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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.
Elements of Arithmetic, Algebra, and Geometry - Strona 107
autor: George Lees - 1826
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## Clavis Arithmeticae: Or, A Key to Arithmetick in Numbers & Species ;wherein ...

John Parsons - 1705 - Liczba stron: 162
...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,...
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## A Compendium of Algebra: To which is Added, a Treatise of Interest and ...

John Ward - 1724 - Liczba stron: 220
...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...
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## Short, but yet plain elements of geometry: shewing how by a brief and easie ...

Ignace Gaston Pardies - 1734 - Liczba stron: 164
...never fo 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.) - 1747 - Liczba stron: 480
...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 and ..., Tom 2

Isaac Dalby - 1806
...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 = bf Therefore ad + ag = be + bf...
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## A Course of Mathematics ...: Designed for the Use of the Officers and ..., Tom 1

Isaac Dalby - 1807
...PC. And if any number of right lines are proportional, BR : BS :: RD : SP :: DA : PC ; then, as any antecedent is to its consequent, so is the sum of...the antecedents to the sum of all the consequents. For BA is the sum of the antecedents, and BC that of the consequents, and the corresponding segments...
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## Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - Liczba stron: 493
...named inverse, or ptrturbate, equality. PROP. XIX. THEOR. If there be any number of proportionals, as one antecedent is to its consequent, so is the...antecedents to the sum of all the consequents. Let A:B::C:D::E:F::6:H; then A:B::A+C +E+G:B + D+F+H. Because A : B : : C : D, AD=BC ; and since A : B...
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## Practical Arithmetic: In Four Books ... Extracted from the Large and Entire ...

John Gough - 1813 - Liczba stron: 348
...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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## A Course of Mathematics: Designed for the Use of the Officers and ..., Tom 2

Isaac Dalby - 1813
...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, &c. then a : a :•• b •• b whence ab = ab a:b::e:d, ad=.cb a:b::f\g ag =fb, &c....
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## Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - 1817 - Liczba stron: 432
...named inverse, or perturbate, equality. PROP. XIX. THEOR. If there be any number of proportionals, as one antecedent is to its consequent, so is the...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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