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" When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. "
Short, But Yet Plain Elements of Geometry: Shewing how by a Brief and Easie ... - Page 82
by Ignace Gaston Pardies - 1734 - 164 pages
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Clavis Arithmeticae: Or, A Key to Arithmetick in Numbers & Species ;wherein ...

John Parsons - Algebra - 1705 - 284 pages
...THEOREM 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, &c. For fince...
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A Compendium of Algebra: To which is Added, a Treatise of Interest and ...

John Ward - Algebra - 1724 - 242 pages
...fo many Quantities are in 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 bbbb_ bbbbb...
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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
...fo 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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A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 2

Isaac Dalby - Mathematics - 1806 - 526 pages
...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 a- * •••fg "g =...
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A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 1

Isaac Dalby - Mathematics - 1807 - 476 pages
...a rank of proportionals standing in order, two and two. — As any antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. Let the proportionals be 3 : 5 : : 9 : 15 : : 36 : 60. Then 3 : 5 (or 9 : 15) : ;3 + 9...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...PROP. 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...
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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....
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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,...
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A Treatise of Practical Arithmetic

Robert Patterson - Arithmetic - 1819 - 174 pages
...and 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...
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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,...
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