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" If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I. "
Elements of Geometry: With Practical Applications to Mensuration - Page 52
by Benjamin Greenleaf - 1863 - 320 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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A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 2

Isaac Dalby - Mathematics - 1806 - 526 pages
...— a : : d+ c -. d — c. (87.) 91. If there be any number of proportional quantities, Then either antecedent, is to its consequent, as the sum of all the antecedents, to the sum of all the consequents. Let a : b :: c : d : :f:g : Tiien a : b : : c : d, hence ad = be...
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The Modern Preceptor Or a General Course of Education: Containing ..., Volume 1

John Dougall - 1810 - 580 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 ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811
...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 : : OTA : ;B : : A : B, &c ; then will - — A : B : : A + 'A -f nA. : : B + mz + B, &c....
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 1

Charles Hutton - Mathematics - 1812
...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. B -f- B...
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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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Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - Geometry - 1817 - 454 pages
...number of proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. Let A : B : : C : D : : E : F : : G : H; then A : B : : A+C+E+G : B+D+F+H. Because A : B : : C : D, (V. 6.) AD = BC; and, since A...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 618 pages
...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 A For...
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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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