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 Βιβλία Βιβλία 1 - 10 από 140 για In a series of equal ratios, any antecedent is to its consequent, as the sum of all.... In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art. Elements of Plane Geometry: For the Use of Schools - Σελίδα 54
των Nicholas Tillinghast - 1844 - 96 σελίδες
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο ## A new treatise of arithmetick and book-keeping

Alexander Malcolm - 1718 - 245 σελίδες
...middle Terms are the fame. Propofoion 4th, IF four (or more) Numbers arc in Geometrical Proportion; the Sum of all the Antecedents is to the Sum of all the Confequents, in the fame Rath, as any one of thefe Antecedents is to its Confequent. Example, If it... ## A New System of Arithmetick Theorical and Practical: Wherein the Science of ...

Alexander Malcolm - 1730 - 627 σελίδες
...that b— a :/— a: : л : t — l::b: s — a. Thus; Of any Number of lîmilar and equal Ratios, the Sum of all the Antecedents is to the Sum of all the Confequents as any one of the Antecedents to its Confequent (by Thetr. IV. Ceroll. y: Bot in cafe of... ## The Modern Preceptor Or a General Course of Education: Containing ..., Τόμος 1

John Dougall - 1810 - 580 σελίδες
...which each partner has contributed. From the nature of proportionals it follows that of any series, the sum of all the antecedents is to the sum of all the consequents, as each antecedent is to its consequent : that is, that the sum of all the shares is to the sum of... ## A Course of Mathematics: For the Use of Academies as Well as ..., Τόμος 1

Charles Hutton - 1812
...ratio. >«AA THEOREM LXXII. If any Number of Quantities be Proportional, then any one of the Antecedents will be to its Consequent, as the Sum of all the Antecedents is to the Sum of all the Consequents. LET A : B : : MA : »>B : : "A : HB, Sec ; then will A : D : : A + ntA + «A : : B -f m& + na, See.... ## The Young Man's Best Companion and Guide to Useful Knowledge

John Dougall - 1815 - 476 σελίδες
...contributed to that,stock. From the nature of proportional quantities it follows that in any number the smh of all the antecedents is to the sum of all the consequents, as each antecedent is to its consequent : or in other words that the sum of all the shares is to the... ## A Course of Mathematics in Two Volumes for the Use of Academies, as ..., Τόμος 1

Charles Hutton - 1816
...ratio. fltA A THEOREM LXXH. If any Number of Quantities be Proportional, then any one of the Antecedents will be to its Consequent, as the Sum of all the Antecedents h to the Sum of all the Consequents. LET A : B : : 7BA ' WB : : JJA : «B, &C ; thenwill - --- A k... ## A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - 1822
...OTB±mnA B±nA THEOREM LXXII. If any Number of Quantities be Proportional, then any one of the Antecedents will be to its Consequent, as the Sum of all the Antecedents is to the Sum of all the Consequents. LET A : B : : mA : mB : : nA : UB, &c ; then will ---- A : B ;; A-{-n»Af-ftA ;; B+ms-4-nB, &c. A+»nA+nA... ## Elements of Arithmetic

Etienne Bézout - 1824 - 219 σελίδες
...purpose is founded upon the principle established in article (186), that if many equal ratios are given, the sum of all the antecedents is to the sum of all the consequents, as one antecedent is to its consequent. From this principle we deduce the following example. EXAMPLE... ## The student's algebra

...;c',d, then will b ; a ; ; d ; c. 8. If a number of quantities be proportionals, the antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Thus, if a;6::c:rf::a::y::r:s, then will «:&::a+ctx+r;b + d+ y + s. 9. If four quantities be proportionals,... ## A Course of Mathematics: For the Use of Academies, as Well as ..., Τόμος 1

Charles Hutton - 1831
...тл А THEOREM LXXII. IF any number of quantities be proportional, then any one of the antecedents will be to its consequent, as the sum of all the antecedents, is to the sum of all the conse^uents. Let A : в : : тл : тв : : пл : кн, &с. ; then will ... 'А : в : : А + "»•»•...