Simson - 1762 - 466 Seiten
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1826 - 326 Seiten
...triangles are to one another in the duplieate 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, ag DE to EF, so that the side BC is homologous to EF (def. 13. 5.): the triangle ABC hag to the triangle...
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## Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 236 Seiten
...similar and similarly situated to the given rectilineal figure CE. QEF PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. EF, and let BC be the side homologous to EF ; then the triangle ABC has a duplicate ratio to...
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## Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 Seiten
...ABG equal to that at CDF; hence the remaining angle. AG в is QEF PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. EF, and let вс be the side homologous to EF ; then the triangle ABC has a duplicate ratio...
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## Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 266 Seiten
...triangles, &c. QED Cor. The same may be demonstrated of parallelograms. PROP. XI. THEOREM. Simi'ar 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 : BC...
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## The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 546 Seiten
...Which was to be done. • 12 Def. •11.6. * 16. 5. t Co1utr. • 11. 5. 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...
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## Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 210 Seiten
...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 :...
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## Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 584 Seiten
...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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## Calendar

University of Cambridge - 1830 - 554 Seiten
...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...
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## New Series of The Mathematical Repository, Band 5

Thomas Leybourn - 1830 - 630 Seiten
...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...
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## Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

1835 - 684 Seiten
...the homologous sides of the figures, are to one another, each to each, 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 DKF is divided, are to the similar triangles...
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