 | Royal Military Academy, Woolwich - 1853 - 400 pàgines
...described upon a given straight line similar to one given, and so on. Which was to be done. PRG-POSITION XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
 | Euclides - 1853 - 176 pàgines
...sides, and it has already been proved in triangles. Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COR. 2. And if to ab, fg, two of .the homologous sides, a third proportional m be taken, ab has (v.... | |
 | Thomas Lund - 1854 - 520 pàgines
...which tA = ta, d> b * Sometimes called 'homologous sides'. •f Euclid's enunciation of this is : ' Similar triangles are to one another in the duplicate ratio of their homologous aides'. iB= tb, fC- ic; then AB, ab being ant/ two corresponding, or homologous, sides, the triangle... | |
 | 1855 - 864 pàgines
...centre of gravity of the hemisphere from its vertex being = $ rad. FOURTH CLASS. EUCLID AND ALGEBRA. 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. 2. If two parallel planes be cut by another plane their common sections with it are parallel. 3. If... | |
 | Robert Potts - 1855 - 1050 pàgines
...and inscribed circles of a triangle, the square of the distance between the centres = J? - 2Br. 2. Similar triangles are to one another in the duplicate ratio of their homologous side*. 4. Divide -01 by -0002 and -00001 by -03; find also a irth proportional to -999, 33-3 and -03.'... | |
 | Euclides - 1855 - 270 pàgines
...and this has been proved of triangles (VI. 19). Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COROLLARY 2, — If to AB and FG, two of the homologous sides of the polygon, a third proportional... | |
 | Euclides - 1855 - 230 pàgines
...In like manner it may be proved, that similar four-sided figures, or figures of any number of sides, are to one another in the duplicate ratio of their homologous sides, as has already been proved in the case of triangles. Therefore, universally, similar rectilineal figures... | |
 | Cambridge univ, exam. papers - 1856 - 200 pàgines
...are proportionals. 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 - 408 pàgines
...the base, the triangles on each^side of it are similar to the whole triangle and to one another. 2. Similar triangles are to one another in the duplicate ratio of their homologous sides. 3. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both... | |
 | Henry Latham - 1857 - 390 pàgines
...triangle. 7. Give 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... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
