 | Elias Loomis - Conic sections - 1880 - 452 pages
...C. PROPOSITION VIII. THEOREM. If four quantities are proportional, the sum of 'the first and second is to their difference as the sum of the third and fourth is to their difference. then will A+B: AB :: C+D: CD. ByPr.6, A+B : A ::C+D: C; and by Pr. 7, AB: A:: CD: C. By alternation... | |
 | James Bates Thomson, Elihu Thayer Quimby - Algebra - 1880 - 360 pages
...:c — d; Also a + b : a — b = с + d : c — d; hence COR. 2. — The sum of the first and second is to their difference as the sum of the third and fourth is to their difference. COR. 3. — In any number of equal ratios, the sum of the antecedents is to the sum of the consequents... | |
 | Elias Loomis - 1880 - 456 pages
..."* ' PROPOSITION VTII. THEOREM. If four quantities are proportional, the sum of the first and second is to their difference as the sum of the third and fourth i» to their difference. then will A+B: AB:: C+D: CD. ByPr.6, A+B : A ::C+D: C ; and by Pr. 7, AB:... | |
 | Elias Loomis - Algebra - 1881 - 398 pages
...c—d that is, 306. If four quantities are proportionaI, the sum of the first and second is to Hieir difference, as the sum of the third and fourth is to their difference. Let a : b : : c : d. By composition, Art. 304, a + b: b:: c+d: d. By alternation, Art. 301, a + b : c + d:: b: d. Also... | |
 | Education, Higher - 1881 - 504 pages
...other is also rational. 13. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. 14. Find the number of 3 digits which is equal to 6 times the number formed by its first and third... | |
 | Charles Scott Venable - 1881 - 380 pages
...VIII. When four quantities are proportionals, the sum of the first and second is to their d1fference, as the sum of the third and fourth is to their difference. If a : b = c : d, then a -f- b : a — b = c + d : c — d, For (Theorem VI.) , . -_- -..„-, a —... | |
 | Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...terms by the same quantity. 3. If four magnitudes be proportionals, the gum of the first and second is to their difference as the sum of the third and fourth is to their difference (componendo et dividendo). 5. If ;two sets of four magnitudes be proportionals, and if we divide corresponding... | |
 | Euclides - 1885 - 340 pages
...terms by the same quantity. 3. If four magnitudes be proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference (componendo et dividendo). 8. If jtwo sets of four magnitudes be proportionals, and if we divide corresponding... | |
 | Elias Loomis - Algebra - 1886 - 396 pages
...— Z< : 6 :: c— e?: ct 306. If four quantities are proportional, the sum of the first and second is to their difference, as the sum of the third and fourth is to their difference. Let a:b::c:d. By composition, Art. 304, a+b: b:: c + d: d. By alternation, Art. 301, a + b: c+d:: b: d.... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...proportion, they are in proportion by composition and division; th<it is, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. Hyp. Let a.: b = c :d. Tn prove a -\- b : a — b = c -f- d : c — d. /W. By (287), ^ = '-£?; and... | |
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If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. 
