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" Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 180
av Robert Simson - 1806 - 518 sider
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Parliamentary Papers, Volum 19

Great Britain. Parliament. House of Commons - 1861
...of a circle, which Khali contain an angle equal to a given rectilineal angle. 3. Similar triangles are to one another in the duplicate ratio of their homologous sides. 4. Investigate a rule for finding the greatest common measure of two algebraical expressions. 5. Reduce...
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Calendar

University of St. Andrews - 1891
...at the centres of equal circles from the ratio of the arcs on which they stand. 6. Similar triangles are to one another in the duplicate ratio of their homologous sides. To construct a triangle similar to a given triangle and equal to half of it. 7. If two straight lines...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - 1851
...The sides about the equal angles of equiangular triangles are proper" tionals. 2. Similar triangles are to one another in the duplicate ratio of their homologous sides. 3- The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle is equal...
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Proceedings of the Edinburgh Mathematical Society, Volumer 18-20

Edinburgh Mathematical Society - 1900
...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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Nature, Volum 34

Sir Norman Lockyer - 1886
...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...
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Register

University of Cambridge - 1844
...from (E), and u the distance of E' from E. FRIDAY, January 5, 18-14. 9. ..Hi. 1. SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. 2. Every solid angle is contained by plane angles which are together less than four right angles. 3....
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The Cambridge University Calendar

University of Cambridge - 1830
...intensity. SATURDAY MoRNING .... 9 to 11. First, Second, TJiird and Fourth Classes. 1. SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. t 2. If two straight lines meeting one another, be parallel to two straight lines which meet one another,...
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