 | John Parsons - 1705 - 284 Seiten
...7. In Proportional Quantities how many foever they be, as one Antecedent is to its Confeqnent i 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.... | |
 | John Ward - 1724 - 242 Seiten
...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... | |
 | Ignace Gaston Pardies - 1734 - 192 Seiten
...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 :... | |
 | John Barrow - 1750 - 496 Seiten
...Magnitudes are in continual Proportion, it will be, as any one of the Antecedents, is to its Confequent ; fo is the Sum of all the Antecedents, to the Sum of all the Conjequents. As in thefe a. ar. arr. arrr. arrrr, &c. As a : 'ar : : n -\-ar-\-arr-\-arrr : ar -\-... | |
 | John Ward - 1771 - 510 Seiten
...Number of Quantities are in 4f it will be, as any one of the Antecedents is to it's. Confequent ; fo is the Sum of all the Antecedents, to the Sum' of- all the Confequents. tríele/ / a . ± . — . -f --- 11- . L,. &c. decreafmg. . . fa.ae.aee.aeee. aeeee .... | |
 | Sir John Leslie - 1809 - 542 Seiten
...Cor. Hence also, if A:B::C:D and B:E::F:C; then E: A:: D: F. The principle of this and the preceding Proposition, is named inverse, or perturbate, equality....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::... | |
 | Sir John Leslie - 1809 - 522 Seiten
...A :: D : F. The principle of this and the preceding Proposition, is named inverse, or perturfrate, equality. PROP. XIX. THEOR. If there be any number...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,... | |
 | Sir John Leslie - 1811 - 524 Seiten
...A : B : : C : D and B : E : : F : C ; then E : A : : D : F. The principle of this and the preceding Proposition, is named inverse, or perturbate, equality....antecedent is to its consequent, so is the sum of ail the antecedents to the sum of aH the consequents. Let A : B :: C: D :: E : F :: G: H; then A: B::... | |
 | Isaac Dalby - 1813 - 538 Seiten
...If there be any number of proportional quantities, The» 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 •• •• bb whence ab = ab a\b::c:d, ad=zcò a:b::/:g ag =//>, Sec.... | |
 | John Gough - 1813 - 358 Seiten
...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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Proposition is 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 sum of all the antecedents to the sum of all the consequents. . 
