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" Therefore, universally, similar rectilineal figures 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 ... - Página 180
por Robert Simson - 1806 - 518 páginas
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 200 páginas
...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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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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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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Some account of the origin and objects of the new Oxford examinations for ...

sir Thomas Dyke Acland (11th bart.) - 1858 - 272 páginas
...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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Elements of Geometry and Mensuration: With Easy Exercises, Designed for ...

Thomas Lund - 1859 - 390 páginas
...tt/ DX * Sometimes called 'homologous sides'. 'f- Euclid's enunciation of this is: 'Similar triangles are to one another in the duplicate ratio of their homologous sides'. X zB=z&, zC=zc; then AB, ab being any two corresponding, or homologous, sides, the triangle ABC shall...
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A Treatise on Practical Mensuration

Anthony Nesbit - 1859 - 494 páginas
...triangle ABC is to the triangle ADE, as the square of BC to the square of DE. That is, similar triangles are to one another in the duplicate , ratio of their homologous sides. (Euc. B VI. 19. Simp. IV. 24. Em. II. 18.) THEOREM XIV. In any triangle the double of the square of...
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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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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 páginas
...AB has to the homologous side FG. COR. 1. — In like manner it may be proved that similar foursided figures, or of any number of sides, are one to another...duplicate ratio of their homologous sides. COR. 2. — If to AB, FG, two of the homologous sides, a third proportional M be taken, AB has (V. Def. 18)...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 páginas
...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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