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" SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. "
The school edition. Euclid's Elements of geometry, the first six books, by R ... - Pagina 271
door Euclides - 1864
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Proceedings of the Edinburgh Mathematical Society, Volumes 17-18

Edinburgh Mathematical Society - 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 :...
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Special Reports on Educational Subjects, Volumes 6-7

Great Britain. Board of 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...
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Sessional Papers, Volume 22,Deel 2

Great Britain. Parliament. House of Commons - 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...
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Examination Papers

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...
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Report of the Committee of Council on Education in Scotland...[without Appendix]

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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Calendar

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....
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Manual

1903
...the special case when AB is one side of an equilateral triangle inscribed in the circle. 8. Show that similar triangles are to one another in the duplicate ratio of their homologous sides. ABC is a triangle. Two circles are drawn, one to touch Alt at A and to pass through C, the other to...
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The Possibility of a Science of Education

Samuel Bower Sinclair - 1903 - 126 pagina’s
...method of teaching 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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A Text-book of Euclid's Elements for the Use of Schools, Boek 1

Euclid - 1904 - 456 pagina’s
...sh CD DC FE jular to the A FD. FE.' ewn that DE. CF, ED. DFE, vI. 4. V. 14. VI. 4. PROPOSITION 19. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. A Let ABC, DEF be similar triangles, having the L ABC equal to the L DEF, and let BC and EF be homologous...
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Annual Report of the Commissioners ..., Volume 71

1905
...Describe an isosceles triangle having each of the angles at the base double of the vertical angle. 4. Similar triangles are to one another in the duplicate ratio of their homologous titles. 5. If any similar rectilineal figure be similarly described on the three sides of a right-angled...
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