| William Pease - 1846
...another, AC will be the homologous side of a similar polygon, equal to the sum of the given polygons. For **"universally, similar rectilineal figures are to one...in the duplicate ratio of their homologous sides."** Duplicate ratio is the ratio of the square of one quantity to the square of another. EXAMPLES. 1. Make... | |
| Dennis M'Curdy - 1846 - 138 sider
...(b) p. 32, 1 ; (c) p. 4, 6 ; ( d) p. 22, 5 ; (c) def. 1, 6 and def. 35, 1. 19 Th. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** Given the similar triangles ABC, DEF; having the angles at B, E, equal, and AB to BC as DE to EF: then... | |
| Euclides - 1846
...And, in like manner, it may be proved, that similar figures of any number of sides more than three **are to one another in the duplicate ratio of their homologous sides** ; and it has already been proved (9. 19) in the case of triangles. Wherefore, universally, Similar... | |
| Euclides - 1846
...AEDCB) may be divided into similar triangles, equal in number, and homologous to all. And the polygons **are to one another in the duplicate ratio of their homologous sides.** PART 1. — Because in the triangles FGI and AED, the angles G and E are G ( equal, and the sides about... | |
| Joseph Denison - 1846
...similar, and consequently the approximating sides homologous, and (6 Euclid 19) because similar triangles **are to one another in the duplicate ratio of their homologous sides;** the evanescent triangles are in the duplicate ratio of the homologous sides; and this seems the proper... | |
| Samuel Hunter Christie - 1847
...of the ratios of their bases and altitudes : the bases being similar rectilineal figures (Def. 13) **are to one another in the duplicate ratio of their homologous sides** (VI. 20); and the solids being similar, their altitudes are in the simple ratio of the homologous sides:... | |
| Anthony Nesbit - 1847 - 426 sider
...Quantity of Land, by a Line parallel to any one of its Sides. RULE. — The areas of similar triangles **are to one another in the duplicate ratio of their homologous sides** : hence, as the area of the triangle ABC is to the square of the side AC, or BC, so is the area of... | |
| THOMAS GASKIN, M.A., - 1847
...you recollect. How did Legendre escape the difficulty by an analytical process. 2. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** 3. If a straight line be at right angles to a plane, every plane which passes through it is at right... | |
| Euclides - 1848
...similar, and similarly situated, to a given rectilineal figure. PROP. XIX. THEOREM. Similar triangles **are to one another in the duplicate ratio of their homologous sides. COR.** From this it is manifest, that if three straight lines be proportionals, as the first is to the third,... | |
| J. Goodall, W. Hammond - 1848
...angle. (The first case only of this proposition need be demonstrated.) Section 2. 1. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** 2. If one angle of a triangle be equal to the sum of the other two, the greatest side is double of... | |
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