 | 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... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...more sides may be described, on a given line, similar to a given fig. QEF PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar AS, having L s at A, B, C= s.sa.tD,E,F respectively, so that BC and EF are... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
