| E. M. Reynolds - 1868 - 112 pagina’s
...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... | |
| Robert Potts - 1868 - 410 pagina’s
...has already been proved in triangles: (vi. 19.) therefore, universally, similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides.** AB has to Jf the duplicate ratio of that which AB has to FG: (v. def. 10.) but the four-sided figure... | |
| Sir Norman Lockyer - 1904
...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
...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
...; 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
...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 - 1871
...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 - 1872 - 349 pagina’s
...has been already proved for triangles, vi. 19. Therefore, universally, similar rectilinear figures **are to one another in the duplicate ratio of their homologous sides.** COR. II. If MN be a third proportional to AB and FG, AB has to MN the duplicate ratio of AB to FG,... | |
| Euclid - 1872 - 261 pagina’s
...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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