 | Civil Service Commission of Canada - 1910 - 240 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 - 254 páginas
...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 - 670 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 - 554 páginas
...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... | |
 | University of Durham - 1879 - 158 páginas
...angle at the base. 6. Define similar triangles, duplicate ratio : — Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 8. Define a conic section, the tangent to a conic section : — If S be the focus, P any point on the... | |
 | 1870 - 964 páginas
...triangles, having ! h.- same ratio to one another that the polygons Jan. 1870. have7. Similar triangles are to one another in the duplicate ratio of their homologous sides. 8. If from any point without a circle lines be drawn touching it, the angle contained by the tangents... | |
 | University of Bombay - 1903 - 1170 páginas
...T, so that DX and DY may be equal. 9. Give the definition of duplicate ratio. 10 Similar triangles are to one another in the duplicate ratio of their homologous sides. Deduce that the duplicate ratios of equal ratios are equal, and also that similar triangles are to... | |
 | Manchester univ - 1877 - 544 páginas
...that equal magnitudes have the same ratio to the same magnitude and conversely. 10. Similar triangles are to one another in the duplicate ratio of their homologous sides. Bisect a triangle by a line perpendicular to one of the sides. 11. Enunciate and prove the general... | |
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Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
