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" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ... - Page 6
by John Mason Good - 1813
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...be described upon a given straight line similar to one given, and so on. QEF PROP. XIX.— THEOBEM. Similar triangles are to one another in the duplicate ratio of their homologous sides. (References— Prop. v. 11, 16, def. 12; vi. 1, 11, 15.) Let ABC, DEF be similar triangles, having...
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Calendar of the McGill University, Montreal

McGill University - 1865
...proportion, and show that it agrees with Euclid's. 9. Find a third proportional to two given lines. 10. Similar triangles are to one another in the duplicate ratio of their homologous sides. 11. If 3 men can mow 7 acres of grass in 5 days of 9 hours each, in how many days of 8 hours each will...
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Rudimentary treatise on mensuration and measuring

Thomas Baker (C.E.) - 1865
...greatest angle : theorem, 17 ; any two angles being Rven, the, becomes known : theorem, ' ; similar, are to one another in the duplicate ratio of their homologous sides: theorem, 17. Triangular prism, definition of, 52. Triangular fields, method of surveying with chain...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - Geometry - 1855 - 317 pages
...similarly described triangle upon the second. BC EF : EF AB BC : DE AB DE : BC BC EF : EF AB DE : EF PROP. XX. THEOR. Similar polygons may be divided into the same number of similar triangles, ing the same ratio to one another that the polygons have ; and the polygon* have to one another the...
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A Collection of Elementary Test Questions in Pure and Mixed Mathematics with ...

James Robert Christie - Mathematics - 1866 - 404 pages
...together with the segmenta of the former will be equal to the square of the radius of the circle. i 3. Similar triangles are to one another in the duplicate ratio of their homologous sides. 4. If two straight lines be at right angles to the same plane, they shall be parallel to one another....
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...Of similar triangles, having the same ratio to one another that the polygons have; and the polygons are to one another in the duplicate ratio of their homologous sides. Let ABCDE, FGHKL be similar polygons, and let AB be the side homologous to the side FG : the polygons...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 pages
...described upon a given straight line similar to one given, and so on. QEF PROPOSITION XIX. THEOREM. 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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Report of the commissioners, Volume 6

Schools inquiry commission - 1868
...inscribed in a circle is equal to the interior and opposite. 7. Describe a circle about a given square. 8. Similar triangles are to one another in the duplicate ratio of their homologous sides. XIX. (Two hours.) Maximum. 1. Translate into French : — Two worthy peasants went together to find...
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Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 261 pages
...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...
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The Calendar of Owens college, Manchester

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...
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