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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 ... - Pagina 271
door Euclides - 1864
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An elementary course of mathematics, Volume 2

Samuel Hunter Christie - 1847
...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
...describe a 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
...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, Volume 2

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 first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 pagina’s
...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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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...and it has already been proved in triangles ; therefore, universal!}', similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. the duplicate ratio of that which AB has to FG ; therefore, as AB is to M, so is the figure upon AB...
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Elements of geometry and mensuration

Thomas Lund - 1854 - 192 pagina’s
...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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