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Similar triangles are to one another in the duplicate ratio of their homologous sides.
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Seite 167
von Robert Simson - 1762 - 466 Seiten
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## A complete treatise on practical land-surveying

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...
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## How to Prepare for Civil Service Competition, Under the New Regulations

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...
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## The Edinburgh university calendar

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...
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## Elements of geometry, containing books i. to vi.and portions of books xi ...

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...
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## The elements of geometry, in eight books; or, First step in applied logic

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...
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## Euclidian Geometry

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...
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## Recent military, naval, and civil service examination papers in mathematics ...

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...
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## Annual Report of the Commissioners ..., Band 40

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...
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## The Elements of Euclid, containing the first six books, with a selection of ...

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...
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## Rudimentary treatise on mensuration and measuring

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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