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" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... - Pągina 28
per Euclides - 1821
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846 - 272 pągines
...AEDCB) may be divided into similar triangles, equal in number, and homologous to all. And the polygons are to one another in the duplicate ratio of their homologous sides. PART 1. — Because in the triangles FGI and AED, the angles G and E are G ( equal, and the sides about...
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The Solutions of the Geometrical Problems: Consisting Chiefly of Examples in ...

Thomas Gaskin - 1847 - 301 pągines
...angle $ = 45. See fig. 121 . 19= See Appendix, Art. 31. ST JOHN'S COLLEGE. DEC. 1843. (No. XIV.) 1. SIMILAR triangles are to one another in the duplicate ratio of their homologous sides, 2. Draw a straight line perpendicular to a plane from a given point without it. 3. Shew that the equation...
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A Complete Treatise on Practical Land-surveying: In All Its Departments ...

Anthony Nesbit - 1847 - 492 pągines
...both ; then the triangle ABC is to the triangle ADE, as the square of BC to the square of D E. That is similar triangles are to one another in the duplicate ratio of their homologous sides. (Euc. VI. 19. Simp. IV. 24. Em. II. 18.) THEOREM XIV. In any triangle ABC, double the square of a line...
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An elementary course of mathematics, Volum 2

Samuel Hunter Christie - 1847 - 172 pągines
...of the ratios of their bases and altitudes : the bases being similar rectilineal figures (Def. 13) are to one another in the duplicate ratio of their homologous sides (VI. 20); and the solids being similar, their altitudes are in the simple ratio of the homologous sides:...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pągines
...rectilineal figure similar, and similarly situated, to a given rectilineal figure. PROP. XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. COR. From this it is manifest, that if three straight lines be proportionals, as the first is to the...
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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1848 - 394 pągines
...Morning Paper. 1. Find a mean proportional between two given straight lines. In this case shew how similar triangles are to one another in the duplicate ratio of their homologous sides. 2. The parallelograms about the diameter of any parallelogram are similar to the whole and to one another....
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848 - 390 pągines
...from the opposite angle. (The first case only of this proposition need be demonstrated.) Section 2. 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. 2. If one angle of a triangle be equal to the sum of the other two, the greatest side is double of...
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Minutes ...: Correspondence, Financial Statements, Etc., and ..., Volum 2

Great Britain. Committee on Education - 1848 - 606 pągines
...from the opposite angle. (The first case only of this proposition need be demonstrated.) Section 2. 1. Similar triangles are to one another in the duplicate ratio of their homologuous sides. 2. If one angle of a triangle be equal to the sum of the other two, the gteatest...
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Reports on Elementary schools

Her MAjesty' Inspectors of schools - 1850 - 912 pągines
...of the second. 5. Solve Kiic. IV. 6. To inscribe a square in a given circle. 7. Prove Kuc. VI. 19. Similar triangles are to one another in the duplicate ratio of their homologous sides. 8. Solve Kuc. VI. 30. To divide a given finite itraight line in extreme and mean ratio. 9. In the construction...
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General Report on Public Instruction in the Bengal Presidency

1851 - 628 pągines
...Morning Paper. 1. Find a mean proportional between two given straight lines. In this case shew how similar triangles are to one another in the duplicate ratio of their homologous sides. 2. The parallelograms about the diameter of any parallelogram are similar to the whole and to one another....
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