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" ABC : FGH : : ACD : FHI. By the same mode of reasoning, we should find ACD : FHI : : ADE : FIK; and so on, if there were more triangles. And from this series of equal ratios, we conclude that the sum of the antecedents... "
Elements of Geometry and Trigonometry Translated from the French of A.M ... - Page 89
by Charles Davies - 1849 - 359 pages
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 pages
...ACD, FHI, we shall have ACD : FHI : : AC2 : FH2 ; therefore by reason of the common ratio, AC2 : FH'J, we have ABC: FGH:: ACD: FHI. By the same mode of reasoning,...there were more triangles. And from this series of identical ratios, we conclude that the sum of the antecedents ABC+ACD+ADE, or the polygon ABCDE, is...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...ACD, FHI, we shall have ACD : FHI : : AC2 : FH2 ; therefore, by reason of the common ratio, AC2 : FH2, we have ABC : FGH : : ACD: FHI. By the same mode of...the polygon ABCDE, is to the sum of the consequents FGH+FHI+FIK, or to the polygon FGHIK, as one antecedent ABC, is to its consequent FGH, or as AB2 is...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1830 - 344 pages
...ACD, FHI, we shall have ACD : FHI : : AC2 : FH2 ; therefore, by reason of the common ratio, AC2 : FH2, we have ABC : FGH : : ACD : FHI. By the same mode of reasoning, we should find ACD : FHI : : ADE : FJK ; and so on, if there were more triangles. And from this series of equal ratios, we conclude...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...ACD, FHI, we shall have ACD : FHI : : AC2 : FH8; therefore, by reason of the common ratio, AC2 : FH2, we have ABC : FGH : : ACD : FHI. . ... By the same...there were more triangles. " And from this series df equal ratios, we conclude that the sum of the antecedents ABC + ACD + ADE, or the polygon ABCDE,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 359 pages
...ACD, FHI, we shall have ACD : FHI : : AC2 : FH2; therefore, by reason of the common ratio, AC2 : FH2, we have ABC : FGH : : ACD : FHI. By the same mode...ratios, we conclude that the sum of the antecedents ABC + ACD + ADE, or the polygon ABCDE, is to the sum of the.consequents FGH + FHI + FIK, or to the...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 384 pages
...equal ratios, we conclude that the sum of the antecedents ABC + ACD + ADE, or the polygon ABCDE,is to the sum of the consequents FGH + FHI + FIK, or...one antecedent ABC, is to its consequent FGH, or as AB2 is to FG2 (Prop. XXV.) ; hence the areas of similar polygons are to each other as the squares described...
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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 96 pages
...AC2 : FH2 ; and since ACD, FHI, are similar, ACD : FHI : : AC2 : FH2 ; hence (B. IV. Prop. 4, Cor. 2) ABC : FGH: : ACD : FHI ; by the same mode of reasoning we should find ACD : FHI : : ADE : FIK ; writing these last two proportions as a continued proportion, ABC : FGH : : ACD : FHI : : ADE : FIK...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 237 pages
...FHI : : AC3 : FH2 ; therefore, (11. 3,) ABC : FGH : : ACD : FHI. By the same mode of reasoning, we find ACD : FHI : : ADE : FIK; and so on, if there were more triangles. And from this se ries of equal ratios, we have the sum of the antecedents ABC + ACD+ADE, or the polygon ABCDE, to...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...mode of reasoning, we should find ACD : GKL : : ADF : GLM; and so on, if there were more triangles. From this series of equal ratios, we conclude that the sum of the antecedents ABC + ACD+ADF, or the polygon ABCDF, is to the sum of the consequents GHK + GKL + GLM, or the polygon...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...reason of the common ratio, AC to FH , we have (B, IL, p. 4, c.) ABC : FGH :: ACD : FHI. By the same reasoning, we should find ACD : FHI :: ADE : FIK;...ratios, we conclude that the sum of the antecedents ABC -{-ACD -\-ADE, which make up the poly* gon AEDCB, is to the sum of the consequents FGH+ FHI+FIK,...
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