 | Education - 1851 - 626 pages
...Paper. 1. Find a mean proportional between two given straight lines. In this case shew how similar triangles are to one another in the duplicate ratio of their homologous sides. 2. The parallelograms about the diameter of any parallelogram are similar to the whole and to... | |
 | Euclides - Geometry - 1853 - 176 pages
...triangles are to one another in tlie duplicate ratio oftheir homologous sides. LET abc, def be similar triangles, having the angle b equal to the angle e, and let ab he to b c. as de to ef, so that the side bc, is homologous to ef (v. def. 1 2) : the triangle abc has... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...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... | |
 | Thomas Lund - Geometry - 1854 - 520 pages
...= 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... | |
 | John Playfair - Geometry - 1855 - 334 pages
...Similar triangles are to one another m the duplicate ratio of the homologous Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AD be to BC, as DE to EF, so that the side BC is homologous to EF (def. 13. 5.) : the triangle ABC... | |
 | Education - 1855 - 864 pages
...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.... | |
 | Robert Potts - 1855 - 1050 pages
...given point, either without or in the circumference, which shall touch a given circle. 16. Similar triangles are to one another in the duplicate ratio of their homologous sides. 18. ABC is a triangle having each of the angles at JB, C double of that at A, CD is drawn bisecting... | |
 | Cambridge univ, exam. papers - 1856 - 252 pages
...the sides of the original triangle is equal to twice the sum of the three perpendiculars. 5. Similar triangles are to one another in the duplicate ratio of their homologous sides. Any two straight lines, BB', CC', drawn parallel to the base DD' of a triangle ADD', cut AD... | |
 | 1857 - 408 pages
...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... | |
 | Middle-class education - 1857 - 70 pages
...algebraical expression for the mean proportional between two given quantities ? 19. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 20. Show that, if an equilateral triangle be inscribed in a circle, the square of its side is... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
