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" CF ; but K has to M the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram AC has to the parallelogram CF the ratio which is compounded of the ratios of the sides. Wherefore equiangular parallelograms, &c. "
Manual of Euclid: Books IV, V, VI, and Propositions 1-21 of Book XI - Página 92
por Euclid - 1868 - 141 páginas
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 páginas
...parallelogram CF ; ex aequali (22. 5.), K is to M, as the parallelogram AC to the parallelogram CF ; but K has to M the ratio which is compounded of the ratios...ratio which is compounded of the ratios of the sides. . COR. Hence, any two rectangles are to each other as the products of their bases multiplied by their...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...parallelogram GF; ex aequali, K is to M, as the parallelogram AC to the parallelogram CF: (v.22.) but K has to M the ratio which is compounded of the ratios...parallelograms, &c. QED PROPOSITION XXIV. THEOREM. Parallelograms about the diameter of any parallelogram, are similar to the whole, and to one another....
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 páginas
...parallelogram CF ; ex requali f, K is to t 22. «. M, as the parallelogram AC to the parallelogram CF : but K has to M the ratio which is compounded of the ratios...equiangular parallelograms, &c. QED PROPOSITION XXIV. THEOR. — The parallelograms about the diameter of any parallelogram, are similar to the whole, and...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 páginas
...parallelogram CF ; ex sequali (22. 5.), K is to M, as the parallelogram AC to the parallelogram CF ; but K hag to M the ratio which is compounded of the ratios of...ratio which is compounded of the ratios of the sides. COR. Hence, any two rectangles are to each other as the products of their bases multiplied by their...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...therefore, ex asquali, the parallelogram AC is to the parallelogram CF as K to M : But K is to M in the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram AC is to the parallelogram CF in the ratio which is compounded of the ratios of the sides. Wherefore,...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich, Thomas Stephens Davies, Stephen Fenwick, William Rutherford - 1853
...parallelogram CF ; ex oequali (22. v.), K is to M, as the parallelogram AC to the parallelogram CF : but K has to M the ratio which is compounded of the ratios...the sides. Wherefore, equiangular parallelograms, etc. QED PROPOSITION XXIV. THEOR. Tlie parallelograms about the diameter of any parallelogarm, are...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 páginas
...С f : ex œquali (v. 22), k is to Щ, as the parallelogram a С to the parallelogram С f : but k has to m the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram a С has to the parallelogram С f the ratio which is compounded of the ratios of the sides. Wherefore,...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 páginas
...parallelogram CF ; ex aquali (22. 5.), K is to M, as the parallelogram AC to the parallelogram CF; but K has to M the ratio which is compounded of the ratios...of the sides; therefore also the parallelogram AC Las to the parallelogram CF the ratio which is compounded of the ratios of the sides. DR Coa. Hence,...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855
...parallelogram CF ; ex cequali, K is to M, as the parallelogram AC is to the parallelogram CF (/). But K has to M the ratio which is compounded of the ratios of the sides ; therefore also Ihe parallelogram, AC has to the parallelogram, CF the ratio which is compounded of the ratios of the...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...Wherefore, ex cequali, K is to M, as the parallelogram AC is to the parallelogram CF (V. 22). But K has to M the ratio which is compounded of the ratios of the sides, fherefore also the parallelogram AC has to the parallelogram CF, the ratio which is compounded of the...
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