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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.
The first principles of algebra, for the use of the boys of the Royal ... - Page 118

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,...

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...

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 :...

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 ....

A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 2

Isaac Dalby - Mathematics - 1806 - 526 pages
...-. 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,...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...

A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 1

Isaac Dalby - Mathematics - 1807 - 476 pages
...are proportional, BR : BS :: RD : SP :: DA : PC ; then, as any antecedent is to its consequent, so is the sum of all 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...

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,...

A Course of Mathematics: Designed for the Use of the Officers and ..., Volume 2

Isaac Dalby - Mathematics - 1813 - 538 pages
...: 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, &c. then a : a :•• b •• b whence ab = ab a:b::e:d, ad=.cb a:b::f\g ag =fb, &c....