 | 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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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
