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" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
The Solutions of the Geometrical Problems: Consisting Chiefly of Examples in ... - Page 117
by Thomas Gaskin - 1847 - 263 pages
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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1852 - 348 pages
...triangle, right angled at A, if CD be drawn bisecting the angle C, show that AB : AC :: BC — AC : AD. .3. Similar triangles are to one another in the duplicate ratio of their homologous sides. 4. Planes to which the same straight line is perpendicular, are parallel to one another. 5. If two...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...given straight line similar to one given, and so on. Which was to be done. PRG-POSITION XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 176 pages
...sides, and it has already been proved in triangles. Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COR. 2. And if to ab, fg, two of .the homologous sides, a third proportional m be taken, ab has (v....
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Elements of geometry and mensuration

Thomas Lund - Geometry - 1854 - 520 pages
...which tA = ta, d> b * Sometimes called 'homologous sides'. •f Euclid's enunciation of this is : ' Similar triangles are to one another in the duplicate ratio of their homologous aides'. iB= tb, fC- ic; then AB, ab being ant/ two corresponding, or homologous, sides, the triangle...
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General Report on Public Instruction in the Bengal Presidency

Education - 1855 - 864 pages
...triangle, right angled at A, if CD be drawn bisecting the angle C, show that AB : AC :: BC — AC : AD. 8. Similar triangles are to one another in the duplicate ratio of their homologous sides. 4. Planes to which the same straight line is perpendicular, are parallel to one another. 5. If two...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 pages
...and inscribed circles of a triangle, the square of the distance between the centres = J? - 2Br. 2. Similar triangles are to one another in the duplicate ratio of their homologous side*. 4. Divide -01 by -0002 and -00001 by -03; find also a irth proportional to -999, 33-3 and -03.'...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 270 pages
...and this has been proved of triangles (VI. 19). Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COROLLARY 2, — If to AB and FG, two of the homologous sides of the polygon, a third proportional...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855 - 230 pages
...In like manner it may be proved, that similar four-sided figures, or figures of any number of sides, are to one another in the duplicate ratio of their homologous sides, as has already been proved in the case of triangles. Therefore, universally, similar rectilineal figures...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 200 pages
...are proportionals. Shew how this proposition may be proved by superposition as in Prop. 4, B. 1. 4. Similar triangles are to one another in the duplicate ratio of their homologous sides. What can you infer from this as to the ratio of squares to each other ? 5. Describe a rectilineal figure...
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National Society's Monthly Paper

1857 - 408 pages
...the base, the triangles on each^side of it are similar to the whole triangle and to one another. 2. Similar triangles are to one another in the duplicate ratio of their homologous sides. 3. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both...
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