| E. J. Brooksmith - Mathematics - 1889
...will touch the circle circumscribing ABC in the point A. 8. Describe a circle about a given square. 9. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 10. In a right-angled triangle if a line be drawn from the right angle perpendicular to the base it... | |
| William Ernest Johnson - Plane trigonometry - 1889 - 504 pages
...product of two lengths. This is equivalent to Euclid's statement that " Similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides."** 24. The area of any rectilineal figure may be found by dividing it into triangles : and applying the... | |
| Eldred John Brooksmith, Robert Moir Milne - 1890 - 132 pages
...one another, and shall have those angles equal about which the sides are proportionals. 6. Prove that **similar triangles are to one another in the duplicate ratio of their homologous sides.** If ABC be an obtuse-angled triangle, having the obtuse angle BAC; and if AD, AE, be drawn to meet BC... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...AB : BC 1 and cd : da ::CD : DA'./ [VI. 4Again v LS bac, cad= L s BAC, CAD; PROPOSITION 19. THEOREM. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Let As ABC, DEF have LS A, B, C equal to LS D, E, F respectively, so that BC is homologous to EF; then... | |
| Thomas Baker - Railroads - 1891 - 231 pages
...then, the tnanr/ff ABC is to the triangle AED a* the square of AB is to tlte square of AE : that is, **similar triangles are to one another in the duplicate ratio of their homologous sides.** (Euc. VI. 19.) THEOREM VIII. All similar figures are to one another as the squares of then homologous,... | |
| Seth Thayer Stewart - Geometry - 1891 - 406 pages
...vi., PROP, n.) Conclusion : A and B, being any regular polygons, etc. PROPOSITION XII. 4O3. Theorem : **Similar polygons may be divided into the same number of similar triangles** similarly placed. Statement : Similar polygons, ABD and GHJ, may be divided into the same number of... | |
| Euclid - Geometry - 1892 - 518 pages
...DEF; Proved. .'. the A ABC : the A DEF in the duplicate ratio of BC : EF. QED PROPOSITION 20. THEOREM. **Similar polygons may be divided into the same number of similar triangles, having the same ratio** each to each that the polygons have; and the polygons are to one another in the duplicate ratio of... | |
| Queensland. Department of Public Instruction - Education - 1892
...LM, and PQ are drawn through O parallel to BC, CA, and AB, show that HK BC LM CA ' AB PQ _ = 2. 7. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 8. Given the base of a triangle, the perpendicular, and the sum of the sides, construct it. !). If... | |
| 1894
...parallel to AD. 4. Similar triangles are to one another in the duplicate ratio of their homologous sides. **Similar triangles are to one another in the duplicate ratio of their** corresponding altitudes. 6. Shew how to solve two equations which contain two unknown quantities when... | |
| Frederick Coate Wade - Church and state - 1895 - 122 pages
...produced, it will cut them proportionally ; and conversely. Is this converse universally true ? 10. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Bisect a triangle by a line drawn parallel to one of its sides. ALGEBRA. 1. Investigate a rule for... | |
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