 | Euclid - 1868 - 138 pages
...оfio\oyov ir\ivpnv. Similar polygons are divisible into similar triangles equal in number and homologous to the polygons ; and the polygons are to each other in the two-fold ratio of their homologous sides. Statement. — Let GL and EB be the similar polygons, and... | |
 | Woolwich roy. military acad - 1868 - 426 pages
...them in the other, show also that this ratio is consistent with the proposition that similar triangles are to each other in the duplicate ratio of their homologous sides. PURE MATHEMATICS. Section I. 10| TO 12 AM REV. WN GRIFFIN, MA 1. Define the tangent and cotangent of... | |
 | Dublin city, univ - 1871 - 366 pages
...lines ; show this, and prove the propositions in the second book of Euclid upon which it depends. 4. Similar polygons may be divided into similar triangles,...proportional to the polygons, and the polygons are in the duplicate ratio of the homologous sides ? Find a mean proportion between two similar polygons.... | |
 | William Alexander Willock - Circle - 1875 - 196 pages
...proportional to it and AtB,, or in the duplicate ratio of the homologous sides, AB and 4,-B,, «* stated. 32. Similar Polygons may be Divided into Similar Triangles, equal in number ; and their Homologous Dtagonals are proportional to their homologous stdes. Let ABCDE and A,BC,D,E, be the... | |
 | Education - 1870 - 386 pages
...in a right-angled triangle. The demonstration involves the following principles : "Similar triangles are to each other in the duplicate ratio of their homologous sides. " Let a, b, c be a triangle* with the angle at b right Bisect ac in d. Draw de parallel to a 6, and... | |
 | Humanities - 1877 - 626 pages
...also, if not with Plutarch to Pythagoras, at least to his early successors. The theorem that similar polygons are to each other in the duplicate ratio of their homologous sides involves a first sketch, at least, of the doctrine of proportion. That we owe the foundation and development... | |
 | Samuel H. Winter - 1877 - 452 pages
...given straight line describe an isosceles triangle equal to a given triangle. 10. Similar triangles are to each other in the duplicate ratio of their homologous sides. 11. Given a point O in the line AB, find two other points C, D, such that a line OP given in direction... | |
 | New Zealand Institute - 1877 - 810 pages
...nineteenth proposition of the sixth book may bo taken. It is required to prove that " similar triangles are to each other in the duplicate ratio of their homologous sides." Most of us, in thinking over the proof in the Elements, will remember the number of anxious students... | |
 | Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 pages
...given straight line describe an isosceles triangle equal to a given triangle. 10. Similar triangles are to each other in the duplicate ratio of their homologous sides. 11. Given a point 0 in the line AB, find two other points CD, such that a line OP given in direction... | |
 | Woolwich roy. military acad - 1884 - 148 pages
...figures; if the figures be triangles, is there anything superfluous in the definition ? Similar triangles are to each other in the duplicate ratio of their homologous sides. ABC is a triangle, AE and BF intersecting in G are drawn to bisect the sides BC, AC in E and F; compare... | |
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... polygons are to each other in the duplicate ratio of their homologous sides. 
