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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 ... - Página 165
por Euclides - 1814
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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1848
...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
...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 of the Committee of Council on Education, with Appendices, Volumen2

Great Britain. Committee on Education - 1848
...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
...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
...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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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...proportionals, they are similar to one another : and in the same manner a rectilineal figure of six or more sides may be described upon a given straight line...similar to one given, and so on. Which was to be done. PRG-POSITION XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homologous...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 páginas
...sides, and it has already been proved in triangles. Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COR. 2. And if to ab, fg, two of .the homologous sides, a third proportional m be taken, ab has (v....
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Elements of geometry and mensuration

Thomas Lund - 1854 - 192 páginas
...which tA = ta, d> b * Sometimes called 'homologous sides'. •f Euclid's enunciation of this is : ' Similar triangles are to one another in the duplicate ratio of their homologous aides'. iB= tb, fC- ic; then AB, ab being ant/ two corresponding, or homologous, sides, the triangle...
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General Report on Public Instruction in the Bengal Presidency

1855
...centre of gravity of the hemisphere from its vertex being = $ rad. FOURTH CLASS. EUCLID AND ALGEBRA. 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. 2. If two parallel planes be cut by another plane their common sections with it are parallel. 3. If...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855
...and inscribed circles of a triangle, the square of the distance between the centres = J? - 2Br. 2. Similar triangles are to one another in the duplicate ratio of their homologous side*. 4. Divide -01 by -0002 and -00001 by -03; find also a irth proportional to -999, 33-3 and -03.'...
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