 | Euclides - 1885 - 340 pages
...triangles; (2) the corresponding triangles have the same ratio to one another which the polygons have ; (3) the polygons are to each other in the duplicate ratio of their homologous sides. Dem.— Let ABHIJ, CDEFG be the polygons, and let the sides AB, CD be homologous. Join AH, AI, €E,... | |
 | Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...triangles; (2) the corresponding triangles have the same ratio to one another which the polygons have; (3) the polygons are to each other in the duplicate ratio of their homologous sides. Dem. — Let ABHIJ, CDEFG be the polygons, and let the sides AB, CD be homologous. Join AH, AI, CE,... | |
 | Encyclopedias and dictionaries - 1888 - 916 pages
...problem, 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 and the similarity of figurée.* That... | |
 | George Johnston Allman - Geometry - 1889 - 266 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... | |
 | E. J. Brooksmith - Mathematics - 1889 - 356 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 m E and F; compare... | |
 | Euclid - Geometry - 1890 - 442 pages
...corresponding pairs of triangles in (a) have to each other the same ratio that the polygons have : (y) similar polygons are to each other in the duplicate ratio of their homologous sides : (8) similar polygons are to each other as the squares on their homologous sides : (e) similar polygons... | |
 | Canada. Department of the Interior - 1900 - 564 pages
...the given point, show what ratio subsists between the latter two lines. 12. Show that similar figures are to each other in the duplicate ratio of their homologous sides. PLANE TRIGONOMETRY. Time, 3 hours. 1. To express the sine and the cosine of the sum of two angles in... | |
 | 1900 - 650 pages
...corresponding triangles have the same ratio to one another which the polygons have ; (3) the polygon« are to each other in the duplicate ratio of their homologous sides. 5. Prove that if two triangles have one angle in one equal to one angle in the other, and the sides... | |
 | University of Toronto - 1901 - 1190 pages
...two Hues, find a line 0 such that the ratio of A to C is the duplicate of A to B. Similar triangles are to each other in the duplicate ratio of their homologous sides. (VI. 19.) 5. If two triangles have one angle of the one equal to one angle of the other and the sides... | |
 | Samuel Bower Sinclair, Frederick Tracy - Educational psychology - 1912 - 204 pages
...which, on second thought, you discarded? For example, in considering the statement: "Similar triangles are to each other in the duplicate ratio of their homologous sides," a student who had at first learned to consider a plane triangle as three lines and not as a plane figure,... | |
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... polygons are to each other in the duplicate ratio of their homologous sides. 
