 | Dennis M'Curdy - 1846 - Liczba stron: 166
...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... | |
 | Charles William Hackley - 1846 - Liczba stron: 542
...quantities, the first will have to the second the same ratio that t}ie sum of all the antecedents has to the sum of all the consequents. Let a, b, c, d, e, f, g, h be any number of proportional quantities, such that a:b::c:d::eif:igzhr Then a:l>::a+c+e+g:b+d+f+h.... | |
 | James Bates Thomson - 1846 - Liczba stron: 276
...what is the ratio of their sum or difference ? In several couplets of equal ratios, what ratio has the sum of all the antecedents to the sum of all the consequents ? 3. If the antecedent of a couplet be 65, and the ratio 13, what is the consequent1? 4. If the consequent... | |
 | Great Britain. Admiralty - 1846 - Liczba stron: 128
...represented numerically as a : b :: c : d:: e :f, &c.; then will one antecedent be to its consequent, as the sum of all the antecedents to the sum of all the consequents; or a:b::a+c+e, &c.: b + d+f, &c. «• Since -r= .-. ab+ad-t-af, &c. = ba + bc+be, &c. That is, a(b+d+f)... | |
 | Great Britain. Admiralty - 1846 - Liczba stron: 128
...represented numerically as a : b:: c : d :: e :f, &c. ; then will one antecedent be to its consequent, as the sum of all the antece-dents to the sum of all the consequents; or a : b :: a+c+e, &c.: b + d+f, &c. Since -r = -y .-. ab+ad+af, &c. = ba + bc+be, &c. That is, a(b... | |
 | Charles William Hackley - 1846 - Liczba stron: 542
...quantities, the first will have to the second the same ratio that the sum of all the antecedents has to the sum of all the consequents. Let a, b, c, d, e,f, g, h be any number of proportional quantities, such that a : b : : c : d : : e :/: : g : h. Then... | |
 | Samuel Alsop - 1846 - Liczba stron: 300
...whatever should be the number of proportions. 51. If any number of like magnitudes be proportional ; as one antecedent is to its consequent, so is the sum of the antecedents to the sum of the consequents. Let a : b : : с : d : : e :f : : g : h. then will a:b... | |
 | Elias Loomis - 1846 - Liczba stron: 380
...same ratio, the first will have to the second the same ratio that the sum of all the antecedents has to the sum of all the consequents. Let a, b, c, d, e,f be any number of proportional quantities, such that a : b : : c : d : : e :f, then will o : b :... | |
 | Elias Loomis - 1846 - Liczba stron: 376
...same ratio, the first will have to the second the same ratio thai the sum of all the antecedents has to the sum of all the consequents. Let a, b, c, d, e,/be any number of proportional quantities, suchthat a : b : : с : d : : e :f, then will a : b :... | |
 | Joseph Ray - 1848 - Liczba stron: 250
...having the same ratio, any one 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 : : m : n, &c. Then will a : b : : a+c+m : b+d+n ; Since a : 6 : : c : d, we have bc=ad. Since a :... | |
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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. 
