 | Euclides - 1840 - 192 pàgines
...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 - 634 pàgines
...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 - 216 pàgines
...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 - 492 pàgines
...a — о с - a 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,...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... | |
 | James Bates Thomson - 1844 - 268 pàgines
...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 - 444 pàgines
...multiplying these equals together, ^ X j = ¿ X p= • •'• ~ = j ; hence a : e=e :/. QED 113. Prop. 12. If there be any number of proportionals, as one antecedent...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... | |
 | James Wood - 1845 - 442 pàgines
...a — b с — 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,...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... | |
 | Nathan Scholfield - 1845 - 894 pàgines
...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... | |
 | Admiralty - 1845 - 152 pàgines
...: 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... | |
 | Dennis M'Curdy - 1846 - 166 pàgines
...the ratios of ABE to FGL, BCE to GHL, and CDE to HKL are all equal ; and, as one of the antecedents is to its consequent, so is the sum of all the antecedents to the sum of all the consequents (4). Thus the ratio of ABE to FGL equals that of ABCDE to FGHKL ; which is the duplicate ratio of the... | |
| |
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. 
