| Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...OABCD : oabcd :: AOAB : Aoab, ie in dupl. ratio of OA : oa. COR. i. — Similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides.** COR. ii. — If to the homologous sides BC, EF of two similar rectilineal figures P and Q a third proportional... | |
| Thomas Baker - Railroads - 1891 - 231 pages
...then, the tnanr/ff ABC is to the triangle AED a* the square of AB is to tlte square of AE : that is, **similar triangles are to one another in the duplicate ratio of their homologous sides.** (Euc. VI. 19.) THEOREM VIII. All similar figures are to one another as the squares of then homologous,... | |
| Queensland. Department of Public Instruction - Education - 1892
...LM, and PQ are drawn through O parallel to BC, CA, and AB, show that HK BC LM CA ' AB PQ _ = 2. 7. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 8. Given the base of a triangle, the perpendicular, and the sum of the sides, construct it. !). If... | |
| 1894
...parallel to AD. 4. Similar triangles are to one another in the duplicate ratio of their homologous sides. **Similar triangles are to one another in the duplicate ratio of their** corresponding altitudes. 6. Shew how to solve two equations which contain two unknown quantities when... | |
| Frederick Coate Wade - Church and state - 1895 - 122 pages
...produced, it will cut them proportionally ; and conversely. Is this converse universally true ? 10. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Bisect a triangle by a line drawn parallel to one of its sides. ALGEBRA. 1. Investigate a rule for... | |
| Edinburgh Mathematical Society - Mathematics - 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 :... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
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