 | Cambridge univ, exam. papers - 1856 - 200 pages
...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 pages
...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... | |
 | Middle-class education - 1857 - 70 pages
...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... | |
 | Henry Latham - 1857 - 390 pages
...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... | |
 | sir Thomas Dyke Acland (11th bart.) - 1858 - 270 pages
...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... | |
 | Thomas Lund - Geometry - 1859 - 390 pages
...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... | |
 | Anthony Nesbit - Measurement - 1859 - 494 pages
...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... | |
 | Sandhurst roy. military coll - 1859 - 672 pages
...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... | |
 | Euclides - 1860 - 288 pages
...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)... | |
 | Eucleides - 1860 - 396 pages
...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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Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
