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" ... rectilineal figures are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid - Página 131
por Euclid - 1838 - 416 páginas
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855
...another in the duplicate ratio of their homologous sides, as has already been proved in the case of triangles. Therefore, universally, similar rectilineal...in the duplicate ratio of their homologous sides. COROLLARY 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...in the duplicate ratio of their homologous sides ; and this has been proved of triangles (VI. 19). Therefore, universally, similar rectilineal figures...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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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855
...point, either without or in the circumference, which shall touch a given circle. 16. Similar triangles are to one another in the duplicate ratio of their homologous sides. 18. ABC is a triangle having each of the angles at JB, C double of that at A, CD is drawn bisecting...
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General Report on Public Instruction in the Bengal Presidency

1855
...A, if CD be drawn bisecting the angle C, show that AB : AC :: BC — AC : AD. 8. Similar triangles are to one another in the duplicate ratio of their homologous sides. 4. Planes to which the same straight line is perpendicular, are parallel to one another. 5. If two...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...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 - 408 páginas
...heavenly body its true one. SECT. V. — 1. Show how to prove experimentally to children that similar figures are to one another in the duplicate ratio of their homologous sides; and express the proposition itse.f in fit terms for such a purpose. Illustrate the proposition, when...
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Considerations on the Suggestions of the University Commissioners with ...

Henry Latham - 1857 - 59 páginas
...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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Middle-class education. 2

Middle-class education - 1857
...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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Some account of the origin and objects of the new Oxford examinations for ...

sir Thomas Dyke Acland (11th bart.) - 1858
...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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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 1869 páginas
...root of 321489. Voluntary Portion. 1. To describe a circle about a given square. 2. Similar triangles are to one another in the duplicate ratio of their homologous sides. 3. One of the two digits of a number is double the other, and if 27 be added to the number the digits...
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