 | Anthony Nesbit - 1870 - 578 pages
...proposed 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... | |
 | Patrick Weston Joyce - Civil service - 1871 - 170 pages
...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... | |
 | Edinburgh univ - 1871 - 392 pages
...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... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...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... | |
 | L J V. Gerard - 1874 - 428 pages
...have an equal angle formed by proportional sides, are similar to each other. Let ABC and DEF be two triangles having the angle B equal to the angle E, and let AB be to DE as BC is to E F. If AB be equal to DE, the side BC is equal to EF [Gen. Def. 28] : therefore the... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...proportionals are said to be homologous to one another; so also are the consequents. PROPOSITION (q). Similar triangles are to one another in the duplicate ratio of their homologous sides. Let the similar triangles ABC, AHK be placed so as to have the sides AB, AC along the homologous... | |
 | Braithwaite Arnett - 1874 - 130 pages
...base shall have the same ratio which the other sides of the triangle have to one another. 7. Similar triangles are to one another in the duplicate ratio of their homologous sides. 8. A and B are fixed points, and P is a moveable point such that PA always bears a fixed ratio... | |
 | 1874 - 682 pages
...the term 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... | |
 | Euclides - 1874 - 342 pages
...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 homologous sides. Let ABC, DEF lie similar triangles, having the angle B equal to the angle E, and let AB be to... | |
 | Thomas Baker (C.E.) - 1874 - 208 pages
...triangle ABC is to the triangle AED as the square of A. B is to the square of AE : that is, similar triangles are to one another in the duplicate ratio of their homologous sides. (Euc. VI. 19.) THEOREM VIII. All similar figures are to one another as the squares of their... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
