 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...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... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...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)... | |
 | James Bates Thomson - Algebra - 1846 - 276 pages
...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... | |
 | Samuel Alsop - Algebra - 1846 - 300 pages
...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... | |
 | Samuel Alsop - Algebra - 1848 - 336 pages
...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 :/ : : gi h. then will о... | |
 | Henry Bailey Browning - 1849 - 160 pages
...53]. VII. If А, B, С, D, E, F are quantities of the same kind, and A : B as С : D as E : F, then, as one antecedent is to its consequent so is the sum of the antecedents to the sum of the consequents ; that is, A : B : : A+C+E : B+D +F. Let A, B, C, D,... | |
 | Horatio Nelson Robinson - Algebra - 1850 - 256 pages
...number of proportionals have the same ratio, any one of the antecedents will be its consequent, and as the sum of all the antecedents to the sum, of all the consequents. Let a : 6= a : b Also, a : b— c : d a : b=m : n &c.=&c. Then we are to prove that a : b=(a+c+m) : (b+d+n)... | |
 | Janet Taylor - Nautical astronomy - 1851 - 674 pages
...of similar triangles, each pair being as the squares of their homologous or like sides; and, as any one antecedent is to its consequent, so is the sum...the antecedents to the sum of all the consequents; [Eu. v. 12.]; therefore as the square of any side of a polygon is to the square of the corresponding... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...unlike in kind. PROPOSITION X. -THEOREM. If any number of homogeneous magnitudes be proportionals, then as one antecedent is to its consequent, so is the...the antecedents to the sum of all the consequents. First, let there be four proportionals, and let any equimultiples of the antecedents and any equimultiples... | |
 | John Radford Young - 1855 - 218 pages
...4m'a3 + Zm'ab—aiV Theorem 5. If any number of quantities of the same kind are proportionals, then as one antecedent is to its consequent, so is the...antecedents to the sum of all the consequents. Let there be a, : b : : c : d : : e : f, &c. Put j=-=- &e. =m; then a=mb, c=md, e=mf, &c. &c.) .'. 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. 
