| 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
...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 sider
...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... | |
| Euclid - 1872 - 261 sider
...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... | |
| Euclides - 1874
...duplicate ratio of their homologous sides ; and it has already been proved in triangles (VI. 19) ; **therefore, universally, similar rectilineal figures...in the duplicate ratio of their homologous sides.** COT. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken (VI. 11), 1.... | |
| George E. Webster - 1874
...equal, then the greatest area is possessed by the figure which has the largest number of sides. (7) **Similar rectilineal figures are to one another in the duplicate* ratio of their homologous^ sides.** (8) If three straight lines oe proportionals, as the first quantity is to the third quantity, so is... | |
| 1874
...duplicate ratio, and illustrate its meaning as you would to a class. (b.) Prove that similar triangles **are to one another in the duplicate ratio of their homologous sides.** 2. Describe a circle which will pass through a given point, and touch a given circle in a given point.... | |
| Francis Cuthbertson - 1874 - 349 sider
...ratio of AB to AH. Hence, proceeding as in Proposition VIII., it may be proved that Similar polygons **are to one another in the duplicate ratio of their homologous sides.** PROPOSITION (r). If four straight lines are proportional, the duplicate ratio of the first two is the... | |
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