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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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New Elementary Algebra

Benjamin Greenleaf - 1876 - 332 pages
...b : : c : d ; then, a — b : b : : c — d THEOREM VIII. 322, If four quantities be in proportion, the sum of the first and second is to their difference as the sum of tht third and fourth is to their difference. Let a : b : : c : d; Then, a-\-b : a — 6: : c-\-d :...
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Elementary Arithmetic: With Brief Notices of Its History, Volumes 1-12

Robert Potts - Arithmetic - 1876 - 418 pages
...sum or difference of the third and fourth has to the fourth. 5. 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. 6. If the corresponding terms of two proportions be multiplied together,...
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Elementary Arithmetic: With Brief Notices of Its History, Volumes 1-12

Robert Potts - Arithmetic - 1876 - 392 pages
...sum or difference of the third and fourth has to the fourth. 5. 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. 6. If the corresponding terms of two proportions be multiplied together,...
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A Mathematical Course for the Matriculation Examination of the ..., Part 1

1877 - 188 pages
...6 : a + a Ь _ a* — a* b* ¡Hfl a2 — 6* a* + 6* a« — 6»' 7. Show 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. If a : L : : с : d, show that 8. Find the sum of a given number of terms of...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...Therefore, by Pr.l, 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 to their difference. Let A:B::C:D; then will A+B: A— B::C+D: C— D. ByPr.6, A+B : A::C+D:C; and...
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Mathews' matriculation mathematics: being all the papers in arithmetic and ...

London univ, exam. papers - 1878 - 164 pages
...expression ; and determine its numerical value when a=2b: — a ab a2 aW 7. Show 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. If a : b : : a : d show that 8. Find the sum of a given number of terms of...
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Annual Report

Public schools - 1878 - 710 pages
...value of s/97 + 56^/3— v/97 — 56^3. (•) (/>) Prove that " 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 their difference." (') 6. (a) From two towns 102 miles apart, A and B set out to meet each other:...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...— , we have AC AB : A :: CD : C. Proposition 11. Theorem. — If four quantities be 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. If A : B : : C : D, then A+B : AB : : C+D : CD. From (IV. 9) From (IV. 10)...
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Elementary algebra: with brief notices of its history

Robert Potts - Algebra - 1879 - 672 pages
...first and second, is to the second, as the difference of tJie third and fourth is to the fourth. (3) The sum of the first and second is to their difference, as the sum of the third and fourth is to their difference. (Eue. V. 17, 18.) (1) Since a : b : : с : d, .'. - - - , add 1 to these equals...
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New Elementary Algebra: Designed for the Use of High Schools and ..., Book 1

Benjamin Greenleaf - Algebra - 1879 - 350 pages
...travel A,s distance. How far did each travel ? 10. Prove that "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 their difference." 1. Add 3. Find a number of three digits, such thnt the sum of the digits shall...
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