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" If any number of magnitudes are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. "
A Course of Mathematics ...: Designed for the Use of the Officers and Cadets ... - Page 55
by Isaac Dalby - 1806
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Clavis Arithmeticae: Or, A Key to Arithmetick in Numbers & Species ;wherein ...

John Parsons - Algebra - 1705 - 284 pages
...7. In Proportional Quantities how many foever they be, as one Antecedent is to its Confeqnenti fo is the Sum of all the Antecedents to the Sum of all the Confequents, As if A : a :: B : i :: C : c :: D : i/, &c. then will ^ : d :: ,4+B+C+D, &C. . a+b+c+d,...
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A Compendium of Algebra: To which is Added, a Treatise of Interest and ...

John Ward - Algebra - 1724 - 242 pages
...continued Proportion 5 it will always be, As one of the Antecedents : Is to its Confequent : : So is the Sum of all the Antecedents : To the Sum of all the Confequents. T, . . . . . bb bbb bbbb That is, a : b : : a4- b + — -\ -4- : 1 ' a aa ' aaa ,bb bbb...
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Short, But Yet Plain Elements of Geometry: Shewing how by a Brief and Easie ...

Ignace Gaston Pardies - Geometry - 1734 - 192 pages
...many Quantities are thus proportional : It will be as any one Antecedent to its Confequent: : So is the Sum of all the Antecedents to the Sum of all the Confequents. v. gr. If 4 : la :: a : 5, : : 3 : 9 : : 5 : 15 : then fhall 14 141:: 4:11. I4< If a :...
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The Young Mathematician's Guide: Being a Plain and Easy Introduction to the ...

John Ward (of Chester.) - Mathematics - 1747 - 516 pages
...many Quantities are in -ff ¡t will be, as any one of the Antecedents js to it's Confequents ; fp is the Sum of all the Antecedents, to the Sum of all the Confequents. , fa . ae . aee.aeee.aeeee. aeíí &c. increafmg, ^fSln\ aaa '* a г , r thcfe. I a ....
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...XIX. THEOR. If there be any 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, AD=BC ; and since A : B:: E: F,...
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Practical Arithmetic: In Four Books ... Extracted from the Large and Entire ...

John Gough - Arithmetic - 1813 - 358 pages
...Proposition f. In r.ny geometrical progression, as any one of the antecedents is to its consequent/so is the sum of all the antecedents to the sum of all the consequents, 2, 4 S, 16, 32, 6*, &c. 2 : 4 : : 2+4-f-8-fl6-( 32(62] !-f 8+16+32-f 64(124) Problem II. To continue...
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Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - Geometry - 1817 - 456 pages
...XIX. THEOR. If there be any 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,...
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An Elementary Treatise on Algebra

Bewick Bridge - Algebra - 1818 - 254 pages
...quantities, "•' a : b :• с : d : : e • /:: g. h &c. &c., then will the ßrst be •" to the second as the sum of all the antecedents to the sum of " all the consequents." And so on for any number of these proportions. Тн. 15. " If there be a set of quantities, a, b, c,...
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A Treatise of Practical Arithmetic

Robert Patterson - Arithmetic - 1819 - 174 pages
...the sum of all the consequents = s — I : but as one of the antecedents is to its consequent, so is the sum of all the antecedents, to the sum of all the consequents-)-. That is, / : IR : : s — g : * — /. Ilente - — Rg l- Theor. 1. And from the above r series it...
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A Treatise on the Elements of Algebra

Bewick Bridge - Algebra - 1821 - 648 pages
...proportional quantities, " a:b::c:d :: e :f :: g : h &c.&c., then will thejfrj/ be " to the second as the sum of all the antecedents to the sum of " all the consequents." And so on for any number of these proportions. TH. 15. " If there be a set of quantities, a, b, c,...
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