 | Robert Potts - 1879 - 668 pages
...b c-\-d с — da^-b c-\-<l b " ddd ' a — Ь~ с — d' and «+i : a — b : : c-\-d : e — d or the sum of the first and second is to their difference, as the sum of tho third and fourth is to their difference. 7. Prop. If four quantities of the same kind be proportionals,... | |
 | Benjamin Greenleaf - Algebra - 1879 - 350 pages
...: Ъ : : с — d : d. THEOREM VIII. 322, If four quantities be in proportion, the sum of the jirst and second is to their difference as the sum of the third and fourth is to their difference. Let a : b : : с : d; Then, a -f- 6 : a — 6: : с -\- d : с — d By Theo.... | |
 | James Bates Thomson, Elihu Thayer Quimby - Algebra - 1880 - 360 pages
...Therefore, а + b: c + d = a — b :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... | |
 | Education, Higher - 1881 - 504 pages
...obtained by dividing one by the 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... | |
 | James Mackean - 1881 - 510 pages
...II., —т— = — j— , ... а-b:b::с -d:d. This is called Division, or Dividendo. PROP. XIII. — The sum of the first and second is to their difference as tlie sum of the third and fourth is to tlieir difference. mi TTT а + bc + d Theorem III., 5= -,, ..... | |
 | Euclides - 1885 - 340 pages
...and increased by increasing its 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,... | |
 | Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...increased by increasing its 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,... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...If four quantities are in 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.... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...four quantities are in proportion, they are in proportion by composition and division; that is, (he 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. To prove a-\-b: a — b = c -\- d : c — d. Pro*/.... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...If four quantities are in proportion, they are in proportion by Composition and Division; that is, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. Let To prove (By 204), and (by 205) hv division. a: b a + b : a - - b a + b... | |
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If four magnitudes 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. 
