| 1903
...straight line bisecting the angle E makes equal angles with AB and CD. 6. Prove that similar triangles **are to one another in the duplicate ratio of their homologous sides.** Or, 6A. Prove that if two chords of a circle intersect either within or without the circle, the rectangle... | |
| Euclid - 1904 - 484 páginas
...of similar triangles, having the same ratio each to each that the polygons have ; and the polygons **are to one another in the duplicate ratio of their homologous sides.** H Let ABCDE, FGHKL be similar polygons, and let AB and FG be homologous sides. Then (i) the polygons... | |
| Great Britain. Education Department. Department of Science and Art - 1908 - 328 páginas
...remaining angles are either equal or supplementary. (30) 44. Show that the areas of similar triangles **are to one another in the duplicate ratio of their homologous sides.** Show that similar triangles are to each other in the same ratio as the areas of their inscribed circles.... | |
| Euclid - 1908 - 456 páginas
...i0 corresponding sides. And it was also proved in the case of triangles ; therefore also, generally, **similar rectilineal figures are to one another in the duplicate ratio of** the corresponding sides. QED 2. in the same ratio as the wholes. The same word fyiiXo-yos is used which... | |
| Civil Service Commission of Canada - 1910 - 238 páginas
...or at the circumferences, have the same ratio as the arcs on which they stand. 3. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** 4. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the... | |
| Association of Ontario Land Surveyors - 1909
...equiangular pentagon in a circle. 8. Inscribe a circle in a given sector ofi a circle. 9. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** 10. Describe a rectilineal figure which shall be similar to one and equal to another rectilineal figure.... | |
| Great Britain. Board of Education - 1912 - 632 páginas
...AB:BC::DE:EF; prove that AD, BE, CF will meet in a point or be parallel. 9. Prove that similar triangles **are to one another in the duplicate ratio of their homologous sides.** If one diagonal of a quadrilateral bisects the angle between two of the sides and is a mean proportional... | |
| 1879 - 666 páginas
...beautifully demonstrated in Euclid's Sixth Book, Propositions 19 and 20, that " similar rectilinear **figures are to one another in the duplicate ratio of their homologous sides"** — that is, that these figures — meaning the areas of them— are to one another as the squares... | |
| Trinity College (Dublin, Ireland) - 1916
...having the same altitude are to one another as their bases. 6. Prove that the areas of similar triangles **are to one another in the duplicate ratio of their homologous sides.** 7. Show how to construct a triangle equal in area to a given square and similar to a given triangle.... | |
| Great Britain. Scottish Education Dept - 1896 - 642 páginas
...of similar triangles, having the same ratio to one another that the polygons have ; and the polygons **are to one another in the duplicate ratio of their homologous sides.** Describe a polygon which shall be similar to a given polygon, but shall have half its area. 8. Draw... | |
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