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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 ... - Side 271
av Euclides - 1864
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The British Annals of Education for ...: Being The Scholastic ..., Volum 1

1844
...and u the distance of A" from K. FRIDAY, Jan. 5. 9. ..ll£ SENIOR MODERATOR AND JUNIOR EXAMINER. 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. 2. Every solid angle is contained by plane angles which are together less than four right angles. 3....
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Report to the Trustees of the Dick Bequest for the Benefit of the ..., Volum 2

1844
...that their common chord will be bisected at right angles by a straight line joining their centres. 4. Similar triangles are to one another in the duplicate ratio of their homologous sides. 5. About the centre of a given circle describe another circle, equal in area to half the former. TRIGONOMETRY...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...has already been proved in triangles: (vi. 19.) therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COH. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, (vi. 11.) AB...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 sider
...already been proved (VI. 19) in respect to triangles. Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. Cor. 2. If to AB, FG, two of the homologous sides a third proportional M be taken, AB has (V. def....
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 138 sider
...Recite (a) p. 23, 1 ; (b) p. 32, 1 ; (c) p. 4, 6 ; ( d) p. 22, 5 ; (c) def. 1, 6 and def. 35, 1. 19 Th. Similar triangles are to one another in the duplicate ratio of their homologous sides. Given the similar triangles ABC, DEF; having the angles at B, E, equal, and AB to BC as DE to EF: then...
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Commentaries on the Principia of sir Isaac Newton respecting his theory ...

Joseph Denison - 1846
...ultimately become similar, and consequently the approximating sides homologous, and (6 Euclid 19) because similar triangles are to one another in the duplicate ratio of their homologous sides; the evanescent triangles are in the duplicate ratio of the homologous sides; and this seems the proper...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846
...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 Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...And, in like manner, it may be proved, that similar figures of any number of sides more than three are to one another in the duplicate ratio of their homologous sides ; and it has already been proved (9. 19) in the case of triangles. Wherefore, universally, Similar...
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THE SOLUTIONS OF GEOMETRICAL PROBLEMS

THOMAS GASKIN, M.A., - 1847
...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 - 426 sider
...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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