 | Sir Norman Lockyer - 1886 - 684 páginas
...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... | |
 | Association for the Improvement of Geometrical Teaching - 1888 - 208 páginas
...bisect the sides BC, AC in E and F. Compare the areas of the triangles AGB, FGE. THKOR. 12. The areas of similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. Let ABCD, HKLM be two similar figures, having the sides AB, HK homologous : then shall the figure ABCD... | |
 | Canada. Department of the Interior - 1888 - 756 páginas
...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... | |
 | William Ernest Johnson - 1889 - 574 páginas
...have been proportional to the 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... | |
 | New Brunswick. Board of Education - 1889 - 1004 páginas
...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... | |
 | E. J. Brooksmith - 1889 - 356 páginas
...AC the two sides including the right angle : prove that _JL= l 4.JL AD* AB* AC*n. Similar triangles are to one another in the duplicate ratio of their homologous sides. II. ARITHMETIC. (Including the use of Common Logarithms.) [NB — Great importance will be attached... | |
 | Royal Military College, Sandhurst - 1890 - 144 páginas
...parts, having first proved the proposition in Euclid on which your method depends. 6. Similar triangles are to one another in the duplicate ratio of their homologous sides. Explain the following terms : homologous sides, ex asquali, alternando, duplicate ratio. 7. Two equal... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 páginas
...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... | |
 | Thomas Baker - 1891 - 262 páginas
...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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... rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
