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" SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Page 167
by Euclides - 1814
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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 - Education - 1903 - 126 pages
...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, Book 1

Euclid - Euclid's Elements - 1904 - 456 pages
...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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Science Examination Papers

Great Britain. Education Department. Department of Science and Art - 1908
...correspond, show that the remaining angles are either equal or supplementary. (30) 44. Show that the areas of similar triangles are to one another in the duplicate ratio of their homologous sides. Show that similar triangles are to each other in the same ratio as the areas of their inscribed circles....
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English Mechanic and World of Science: With which are ..., Volume 28

Industrial arts - 1879
...beautifully demonstrated in Euclid's Sixth Book, Propositions 19 and 20, that " similar rectilinear figures are to one another in the duplicate ratio of their homologous sides" — that is, that these figures — meaning the areas of them— are to one another as the squares...
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The Dublin University Calendar, Volume 1

Trinity College (Dublin, Ireland) - 1919
...Prove that a right-angled triangle may be divided into two triangles each similar to the whole. 7. Similar triangles are to one another in the duplicate ratio of their corresponding sides. Practical. 8. Construct a square containing 6 square inches without extracting...
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Education in Scotland

Great Britain. Scottish Education Dept - 1896
...of similar triangles, having the same ratio to one another that the polygons have ; and the polygons are to one another in the duplicate ratio of their homologous sides. Describe a polygon which shall be similar to a given polygon, but shall have half its area. 8. Draw...
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Report of the Minister of Education

Education - 1852
...circle. 8. It is required to describe a square that shall be equal to a given rectilineal figure. 9. Similar triangles are to one another in the duplicate ratio of their homologous sides. 12. — EXAMINATION PAPER in Mensuration and the Rudiments of Mechanics. April mh, 1852. TIME : ONE...
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