 | Bewick Bridge - 1839 - Liczba stron: 280
...proportional quantities, a : b :: c : d :: e :f:: g : h &c., then will the first be to the second as the sum of all the antecedents to the sum of all the consequents." For, since ab=ba, and (by THS. 1 and 5)ad=bc,af=be,ah= bg, &c-, we have ab+ad+af+ah+&!.c.—ba+bc+be+bg+f&c.,... | |
 | Euclides - 1840 - Liczba stron: 192
...ABC : FGH : : ACD : FHK : : ADE : FKL ; and as one of the antecedents is to one of the consequents, so is the sum of all the antecedents to the sum of all the consequents, that is to say, the similar triangles have to one another the same ratio as the polygons (v. Prop.... | |
 | John D. Williams - 1840 - Liczba stron: 634
...proportional quantities, a : b : : с : d : : e : f : : g : h, Sax,., then will the first be to the second as the sum of all the antecedents to the sum of all the consequents. For, since a6=ba, and (by theorems 1 and 6,) ad = be. а с then -j-^ о а , m eg • hence —=-jj,OTae:bf::cg:t... | |
 | John D. Williams - 1840 - Liczba stron: 216
...proportional quantities, a : b : '• c : d : : e : f: : g : h, &c., then will the first be to the second as the sum of all the antecedents to the sum of all the consequents. For, since ab=ba, and (by theorems 1 and 5,) ad = 4c, af=be, ah=bg, &c., we have a4+iM?+a/+aA+&c.=4a+4c+4e... | |
 | James Wood - 1841 - Liczba stron: 492
...that is, a + b : a — b :: с + d : с - d. 237. When any number of quantities are proportionals, as one antecedent is to its consequent, so is the...antecedents to the sum of all the consequents. Let a : b :: с : d :: e : f, &c. then a : b :: a + c + e + Sxc. : b+d+f+Szc. Because ---, ad"=bc; in the same... | |
 | James Bates Thomson - 1844 - Liczba stron: 268
...given couplets. Cor. If any number of couplets having the same ratio, be added together, the ratio of the sum of all the antecedents, to the sum of all the consequents, will be equal to the ratio of any one antecedent to its consequent. For by adding two couplets having... | |
 | Scottish school-book assoc - 1845 - Liczba stron: 444
...p= • •'• ~ = j ; hence a : e=e :/. QED 113. Prop. 12. If there be any number of proportionals, as one antecedent is to its consequent, so is the...antecedents to the sum of all the consequents. Let a : b=c : d=e :f=:ff '• h ', then For aS=6a, and -Prop. 1st ad=bc, qf=be, and с&=Ьд; therefore by... | |
 | James Wood - 1845 - Liczba stron: 442
...d that is, a + b : a - b :: с + d : с - d. 248. When any number of quantities are proportionals, as one antecedent is to its consequent, so is the...the antecedents to the sum of all the consequents. (Еисып, B. v. Prop, xn.) If a : b :: с : d :: e : /, &c. then a : b :: a + с + e + Sic. : b... | |
 | Admiralty - 1845 - Liczba stron: 152
...: d'" 92. If there be any number of equal ratios, then will one antecedent be to its consequent, as the sum of all the antecedents to the sum of all the consequents. Let a : b : : c : d : : e : f ace that is, — =r— =— then will a : b : : a + c + e : b + d+f ab=ba •. ad— be af=be .-. ab... | |
 | Nathan Scholfield - 1845 - Liczba stron: 894
...number of quantities are proportional, then any one of the antecedents will be tn its consequent as the sum of all the antecedents to the sum, of all the consequents. Let M : N: :P : Q,: :R : S, &c. ; then will M : N: :(M+P +R) : (N+Q+S). For since M • N: :P : Q, we have... | |
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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. 
