| E. M. Reynolds - 1868 - 172 páginas
...triangle in the second. The proof we leave as an exercise for the learner. The proposition that " Similar figures are to one another in the duplicate ratio of their homologous sides " is true of curvilinear figures as well as of rectilinear. Thus two circles are to one another as... | |
| How - 1868 - 296 páginas
...Greek tongues, and understood (what few lads of my age then understood) , that ' similar triangles are to one another in the duplicate ratio of their homologous sides." In a word, then, I was something of a scholar, and I may well be forgiven if I were a little proud... | |
| Schools inquiry commission - 1868 - 532 páginas
...equal to the interior and opposite. 7. Describe a circle about a given square. 8. Similar triangles are to one another in the duplicate ratio of their homologous sides. XIX. (Two hours.) Maximum. 1. Translate into French : — Two worthy peasants went together to find... | |
| John A. Smith - 1869 - 368 páginas
...Perpendiculars. 10 22384 to be deducted. Donble areas. 1500 1500 19520 21020 map. As the areas of similar figures are to one another in the duplicate ratio of their homologous sides, we have A : a; IS J : s*. From this proportion we obtain— , jlx«* jo /-4V *= , and S=s I — ] .... | |
| Sir Norman Lockyer - 1904 - 688 páginas
...which each of these excellent works takes with Euclid's Prop, ig, Bk. vi.- — " similar triangles are to one another in the duplicate ratio of their homologous sides " — mysterious but high-sounding- to countless generations of schoolboys. Here it is, in identical... | |
| Anthony Nesbit - 1870 - 578 páginas
...quantity of land by a line parallel to any one of its sides. RULE. — The areas of similar triangles are to one another in the duplicate ratio of their homologous sides ; hence, as the area of the triangle ABC is to the square of the side AC, or BC, so is the area of... | |
| Edinburgh univ - 1871 - 392 páginas
...without the circle, is equal to the square of the line which touches it. 6. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. Given (b) the base of a triangle, find an expression for the base of a similar triangle whose area... | |
| Patrick Weston Joyce - 1871 - 170 páginas
...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... | |
| Euclid - 1872 - 284 páginas
...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 páginas
...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... | |
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