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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. "
An Easy Introduction to the Mathematics: In which the Theory and Practice ... - Page 66
by Charles Butler - 1814
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Plane and Solid Geometry: Inductive Method

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...
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Plane and Solid Geometry

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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Annual Report of the Commissioners ..., Volume 66

1900 - 652 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...their 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...
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Examination Papers

University of Toronto - 1900 - 1160 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...
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First Course in Algebra: With Eight Thousand Examples Including Three ...

Albert Harry Wheeler - Algebra - 1908 - 698 pages
...terms may be combined by addition and subtraction ; that is, the sum of the first and second terms is to their difference as the sum of the third and fourth terms is to their difference. (3) may be obtained as follows : Expressing the ratios of the given proportion...
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School Algebra

James William Nicholson - Algebra - 1909 - 332 pages
...composition and division. If four numbers are in ргороШоп, then the sum of the first and second terms is to their difference as the sum of the third and fourth terms is to their difference. HINT. By 303, By 304, ~l- = e-. (2) а +_'/ Divide (1) by (2)...
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The Philosophical Magazine: Comprehending the Various Branches of ..., Volume 33

Physics - 1809 - 550 pages
...— , that is, a — b : b : : c — d : d. Article VI. — When four quantities are proportional, the sum of the first and second is, to their difference,...the sum of the third and fourth to their difference ; that is, when a : b : : c : d , then will a + b : a — b : : c + d : c •— d. For, by Art. IV.,...
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Report of the Minister of Education

Education - 1869 - 464 pages
...sum at a given rate per cent, in a given time. 3. Prove that if any four quantities 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. 4. Define what is meant by " Compound Proportion." 5. Give and prove a rule...
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