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" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
The figures of Euclid with the enunciations, as printed in Euclid's Elements ... - Page 62
by Euclides - 1840
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The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II ...

Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888 - 208 pages
...in D, prove that the rectangle contained by BD and BF is .equal to twice the area of ABC. THEOR. n. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be two similar triangles, having the sides BC, EF homologous^ then shall the triangle...
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Annual Report

Canada. Department of the Interior - 1888 - 756 pages
...rectangles under the sides containing the equal angles. 15. From tho last deduce tho proposition " similar triangles are to one another in the duplicate ratio of their homologous sides.'' No. of Mark-. 13 10 13 13 li 13 13 13 PLANE TRIGONOMETRY. Time, 3 hours. 1. Find the number of degrees...
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Annual Report of the Schools of New Brunswick ... by the Chief ...

New Brunswick. Board of Education - Education - 1889 - 1004 pages
...another, are proportionals ; and those which are opposite to the equal angles, are homologous sides. fi. Similar triangles are to one another in the duplicate ratio of their homologous sides. T. ALGEBRA. Time, 1 hour SO mitt. Ei-Jiibit the work. 1. Find the value of x in each of the following...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889 - 356 pages
...will touch the circle circumscribing ABC in the point A. 8. Describe a circle about a given square. 9. Similar triangles are to one another in the duplicate ratio of their homologous sides. 10. In a right-angled triangle if a line be drawn from the right angle perpendicular to the base it...
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Treatise on Trigonometry ...

William Ernest Johnson - Plane trigonometry - 1889 - 574 pages
...product of two lengths. This is equivalent to Euclid's statement that " Similar rectilineal figures are to one another in the duplicate ratio of their homologous sides." 24. The area of any rectilineal figure may be found by dividing it into triangles : and applying the...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...AB : BC 1 and cd : da ::CD : DA'./ [VI. 4Again v LS bac, cad= L s BAC, CAD; PROPOSITION 19. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let As ABC, DEF have LS A, B, C equal to LS D, E, F respectively, so that BC is homologous to EF; then...
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Sandhurst Mathematical Papers for Admission Into the Royal Military College ...

Royal Military College, Sandhurst - Mathematics - 1890 - 144 pages
...one another, and shall have those angles equal about which the sides are proportionals. 6. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. If ABC be an obtuse-angled triangle, having the obtuse angle BAC; and if AD, AE, be drawn to meet BC...
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A Rudimentary Treatise on Land and Engineering Surveying: For Students and ...

Thomas Baker - Railroads - 1891 - 262 pages
...then, the tnanr/ff ABC is to the triangle AED a* the square of AB is to tlte 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 then homologous,...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry - 1891 - 428 pages
...vi., PROP, n.) Conclusion : A and B, being any regular polygons, etc. PROPOSITION XII. 4O3. Theorem : Similar polygons may be divided into the same number of similar triangles similarly placed. Statement : Similar polygons, ABD and GHJ, may be divided into the same number of...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 pages
...may BH be shewn : CD : DE that Also BA and GH AG HB : DC : FE CF, VI ED; 4. PROPOSITION 19. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. B Let ABC, DEF be similar triangles, having the i.ABC equal to the L. DEF, and let BC and EF be homologous...
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