 | Patrick Weston Joyce - Civil service - 1871 - 170 pages
...twice the rectangle contained by the parts. 2. Deseribe a regular pentagon about a given cirele. 3. Similar triangles are to one another in the duplicate ratio of their homologous sides. 4. If perpendiculars Aa, B&, Cc, be drawn from the angular points of a triangle ALC upon the opposite... | |
 | Henry William Watson - Geometry - 1871 - 320 pages
...— Corresponding angular points in the two polygons are also homologous points. Corollary 2. — Two similar polygons may be divided into the same number of similar triangles, the vertices of the two sets of triangles being homologous points. DEFINITION. 74. — When two straight... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...more sides may be described, on a given line, similar to a given fig. QEF PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar AS, having L s at A, B, C= s.sa.tD,E,F respectively, so that BC and EF are... | |
 | Euclid - Geometry - 1872 - 284 pages
...AEDCB) may be divided inl» similar triangles, equal in number, and homologous to all. Ana 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 ' equal, and the sides about... | |
 | Manchester univ - 1872 - 380 pages
...stand. cal angle and the segments into which the line bisecting it divides the base. 4. Similar polygons are to one another in the duplicate ratio of their homologous sides. 5. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the... | |
 | 1874 - 682 pages
...Explain the term duplicate ratio, and illustrate its meaning as you would to a class. (b.) Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 2. Describe a circle which will pass through a given point, and touch a given circle in a given point.... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...deducing the truth of I. 37, since VI. 6 does not depend on I. 37. PKOP. XIII.— THEOREM. (Euc. VI. 19.) Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC and OPQ be similar triangles, having the angle B equal to the angle P, and AB to BC as OP to... | |
 | Thomas Baker (C.E.) - 1874 - 208 pages
...then, the triangle ABC is to the triangle AED as the square of A. B is to the 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 their homologous,... | |
 | Euclides - 1874 - 342 pages
...described upon a given straight line similar to one given, and so on. QEF PROPOSITION 19.— Theorem. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF lie similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...proportionals are said to be homologous to one another; so also are the consequents. PROPOSITION (q). Similar triangles are to one another in the duplicate ratio of their homologous sides. Let the similar triangles ABC, AHK be placed so as to have the sides AB, AC along the homologous sides... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
