| 1851 - 628 Seiten
...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 - 1853 - 176 Seiten
...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 - 1853 - 400 Seiten
...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 - 1854 - 522 Seiten
...= 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 - 1855 - 334 Seiten
...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... | |
| 1855 - 864 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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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