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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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A Hand-book of Requirements for Admission to the Colleges of the United ...

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...
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Algebra for the Use of Colleges and Schools: With Numerous Examples

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....
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Elementary algebra, with brief notices of its history

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,...
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The Collegiate Algebra: Adapted to Colleges and Universities

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...
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The Cambridge Examiner, Volume 1

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...
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The student's algebra

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= -,, .....
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The first six books of the Elements of Euclid, and propositions i.-xxi. of ...

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,...
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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

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,...
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The Elements of Plane and Solid Geometry ...

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....
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The Elements of Plane and Solid Geometry: With Numerous Exercises

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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