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" SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. "
The school edition. Euclid's Elements of geometry, the first six books, by R ... - Pagina 271
door Euclides - 1864
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Science Examination Papers

Great Britain. Education Department. Department of Science and Art - 1908
...correspond, show that the 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....
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English Mechanic and World of Science: With which are ..., Volume 28

1879
...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...
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The Dublin University Calendar, Volume 1

Trinity College (Dublin, Ireland) - 1919
...Prove that a right-angled triangle may be divided into two triangles each similar to the whole. 7. Similar triangles are to one another in the duplicate ratio of their corresponding sides. Practical. 8. Construct a square containing 6 square inches without extracting...
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Education in Scotland

Great Britain. Scottish Education Dept - 1896
...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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Report of the Minister of Education

1852
...circle. 8. It is required to describe a square that shall be equal to a given rectilineal figure. 9. Similar triangles are to one another in the duplicate ratio of their homologous sides. 12. — EXAMINATION PAPER in Mensuration and the Rudiments of Mechanics. April mh, 1852. TIME : ONE...
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The Durham University Journal, Volume 1

University of Durham - 1879
...eight times either 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...
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Proceedings of the Edinburgh Mathematical Society, Volumes 18-20

Edinburgh Mathematical Society - 1900
...extremes be equal to the square on the mean, the three straight lines are proportional. EUCLID VI. 19. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEFbetwu similar triangles, having the angles at В, С equal to the angles at E, F respectively :...
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