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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 from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...reason of the common ratio, AC to FH , we have (B. n., p. 4, c.) ABC : FGH : : ACD : FHI. By the same reasoning, we should find ACD : FHI : : ADE : FIK; and so on, if there were more triangles. And from th1s .series of equal ratios, we conclude that the sum of the antecedents ABC+ACD+ADE, which makes...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1857 - 444 pages
...reason of the common ratio, AC to FH , we have (B. n., p. 4, c.) ABC : FGH : : ACD : FHI. By the same reasoning, we should find ACD : FHI : : ADE : FIK;...conclude that the sum of the antecedents ABC+ACD+ADE, which makes up the polygon AEDCB, is to the sum of the consequents FGH+ FHI+FIK, which makes up the...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 628 pages
...were more triangles. Therefore the sum of the antecedents ABC, ACD, ADE, which compose the area of the polygon ABCDE, is to the sum of the consequents FGH, FHI, FIK, which compose the area of the polygon FGHIK, as any one antecedent ABC is to its consequent FGH (Prop....
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 pages
...were more triangles. Therefore the sum of the antecedents ABC, ACD, ADE, which compose the area of the polygon ABCDE, is to the sum of the consequents FGH, FHI, FIK, which compose the area of the polygon FGHIK, as any one antecedent ABC is to its consequent FGH (Prop....
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...were more triangles. Therefore the sum of the antecedents ABC, ACD, ADE, which compose the area of the polygon ABCDE, is to the sum of the consequents FGH, FHI, FIK, which compose the area of the polygon FGHIK, as any one antecedent ABC is to its consequent FGH (Prop....
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1866 - 328 pages
...therefore (Prop. X. Bk. II.), ABC:FGH::ACD:FHI. By the same mode of reasoning, it may be proved that ACD : FHI: : ADE : FIK, and so on, if there were more triangles. Therefore the sum of the antecedents ABC, ACD, ADE, which compose the area of the polygon ABCDE, is...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 338 pages
...were more triangles. Therefore the sum of the antecedents ABC, ACD, ADE, which compose the area of the polygon ABCDE, is to the sum of the consequents FGH, FHI, F1K, which compose the area of the polygon FGHIK, as any one antecedent ABC is to its consequent FGH...
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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...therefore (Theo. IX. Bk. II.), ABC: FGH::ACD: FH I. Bv the same mode of reasoning, it may be proved that ACD: FHI: : ADE : FIK, and so on, if there were more triangles. Therefore the sum of the antecedents ABC, ACD, ADE, which compose the area of the polygon ABCDE, is...
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New Elementary Geometry: With Practical Applications : a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1874 - 206 pages
...were more triangles. Therefore the sum of the antecedents ABC, ACD, ADE, which compose the area of the polygon ABCDE, is to the sum of the consequents FGH, FHI, FIK, which compose the area of the polygon FGHIK, as any one antecedent ABC is to its consequent FGH(Theo....
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New Elementary Geometry, with Practical Applications

Benjamin Greenleaf - Geometry - 1875 - 204 pages
...(Theo. IX. Bk. II.), ABC : FGH : : A CD : FH I. Bv the same mode of reasoning, it may be proved that ACD: FHI: : ADE : FIK, and so on, if there were more triangles. Therefore the sum of the antecedents ABC, ACD, ADE, which compose the area of the polygon ABCDE, is...
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