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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. "
An Introduction to Geometry and the Science of Form: Prepared from the Most ... - Page 154
by Anna Cabot Lowell - 1846 - 161 pages
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A New Treatise of Arithmetick and Book-keeping ...: The Whole Illustrated ...

Alexander Malcolm - Arithmetic - 1718 - 396 pages
...Extremes and 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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Elements of Geometry: Including Plane, Solid, and Spherical Geometry

George Washington Hull - Geometry - 1807 - 408 pages
...Ax. 2 bn dq Whence am : bn = cp : dq. QED PROPOSITION XV. THEOREM. 133. In a series of equal ratios, the sum of all the antecedents is to the sum of all the consequents an any antecedent is to its consequent. Let a : b= c : d = e :/. Let r = the common ratio, Then r =...
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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 all...
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811
...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 +...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 1

Charles Hutton - Mathematics - 1812
...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 sum...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 618 pages
...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...consequents, as one antecedent is to its consequent. From this principle we deduce the following example. EXAMPLE I. It is required to divide 120 into three...
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The student's algebra

John Darby (teacher of mathematics.) - 1829 - 214 pages
...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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