 | Isaac Todhunter - 1858 - 530 pàgines
...г = - . а-b c—d or, a + b : а— b :: c + d : c- d. 397. ÏTAeи any number of quantities are proportionals, as one antecedent is to its consequent,...is the sum of all the antecedents to the sum of all tlie consequents. Let a : b :: с : d :: e : f; then, a : b :: a + c + e : b +d+f. For ad=bc, and af=... | |
 | James Elliot - 1860 - 252 pàgines
...and so on. THEOREM VIII. If any Number of Quantities are Proportionals, 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. Thus, if a : p : : b : q : : c : r, then a : p : : a + b + c : p + q + r. DEM. Since a : p :: b : q,... | |
 | Euclides - 1860 - 288 pàgines
...10). PROPOSITION XII. THEOREM. If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so is the sum of all the antecedents to that of the consequents. Given A : B : : C : D, and C : D : : E : F ; to prove that A:B::A+C + E:B... | |
 | Robert Fowler - 1861 - 426 pàgines
...a : I : : m : t. xi. When any number of magnitudes are proportionals, 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. Let a : Ъ : : с : d : : e : f, Then shall о : Ъ : : a + с + e : Ь + d +f; а с а е For =- = -... | |
 | James Bryce - 1861 - 376 pàgines
...± a : b : : d ± с : d. 184. When any number of quantities are proportionals, as one antecedent и to its consequent, so is the sum of all the antecedents to the sum of all the consequents. Let there be any number of proportionals, a :b : : с : d : : e :f ; then ad = bc, and af=be; also ab =... | |
 | Isaac Todhunter - 1866 - 618 pàgines
...is, 7 = -. ; a—bc — d or a+b : a— b :: с + d : c — d. 397. 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; then a : b :: a + с +e : b + d +f. For ad=bc, and af= be, (Art. 386), also... | |
 | James Pryde - 1867 - 506 pàgines
...a c—da — b c—d 42. THEOREM. — If there be any number of quantities which are proportional, as one antecedent is to its consequent, so is the...the antecedents to the sum of all the consequents. _,. ace , a a+ с +е Given ъ = -d=j; to prove that y = T . a ce Then since -r = r, .'. a = rb; and... | |
 | Isaac Todhunter - 1870 - 818 pàgines
...is, í = -•,', ab cd or a + b : a — b :: c + d : c — d. 397. 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; then a : b :: a+c + e : For ad=bc, and o/= be, (Art. 386), also ab = ba ;... | |
 | James Bryce - 1872 - 386 pàgines
...Also, b : 6 ± a : :d :d± c, and b ± a : b : : d ± с : d. 184. When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of аи the antecedents to the sum of all the consequents. Let there he any number of proportionals, a... | |
 | Thomas Kimber - 1874 - 352 pàgines
...proportionals ? Prove that if any number of quantities be in continued proportion, as one of the antecedents is to its consequent so is the sum of all the antecedents to the sum of all the consequents. 9. Prove the rule for finding the sum to и terms of an arithmetic series of which the first term and... | |
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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. 
