 | 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... | |
 | Samuel Greatheed, Daniel Parken, Theophilus Williams, Josiah Conder, Thomas Price, Jonathan Edwards Ryland, Edwin Paxton Hood - 1814
...have met it before. The demonstration of the 19th Prop, of Euclid's Oth book, ie " Similar triangles are to one another in the duplicate ratio of their homologous sides," requires the previous or the syn hro nous establishment of Props, vi. 11, v. 10, v. 11, vi. 15., and\i.... | |
 | Sir Norman Lockyer - 1886 - 688 páginas
...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... | |
 | 1902 - 1360 páginas
...血 I8equalⅠo 土 h０ 8umof 血 6squar ㏄ o 口 仕 @ e 田 agonⅠ 止 ・ 10. Similar triangles are to one another in the duplicate ratio of their homologous sides. Ⅱ ・ The 卯 叩 endic 山 a 乃 旺 awn 升 omthe gide8m ㏄ tatthe 皿 血 ePOlnt . Ⅱ 喀 lesofa... | |
 | Edinburgh Mathematical Society - 1900 - 410 páginas
...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... | |
 | 1904 - 1032 páginas
...liberty which each of these excellent works takes with Euclid's Prop. 19, Bk. vi. — " similar triangles are to one another in the duplicate ratio of their homologous sides " — mysterious but high-sounding to countless generations of schoolboys. Here it is, in identical... | |
 | Cowley Oxon, dioc. school - 1860 - 318 páginas
...circumference upon the same base, that is upon the same part of the circumference. 5. Similar triangles are to one another in the duplicate ratio of their homologous sides. 6. If two triangles have two sides of the one equal to two sides of the other, and have likewise their... | |
 | Great Britain. Committee on Education - 1851 - 1054 páginas
...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... | |
 | 1870 - 962 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... | |
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... rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
