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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

## 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...

## 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...

## 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...

## 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,...

## Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 372 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...

## 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...

## 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...

## 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...