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Llibres Llibres 51 - 60 de 178 sobre Similar triangles are to one another in the duplicate ratio of their homologous sides..
" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Pągina 167
per Robert Simson - 1762 - 466 pągines
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 138 pągines
...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...
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Commentaries on the Principia of sir Isaac Newton respecting his theory ...

Joseph Denison - 1846
...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...
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A Complete Treatise on Practical Land-surveying, in All Its Departments ...

Anthony Nesbit - 1847 - 426 pągines
...proposed Quantity of Land, by a Line parallel to any one of its Sides. RULE. — The areas of similar triangles are to one another in the duplicate ratio of their homologous sides : hence, as the area of the triangle ABC is to the square of the side AC, or BC, so is the area...
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THE SOLUTIONS OF GEOMETRICAL PROBLEMS

THOMAS GASKIN, M.A., - 1847
...according to Euclid's definition, that the magnitudes 4, 5, 7 , 9 are not proportional. 3. Similar triangles are to one another in the duplicate ratio of their homologous sides. How does it appear from Euclid that the duplicate ratio of two magnitudes is the same as that...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...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...
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall - 1848
...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...
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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1848
...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...
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Reports on Elementary schools

Her MAjesty' Inspectors of schools - 1850
...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...
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Minutes of the Committee of Council on Education, with Appendices, Volum 2

Great Britain. Committee on Education - 1850
...same multiple of the second that the first magnitude is of the second. 7. Prove Euc. 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 straight line in extreme and mean, ratio. 9....
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The works of William Cowper, with a life of the author, by the editor R. Southey

William Cowper - 1851
...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...
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