 | Bewick Bridge - Algebra - 1839 - 280 pages
...j-±l—-±l ; .-. = , consequently, O CL O d by Art. 97, a±b :b:: c±d : d. TH. 7. " If four quantities be proportional, the first is to the sum or difference of the first and second as the third to the sum or difference of the third and fourth." For by TH. 6, a±b : b : : c±d : d, and alternately... | |
 | Andrew Bell (writer on mathematics.) - 1839 - 500 pages
...as the sum of the third and fourth to the fourth ; (330.) By addition, when the first is to the sum of the first and second, as the third is to the sum of the third and fourth ; (331.) By division, when the excess of the first above the second is to the... | |
 | John D. Williams - Algebra - 1840 - 216 pages
...— = — 5 — baod consequently, by Art. 80, a-±b : b '.'. c±d : d. TH. 7. If four quantities be proportional, the first is to the sum or difference of the first and second as the third to the sum or difference of the third and fourth. For, by theorem 6, a±4 : b : : c±d . d, and alternately... | |
 | John D. Williams - Algebra - 1840 - 634 pages
...— = — — öd öd consequently, by Art. 80, a±o : b : : c±d : d. Тн. 7. If four quantities be proportional, the first is to the sum or difference of the first and second as the third to the sum or difference of the third and fourth. For, by theorem 6, a±b : b ' '. c±d : d, and alternately... | |
 | George Hutton (arithmetic master, King's coll. sch.) - 1844 - 276 pages
...6: 9:: 8: 12; for 64-9=4, and 84-12=|. 7. If four quantities are proportionals, the first is to the difference of the first and second, as the third is to the difference of the third and fourth; thus if 6 : 3 :: 8:4, then 6 : 6-3 :: 8 : 8-4, or 6 : 3 :: 8 :... | |
 | Euclides - 1846 - 272 pages
...— A to B as C to D, becomes A — B to B as C — I) to D. 18. By Conversion, when it is inferred, that if there be four magnitudes proportional, the...difference of the first and second, as the third is to the sunj or difference of the third and fourth. See Props. 21 and 25, also Cor. 1, Prop. 25. Thus — A... | |
 | Horatio Nelson Robinson - Algebra - 1846 - 276 pages
...: d : : x : y (Theorem 3.) If four magnitudes constitute a proportion, the first may be to the sum of the first and second, as the third is to the sum of the third and fourth. By hypothesis, a : b : : c : d ; then we are to prove that a : a-\-b : : c... | |
 | Horatio Nelson Robinson - Algebra - 1848 - 354 pages
...d : : a; : y (Theorem 3.) If four magnitudes constitute a proportion, the first witt be to the sum of the first and second, as the third is to the sum of the third and fourth. By hypothesis, a : b : : c : d ; then we are to prove that a : ffl+6 : : c... | |
 | James William M'Gauley - 1854 - 284 pages
...extremes, and means, ad-\-bd=bc-\-bd ad=bc 21. We may add: and, then, "the first term is to the sum of the first and second, as the third is to the sum of the third and fourth." a: b: :C:d Adding, a:a-\-b: :c:c-\-d Multiplying extremes, and means, ac-\-ad=ac-\-bc... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...proportional, etc. THEOREM VIII. If four magnitudes constitute a proportion, the first icill be to the sum of the first and second as the third is to the sum of the third and fourth. By hypothesis, A : B : : C:2); then we are to prove that A : A + B :: C :... | |
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Convertendo ; when it is .concluded, that if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth. 
