| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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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