| Edinburgh Mathematical Society - Electronic journals - 1899
...extremes be equal to 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, DBF be two similar triangles, having the angles at B, C equal to the angles at E, F respectively... | |
| 1899
...will be accepted. Dr. MORAN, Head Insi>ector. Mr. PEDLOW, District Inspector. SECTION A. 1. Prove that **similar polygons may be divided into the same number of similar triangles,** and that these triangles have the same ratio to one another that the polygons have. 2. Describe a rectilineal... | |
| Great Britain. Parliament. House of Commons - Great Britain - 1900
...point on a circle 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... | |
| Great Britain. Board of Education - Education - 1900
...point on a circle 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.** SCHOOL SCHOLAESHIP EXAMINATION. — June, 1899. i ALGEBRA. 1. Find the square root of the expression... | |
| Education - 1900
...side of я 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... | |
| University of Toronto - 1900
...in D and find a 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... | |
| University of Sydney - 1901
...forty seconds to 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.... | |
| Arthur Schultze - 1901
...and the lines joining their homologous vertices meet in a point. PROPOSITION XXVI. THEOREM 303. Two **similar polygons may be divided into the same number of similar triangles** similar each to each and similarly placed. A" —— / A —"""——. E Hyp. Polygon ABCDE ~ polygon... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 370 pages
...and the lines joining their homologous vertices meet in a point. x PROPOSITION XXVI. THEOREM 303. Two **similar polygons may be divided into the same number of similar triangles** similar each to each and similarly placed. Hyp. Polygon ABODE ~ polygon A'B'OD'E'. To prove A ABC ~... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 370 pages
...and the lines joining their homologous vertices meet in a point. PROPOSITION XXVI. THEOREM 303. Two **similar polygons may be divided into the same number of similar triangles** similar each to each and similarly placed. A* E' Hyp. Polygon ABCDE ~ polygon A'B'OD'E'. To prove A... | |
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