 | University of Toronto - 1900 - 1164 sider
...mean proportional AE between AD and AB ; draw EF \\ BC ; EF is the required line. 4. Similar triangles are to one another in the duplicate ratio of their homologous sides. 5. If three straight lines be proportionals, the ratio of the first to the third is equal to the ratio... | |
 | 1900 - 898 sider
...triangle, it will cut the other sides (or the other sides produced) proportionately. 7. Similar triangles are to one another in the duplicate ratio of their homologous sides. ABC is a triangle right angled at A, D is the midpoint of EG, and AE. EF are drawn perpendicular to... | |
 | Euclid, Micaiah John Muller Hill - 1900 - 165 sider
...— E : F, where all the magnitudes are of the same kind, then A :B=A + C+E:B+D + F. 44. The areas of similar rectilineal figures are to one another in the duplicate ratio of corresponding sides. 45. (i) If'A:JB=C:D, then figure on A : similar and similarly described figure... | |
 | Great Britain. Parliament. House of Commons - 1900 - 686 sider
...described with 0 as centre and OM as radius, then AM will bisect the angle PAQ. 9. Similar triangles are to one another in the duplicate ratio of their homologous sides. RUGBY SCHOOL SCHOLARSHIP EXAMINATION. — June, 1899. ALGEBRA. 1. Find the square root of the expression... | |
 | University of Sydney - 1901 - 644 sider
...one minute. 7. Triangles of the same altitude are to one another as their bases. 8. Similar triangles are to one another in the duplicate ratio of their homologous sides. 0. Find the diameter of a cylindrical pipe, two feet long, containing a volume of 000 cubic inches.... | |
 | 1903 - 898 sider
...straight line bisecting the angle E makes equal angles with AB and CD. 6. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. Or, 6A. Prove that if two chords of a circle intersect either within or without the circle, the rectangle... | |
 | Samuel Bower Sinclair - 1903 - 140 sider
...the preposition is superior to the former method is as true as the statement that "similar triangles are to one another in the duplicate ratio of their homologous sides." And yet notwithstanding all this there are many good teachers who are vigorously opposed to all study... | |
 | Euclid - 1904 - 488 sider
...of similar triangles, having the same ratio each to each that the polygons have ; and the polygons are to one another in the duplicate ratio of their homologous sides. H Let ABCDE, FGHKL be similar polygons, and let AB and FG be homologous sides. Then (i) the polygons... | |
 | Great Britain. Education Department. Department of Science and Art - 1908 - 328 sider
...remaining angles are either equal or supplementary. (30) 44. Show that the areas of similar triangles are to one another in the duplicate ratio of their homologous sides. Show that similar triangles are to each other in the same ratio as the areas of their inscribed circles.... | |
 | Euclid - 1908 - 456 sider
...i0 corresponding sides. And it was also proved in the case of triangles ; therefore also, generally, similar rectilineal figures are to one another in the duplicate ratio of the corresponding sides. QED 2. in the same ratio as the wholes. The same word fyiiXo-yos is used which... | |
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Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
