 | George Lees - 1826 - 276 pages
...quantities are proportionals, i 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, &c. Then shall a:b:: «+c+c+&c. : b+d+f+&c. For, since a : b : : c : d, ad = be, (No. 108.;) in like... | |
 | Enoch Lewis - Algebra - 1826 - 180 pages
...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. Let a : b : : c :'d : : e :f : : g : h, &c., then (art. 62.) ad=bc, of— be, ah=bg, &c., also ab=ba. .-. ab+ad+af+ah, &c. =ba+bc+be+bg,... | |
 | John Darby (teacher of mathematics.) - 1829 - 212 pages
...Thus, if a', 6; ;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...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,... | |
 | John Playfair - Geometry - 1829 - 210 pages
...proportional, as one of the antecedents is to its consequent, so is the suril of all the antecedents to the sum of all the consequents. Let A : B : : C : D : : E : F : : G : H, &c. that is, let A : B : : C : D, and A : B : : E : F, &c. then A:B::AfC + K + G:B + D +... | |
 | Charles Hutton - Mathematics - 1831 - 660 pages
...THEOREM LXXII. IP 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 : в : : m\ : тв : : ПА : им, &с. ; then will ... л : в : : A + я** + ЯА : в + MB + яв,... | |
 | Charles Hutton - Mathematics - 1831 - 632 pages
...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 + "»•»•... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...A : A — B='C:C — D. PROPOSITION XVI. THEOREM. If any number of magnitudes be proportional, one antecedent is to its consequent, as the sum of all the antecedents to that of the consequents. Let A : B = C : D, and C : D = E : F, then A : B = A For A : A = B : B,... | |
 | Andrew Bell (writer on mathematics.) - 1839 - 500 pages
...then ac = Ъ . b, and a : b = b : с (357.) (362.) ' If any number of quantities be proportional, one antecedent is to its consequent as the sum of all the antecedents to that of the consequents.1 Let a, 5, c, d, e, and /, be proportional, then a: b = a For - = - ; and... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...14, then 7 : 5 : : 14 : 10. Prop. 6. If several numbers are in proportion, any one antecedent will be to its consequent, as the sum of all the antecedents is to the sum of all the consequents. If 2:4::3:6::5:10: : 7 : 14, then is 2:4:: (2+3+5+7) : (4+6+10+14), or- 2 : 4 : : 17 : 34. Prop. 7.... | |
 | William Scott - Algebra - 1844 - 568 pages
..... ._ a_a+c_a + c+e_ •'• b+d+f+h. . .~?~6~6+3~4+</+/~' ScWhence in every series of equal ratios the sum of all the antecedents is to the sum of all the consequents as one antecedent, a, is to its consequent A, or as a sum of antecedents, a+c, a+c+e, &c., is to a... | |
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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. Let A : B : : C : D : : E : F; then will A : B : : A + C + E : B + D + F. 
