 | Euclid, Isaac Todhunter - 1883 - 428 Seiten
...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 Seiten
...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... | |
 | Dalhousie University - 1884 - 184 Seiten
...= 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... | |
 | Euclides - 1884 - 434 Seiten
...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... | |
 | John Harris - 1884 - 188 Seiten
...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 - 1880 - 1304 Seiten
...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 - 1886 - 684 Seiten
...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 Seiten
...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 - 1888 - 208 Seiten
...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... | |
| |
Similar triangles are to one another in the duplicate ratio of their homologous sides. 
