 | Universities and colleges - 1879 - 86 pages
...equal sides are parallel, and the figure is a parallelogram. 2. 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 tlieir difference. 3. The diameter which is perpendicular to a chord bisects the chord and also... | |
 | Isaac Todhunter - Algebra - 1879 - 848 pages
...a : a — b :: с : с — d. This operation is called convertendo. 396. WJien four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third fourth is to their difference. If a : b :: с : d, then a + b : a — b :: c + d : c — d. By Art.... | |
 | 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,... | |
 | 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
...of the quotient obtained by dividing one by the other is also rational. 13. When four quantities are proportionals, the sum of the first and second is...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
...the same quantity, and increased by increasing its terms by the same quantity. 3. If four magnitudes be proportionals, the sum of the first and second...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*/.... | |
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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. 
