 | William Ernest Johnson - 1889 - 574 páginas
...have been proportional to the product of two lengths. This is equivalent to Euclid's statement that " Similar rectilineal figures are to one another in the duplicate ratio of their homologous sides." 24. The area of any rectilineal figure may be found by dividing it into triangles : and applying the... | |
 | New Brunswick. Board of Education - 1889 - 1004 páginas
...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 - 356 páginas
...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 - 538 páginas
...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 - 144 páginas
...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 - 262 páginas
...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 - 508 páginas
...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 - 760 páginas
...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 - 168 páginas
...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 - 340 páginas
...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... | |
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Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
