| E. M. Reynolds - 1868 - 112 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
...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
...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
...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
...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
...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 - 172 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 - 261 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
...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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