 | Euclides - 1884
...figure BLMN similar and oppositely situated to the figure BAGH be obtained? PROPOSITION 19. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. G Let ABC and DEF be similar triangles, having L. B = LE, and LC — LF, so that BC and EF are homologous... | |
 | Dalhousie University - 1884
...= 0, between 1 and 2. GEOMETRY AND MENSURATION.— SECOND YEAR. APRIL 15iH.— 10 AM TO 1 p. M. I. Similar triangles are to one another in the duplicate ratio of their homologous sides. Prove this : and represent the ratio of the two triangles by means of two straight lines whereof one... | |
 | John Harris - Geometry - 1884 - 144 pages
...area of) the eq. triangle DAB of four to nine. It demonstrates therefore (by inspection) the theorem ; Similar triangles are to one another in the duplicate ratio of their respondent sides. (Euclid, IV. 19.) It also demonstrates that if from an eq. triangle a lesser eq.... | |
 | United States. Congress. Senate - United States - 1880
...point on the curve. I the tangents at A, B in D, E ; prove that AB is a mean proportional betwi 12. Similar triangles are to one another in the duplicate ratio of their sides. TRIGONOMETRY. Examiner,— Prof. C. NIVEN. Lieutenants qualifying for gunnery and torpedo officers.... | |
 | Sir Norman Lockyer - Electronic journals - 1886
...book. To mention one only- the proof which he judiciously gives of the fundamental proposition that " similar triangles are to one another in the duplicate ratio of their homologous sides " depends directly on the ist Proposition only of the Sixth Book, instead of the chain being carried... | |
 | Dalhousie University - 1887
...YEAR. APRIL 18.— 10 AM TO 1 PM 1. Explain " duplicate ratio " and prove that, " similar tranples are to one another in the duplicate ratio of their homologous sides." 2. If four straight lines be proportionals, the similar rectilineal figures descriled on them shall... | |
 | Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888
...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... | |
 | Canada. Department of the Interior - 1888
...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... | |
 | New Brunswick. Board of Education - Education - 1889
...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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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
