| 1900
...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... | |
| M. J. M. HILL - 1900
...— 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
...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
...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
...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 - 126 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 - 456 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
...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
...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... | |
| 1879
...beautifully demonstrated in Euclid's Sixth Book, Propositions 19 and 20, that " similar rectilinear **figures are to one another in the duplicate ratio of their homologous sides"** — that is, that these figures — meaning the areas of them— are to one another as the squares... | |
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