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" ... rectilineal figures are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid - Página 131
por Euclid - 1838 - 416 páginas
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - 1892 - 506 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...
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Examinations Papers

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...
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The Manitoba School Question

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...
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Proceedings of the Edinburgh Mathematical Society, Volúmenes17-18

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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Examination Papers

University of Toronto - 1900 - 1158 páginas
...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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The Contents of the Fifth and Sixth Books of Euclid

Micaiah John Muller Hill - 1900 - 165 páginas
...— 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...
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Sessional Papers, Volumen22,Parte2

Great Britain. Parliament. House of Commons - 1900 - 686 páginas
...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...
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Report of the Committee of Council on Education in Scotland...[without Appendix]

1900 - 898 páginas
...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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Calendar of the University of Sydney

University of Sydney - 1901 - 646 páginas
...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....
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The Possibility of a Science of Education

Samuel Bower Sinclair - 1903 - 140 páginas
...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...
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