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" ... rectilineal figures are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid - Página 131
por Euclid - 1838 - 416 páginas
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A Complete Treatise on Practical Land-surveying: In All Its Departments ...

Anthony Nesbit - 1847 - 426 páginas
...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 of...
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An elementary course of mathematics, Volumen2

Samuel Hunter Christie - 1847 - 172 páginas
...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 Solutions of the Geometrical Problems: Consisting Chiefly of Examples in ...

Thomas Gaskin - 1847 - 301 páginas
...you recollect. How did Legendre escape the difficulty by an analytical process. 2. Similar triangles are to one another in the duplicate ratio of their homologous sides. 3. If a straight line be at right angles to a plane, every plane which passes through it is at right...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 páginas
...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 third,...
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848 - 388 páginas
...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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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1848 - 396 páginas
...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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Minutes ...: Correspondence, Financial Statements, Etc., and ..., Volumen2

Great Britain. Committee on Education - 1850 - 914 páginas
...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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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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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 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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