 | 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... | |
 | 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... | |
 | 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.... | |
 | 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.... | |
 | 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.... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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.... | |
 | 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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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... 
