 | 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... | |
 | Samuel Greatheed, Daniel Parken, Theophilus Williams, Josiah Conder, Thomas Price, Jonathan Edwards Ryland, Edwin Paxton Hood - 1814 - 788 páginas
...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.... | |
 | Wales univ, univ. coll. of Wales - 1878 - 188 páginas
...and their difference is equal to the difference of their squares. 12. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 13. If two chords of a circle intersect, the rectangles contained by the segments are equal. 14. ABC... | |
 | University of Cambridge - 1828 - 454 páginas
...SATURDAY MORNING. ... 9 o'clock to 11. Pint, Second, Third and Fourth Classes. • 1. SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. 2. If a straight line be at right angles to a plane, every plane passing through that straight line... | |
 | 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. Parliament. House of Commons - 1861 - 588 páginas
...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... | |
 | University of St. Andrews - 1891 - 440 páginas
...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... | |
 | 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... | |
 | 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... | |
 | 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... | |
| |
Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
