 | Euclides - 1855 - 230 sider
...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... | |
 | Euclides - 1855 - 270 sider
...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... | |
 | Robert Potts - 1855 - 1050 sider
...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... | |
 | 1855 - 864 sider
...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... | |
 | Cambridge univ, exam. papers - 1856 - 200 sider
...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... | |
 | 1857 - 408 sider
...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... | |
 | Henry Latham - 1857 - 390 sider
...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... | |
 | Middle-class education - 1857 - 70 sider
...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... | |
 | sir Thomas Dyke Acland (11th bart.) - 1858 - 270 sider
...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... | |
 | Sandhurst roy. military coll - 1859 - 672 sider
...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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... rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
