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" Therefore, universally, similar rectilineal figures 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 ... - Side 180
av Robert Simson - 1806 - 518 sider
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Scholarship examinations of 1846/47 (-1853/54).

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

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

Great Britain. Committee on Education - 1850
...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. In the...
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General Report on Public Instruction in the Bengal Presidency

1851
...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 sider
...Wherefore similar polygons, &c. QED Сок. 1. In like manner, it may be proved, that similar four-sided figures, or of any number of sides, are one to another...And if to ab, fg, two of .the homologous sides, a third proportional m be taken, ab has (v. def. 10) to m the duplicate ratio of that which ab has to...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...ratio of their homologous sides, 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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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855
...another in the duplicate ratio of their homologous sides, as has already been proved in the case of triangles. Therefore, universally, similar rectilineal...in the duplicate ratio of their homologous sides. COROLLARY 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...in the duplicate ratio of their homologous sides ; and this has been proved of triangles (VI. 19). Therefore, universally, similar rectilineal figures...in the duplicate ratio of their homologous sides. COROLLARY 2, — If to AB and FG, two of the homologous sides of the polygon, a third proportional...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855
...point, either without or in the circumference, which shall touch a given circle. 16. Similar triangles are to one another in the duplicate ratio of their homologous sides. 18. ABC is a triangle having each of the angles at JB, C double of that at A, CD is drawn bisecting...
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General Report on Public Instruction in the Bengal Presidency

1855
...A, if CD be drawn bisecting the angle C, show that AB : AC :: BC — AC : AD. 8. Similar triangles are to one another in the duplicate ratio of their homologous sides. 4. Planes to which the same straight line is perpendicular, are parallel to one another. 5. If two...
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