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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 Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... - Pągina 161
per Sir John Leslie - 1809 - 493 pągines
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## Clavis Arithmeticae: Or, A Key to Arithmetick in Numbers & Species ;wherein ...

John Parsons - 1705 - 162 pągines
...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 - 220 pągines
...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 - 164 pągines
...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 - 480 pągines
...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. aeķķ &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 ..., Volum 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...
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## A Course of Mathematics ...: Designed for the Use of the Officers ..., Volum 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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## Practical Arithmetic: In Four Books ... Extracted from the Large and Entire ...

John Gough - 1813 - 348 pągines
...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 - 1817 - 432 pągines
...terms, and may, therefore, be more generally expressed thus : A : B : : Cor. 2. Hence, in continued proportionals, as one antecedent is to its consequent, so is the sum or difference of the several antecedents to the corresponding sum or difference of the consequents....
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## An Elementary Treatise on Algebra

Bewick Bridge - 1818 - 227 pągines
...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 - 1819 - 156 pągines
...antecedents will = « — g, 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 r series it...
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