 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.  The student's algebra - Page 13by John Darby (teacher of mathematics.) - 1829Full view - About this book
 | 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...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... | |
 | 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, and... | |
 | 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. By (287),... | |
 | 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*/. By (287),... | |
 | Elias Loomis - Geometry - 1895 - 450 pages
...Therefore, by Pr. 2, A - B : A : : C -D : 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 ta their difference. then will A+B: AB ::C+D: CD. ByPr.6, A+B : A ::C+D: C; andbyPr.7, AB: A::CD: C.... | |
 | 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 b a —... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...IX. When four numbers are in proportion, are they 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 ? Is this true when four like magnitudes are in proportion ? when the pairs are unlike... | |
 | 1900 - 650 pages
...= 10 when x = 3, and у = 15 when x = 4 ; find у when x = 10. 5. Prove that when four numbers are proportionals, the sum of the first and second is...difference as the sum of the third and fourth is to their difference. 6. Solve the equation — - За: -~3 =* 10a; + 18. 7. Solve the equations — (6... | |
 | University of Toronto - 1900 - 1164 pages
...of x. 3. (a) If four quantities are proportionals, show that the sum of the first and second of them is to their difference as the sum of the third and fourth is to their difference. (b) Given that pc is greater than, equal to, or less than qd, according as pa is... | |
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