| 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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