| Anthony Nesbit - 1870 - 578 Seiten
...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 - 1871 - 170 Seiten
...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 Seiten
...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 - 1872 - 376 Seiten
...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 Seiten
...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 - 1874 - 400 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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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