| Sir Norman Lockyer - Electronic journals - 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 - Civil service - 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... | |
| 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... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...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 - Geometry - 1872 - 261 pages
...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... | |
| Euclides - 1874
...proportionals. wherefore 10. ABLHG is similar to CDKEF. In the same manner, a rectilineal figure of six **sides may be described upon a given straight line similar to one given, and so on.** QEF PROPOSITION 19.— Theorem. Similar triangles are to one another in the duplicate ratio of their... | |
| Braithwaite Arnett - 1874
...proportionally, this line shall be parallel to the remaining side of the triangle. 10. Define duplicate ratio. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 11. Define a plane. State when a straight line is perpendicular to a plane, and when two planes are... | |
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