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" SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. "
The school edition. Euclid's Elements of geometry, the first six books, by R ... - Pagina 271
door Euclides - 1864
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 pagina’s
...on. PROP. XIX. THEOR. Similar triangles are to one another m the duplicate ratio of the homologous Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AD be to BC, as DE to EF, so that the side BC is homologous to EF (def. 13. 5.) : the triangle ABC...
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General Report on Public Instruction in the Bengal Presidency

1855
...centre of gravity of the hemisphere from its vertex being = $ rad. FOURTH CLASS. EUCLID AND ALGEBRA. 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. 2. If two parallel planes be cut by another plane their common sections with it are parallel. 3. If...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855
...and inscribed circles of a triangle, the square of the distance between the centres = J? - 2Br. 2. Similar triangles are to one another in the duplicate ratio of their homologous side*. 4. Divide -01 by -0002 and -00001 by -03; find also a irth proportional to -999, 33-3 and -03.'...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...and this has been proved of triangles (VI. 19). Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COROLLARY 2, — If to AB and FG, two of the homologous sides of the polygon, a third proportional...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855
...In like manner it may be proved, that similar four-sided figures, or figures of any number of sides, are to one another in the duplicate ratio of their homologous sides, as has already been proved in the case of triangles. Therefore, universally, similar rectilineal figures...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...are proportionals. Shew how this proposition may be proved by superposition as in Prop. 4, B. 1. 4. Similar triangles are to one another in the duplicate ratio of their homologous sides. What can you infer from this as to the ratio of squares to each other ? 5. Describe a rectilineal figure...
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National Society's Monthly Paper

1857
...the base, the triangles on each^side of it are similar to the whole triangle and to one another. 2. Similar triangles are to one another in the duplicate ratio of their homologous sides. 3. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both...
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Middle-class education. 2

Middle-class education - 1857
...the algebraical expression for the mean proportional between two given quantities ? 19. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 20. Show that, if an equilateral triangle be inscribed in a circle, the square of its side is equal...
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Considerations on the Suggestions of the University Commissioners with ...

Henry Latham - 1857 - 59 pagina’s
...triangle. 7. Give Dcf. 5, Book V. of Euclid, and shew whether the areas 3, 4, 7, 8 are proportionals. Similar triangles are to one another in the duplicate ratio of their homologous sides. Shew how to inscribe a rectangle DEFG in a triangle ABC, so that the angles D, E may be in the straight...
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Some account of the origin and objects of the new Oxford examinations for ...

sir Thomas Dyke Acland (11th bart.) - 1858
...the algebraical expression for the mean proportional between two given quantities ? 19. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 20. Show that, if an equilateral triangle be inscribed in a circle, the square of its side is equal...
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