| 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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