| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...Of similar triangles, having the same ratio to one another that the polygons have; and the polygons **are to one another in the duplicate ratio of their homologous sides.** Let ABCDE, FGHKL be similar polygons, and let AB be the side homologous to the side FG : the polygons... | |
| How - 1868 - 296 pages
...English, Latin, and 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... | |
| Robert Potts - 1868 - 434 pages
...described upon a given straight line similar to one given, and so on. QEF PROPOSITION XIX. THEOREM. **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... | |
| Schools inquiry commission - Education - 1868 - 532 pages
...inscribed in a circle is 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... | |
| E. M. Reynolds - Geometry - 1868 - 172 pages
...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... | |
| Sir Norman Lockyer - Electronic journals - 1904 - 688 pages
...furnished by the liberty 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... | |
| John A. Smith - 1869 - 368 pages
...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 — ] .... | |
| Anthony Nesbit - 1870 - 578 pages
...; then the triangle ABC is to the A triangle ADE as the square of BC to the square of DE. That is, **similar triangles are to one another in the duplicate ratio of their homologous sides** (Euc. vi. 19 ; Simp, c^ iv. 24; Em. ii. 18). THEOREM XIV. In any triangle ABC, double the square of... | |
| Edinburgh univ - 1871 - 392 pages
...the part of it 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 - Civil service - 1871 - 170 pages
...twice the 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... | |
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