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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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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 372 páginas
...described, on a given line, similar to a given fig. QEF PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar AS, having L s at A, B, C= s.sa.tD,E,F respectively, so that BC and EF are...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 páginas
...duplicate ratio of their homologous sides ; and it has already been proved in triangles (VI. 19) ; therefore, universally, similar rectilineal figures...in the duplicate ratio of their homologous sides. COT. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken (VI. 11), 1....
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Plane and solid geometry, by G.E. Webster and A. Gardiner

George E. Webster - 1874 - 136 páginas
...equal, then the greatest area is possessed by the figure which has the largest number of sides. (7) Similar rectilineal figures are to one another in the duplicate* ratio of their homologous^ sides. (8) If three straight lines oe proportionals, as the first quantity is to the third quantity, so is...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874 - 234 páginas
...homologous sides. Cor. 2. — In like manner it may be proved that any similar figures of four sides are to one another in the duplicate ratio of their homologous sides, and the same has been proved of triangles (VI. 14); therefore, universally, similar rectilineal figures...
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Euclidian Geometry

Francis Cuthbertson - 1874 - 396 páginas
...ratio of AB to AH. Hence, proceeding as in Proposition VIII., it may be proved that Similar polygons are to one another in the duplicate ratio of their homologous sides. PROPOSITION (r). If four straight lines are proportional, the duplicate ratio of the first two is the...
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Recent military, naval, and civil service examination papers in mathematics ...

Braithwaite Arnett - 1874 - 130 páginas
...shall be parallel to the remaining side of the triangle. 10. Define duplicate ratio. Similar triangles are to one another in the duplicate ratio of their homologous sides. 11. Define a plane. State when a straight line is perpendicular to a plane, and when two planes are...
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Annual Report of the Commissioners ..., Volumen40

1874
...duplicate ratio, and illustrate its meaning as you would to a class. (b.) Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 2. Describe a circle which will pass through a given point, and touch a given circle in a given point....
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 446 páginas
...duplicate ratio of their homologous sides : and it has already been proved in triangles: (vi. 19.) therefore, universally, similar rectilineal figures...in the duplicate ratio of their homologous sides. COB. 2. And if to AB, FG, two of the homologous sides, a third proportional M\K taken, (vi. 11.) AB...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1876 - 238 páginas
...homologous sides, as has already been proved in the case of triangles. Therefore, universally, sjmilar rectilineal figures are to one another 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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Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...

Association for the improvement of geometrical teaching - 1876 - 66 páginas
...ratio compounded of the ratios of their bases and of their altitudes. THEOR. 15. Similar triangles are to one another in the duplicate ratio of their homologous sides. THEOR. 16. The areas of similar rectilineal figures are to one another in the duplicate ratio of their...
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