| New Brunswick. Board of Education - 1889
...proportionals ; and those which are opposite to the equal angles, are homologous sides. fi. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** T. ALGEBRA. Time, 1 hour SO mitt. Ei-Jiibit the work. 1. Find the value of x in each of the following... | |
| E. J. Brooksmith - 1889
...AC the two sides including the right angle : prove that _JL= l 4.JL AD* AB* AC*n. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** II. ARITHMETIC. (Including the use of Common Logarithms.) [NB — Great importance will be attached... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 sider
...da ::CD : DA'./ [VI. 4Again v LS bac, cad= L s BAC, CAD; PROPOSITION 19. THEOREM. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** Let As ABC, DEF have LS A, B, C equal to LS D, E, F respectively, so that BC is homologous to EF; then... | |
| Royal Military College, Sandhurst - 1890 - 132 sider
...parts, having first proved the proposition in Euclid on which your method depends. 6. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** Explain the following terms : homologous sides, ex asquali, alternando, duplicate ratio. 7. Two equal... | |
| Thomas Baker - 1891 - 231 sider
...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 - 1892
...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... | |
| 1893
...vertex, and show how to divide the circumference of a circle into fifteen equal parts. 0. The areas of **similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.** Hence show that any rectilineal figure described on the hypothenuse of a right-angled triangle is equal... | |
| Frederick Coate Wade - 1895 - 122 sider
...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 - 1899
...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... | |
| University of Toronto - 1900
...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... | |
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