 | 1882 - 486 pages
...than a right angle. 4. Inscribe a regular equilateral and equiangular pentagon in a given circle. 5. Similar triangles are to one another in the duplicate ratio of their homologous sides. 6. Two circles whose centres are A and B, intersect in C and D, shew that AB bisects CD at right angles.... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...proportionals ; therefore they are similar to one another. [VI. Definition 1, PROPOSITION 19. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC and DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC... | |
 | Mathematical association - 1883 - 86 pages
...to one another the ratio compounded of the ratios of their bases and of their altitudes. THEOR. 15. Similar triangles are to one another in the duplicate ratio of their homologous sides. THEOR. 16. The areas of similar rectilineal figures are to one another in the duplicate ratio of their... | |
 | Euclides - 1884 - 434 pages
...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 - 184 pages
...= 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 - 188 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 - 1304 pages
...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 - 684 pages
...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 - 206 pages
...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... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
