| 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... | |
| 1857
...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
...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 - 59 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... | |
| 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... | |
| Thomas Lund - 1859 - 362 sider
...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 - 1859 - 450 sider
...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 - 1869 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... | |
| Euclides - 1860
...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
...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... | |
| |