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" In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art. "
Elements of Plane Geometry: For the Use of Schools - Page 54
by Nicholas Tillinghast - 1844 - 96 pages
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A New Treatise of Arithmetick and Book-keeping ...: The Whole Illustrated ...

Alexander Malcolm - Arithmetic - 1718 - 396 pages
...middle Terms are the fame. Propofoion 4th, IF four (or more) Numbers arc in Geometrical Proportion; the Sum of all the Antecedents is to the Sum of all the Confequents, in the fame Rath, as any one of thefe Antecedents is to its Confequent. Example, If it...
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A New System of Arithmetick Theorical and Practical: Wherein the Science of ...

Alexander Malcolm - Algebra - 1730 - 627 pages
...that b— a :/— a: : л : t — l::b: s — a. Thus; Of any Number of lmilar and equal Ratios, the Sum of all the Antecedents is to the Sum of all the Confequents as any one of the Antecedents to its Confequent (by Thetr. IV. Ceroll. y: Bot in cafe of...
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The Modern Preceptor Or a General Course of Education: Containing ..., Volume 1

John Dougall - 1810 - 554 pages
...which each partner has contributed. From the nature of proportionals it follows that of any series, the sum of all the antecedents is to the sum of all the consequents, as each antecedent is to its consequent : that is, that the sum of all the shares is to the sum of...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 1

Charles Hutton - Mathematics - 1812
...ratio. >AA THEOREM LXXII. If any Number of Quantities be Proportional, then any one of the Antecedents will be to its Consequent, as the Sum of all the Antecedents is to the Sum of all the Consequents. LET A : B : : MA : >B : : "A : HB, Sec ; then will A : D : : A + ntA + A : : B -f m& + na, See....
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The Young Man's Best Companion and Guide to Useful Knowledge

John Dougall - Encyclopedias and dictionaries - 1815 - 516 pages
...contributed to that,stock. From the nature of proportional quantities it follows that in any number the smh of all the antecedents is to the sum of all the consequents, as each antecedent is to its consequent : or in other words that the sum of all the shares is to the...
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A Course of Mathematics: In Two Volumes : for the Use of Academies, as Well ...

Charles Hutton - Mathematics - 1816
...ratio. fltA A THEOREM LXXH. If any Number of Quantities be Proportional, then any one of the Antecedents will be to its Consequent, as the Sum of all the Antecedents h to the Sum of all the Consequents. LET A : B : : 7BA ' WB : : JJA : B, &C ; thenwill - --- A k...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 618 pages
...OTBmnA BnA THEOREM LXXII. If any Number of Quantities be Proportional, then any one of the Antecedents will be to its Consequent, as the Sum of all the Antecedents is to the Sum of all the Consequents. LET A : B : : mA : mB : : nA : UB, &c ; then will ---- A : B ;; A-{-nAf-ftA ;; B+ms-4-nB, &c. A+nA+nA...
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Elements of Arithmetic

Etienne Bzout - Mathematics - 1824 - 219 pages
...purpose is founded upon the principle established in article (186), that if many equal ratios are given, the sum of all the antecedents is to the sum of all the consequents, as one antecedent is to its consequent. From this principle we deduce the following example. EXAMPLE...
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The student's algebra

John Darby (teacher of mathematics.) - 1829 - 214 pages
...;c',d, then will b ; a ; ; d ; c. 8. If a number of quantities be proportionals, the antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Thus, if a;6::c:rf::a::y::r:s, then will :&::a+ctx+r;b + d+ y + s. 9. If four quantities be proportionals,...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 1

Charles Hutton - Mathematics - 1831 - 634 pages
...тл А THEOREM LXXII. IF any number of quantities be proportional, then any one of the antecedents will be to its consequent, as the sum of all the antecedents, is to the sum of all the conse^uents. Let A : в : : тл : тв : : пл : кн, &с. ; then will ... 'А : в : : А + "••...
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