 | Euclid - Geometry - 1890 - 442 pages
...equal, all the magnitudes being of the same kind, as one of the antecedents is to its conseqzient, so is the sum of all the antecedents to the sum of all the consequents. (Addenda?) Let A, B, C, D, E, F be the terms of three ratios, such that A:B = C:D=E:F, where the magnitudes... | |
 | Euclid - Geometry - 1892 - 460 pages
...AFGL :: the A EBC : the ALGH :: the A EDC : the ALKH. But when any number of ratios are equal, as each antecedent is to its consequent so is the sum of all...the antecedents to the sum of all the consequents; v. 12. .'. the AABE : the A LFG :: the fig. ABCDE : the fig. FGHKL. (iii) Now the A EAB : the A LFG... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 490 pages
...proportion. Carefully examine each continued proportion and answer the following question about it : Is the sum of all the antecedents to the sum of all the consequents as any antecedent in that continued proportion is to its consequent? If your continued proportions... | |
 | Edinburgh Mathematical Society - Electronic journals - 1899 - 340 pages
...when A>C and therefore B>D, but to the ratio C - A : D - B when A<C and therefore B<D. Or, in words, as one antecedent is to its consequent, so is the sum of the antecedents to the sum of the consequents, or the difference of the antecedents to the difference... | |
 | 1901 - 488 pages
...how long each takes in travelling the whole journey. 7. Prove that when any number of quantities are proportionals, as one antecedent is to its consequent,...the antecedents to the sum of all the consequents. 8. Extract the square root of — 47-12\/l5. 9. If A varies inversely as B, and A = 10 when B = 4,... | |
 | James McMahon - Geometry, Plane - 1903 - 380 pages
...any number of equal ratios, all the magnitudes being of the same kind, then as any of the antecedents is to its consequent so is the sum of all the antecedents to the sum of all the consequents. Given A :B = A' :B' = A": B" ; to prove A:B=A+A' + A":B+B'+ B". Prom the hypothesis, and the definition... | |
 | Euclid - Mathematics, Greek - 1908 - 456 pages
...separando, a, - a.. a, -a. aa a, whence, since, 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, [vn. 12] a* + «»-i +...+«] ai which gives (Zj + «,+ ...+ aB, or £„. If, to compare the result... | |
 | London univ - 1874 - 778 pages
...proportionals ? Prove that if any number of quantities be m 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 n terms of an Arithmetic Series of which the first term and... | |
 | Physics - 1809 - 548 pages
...proportion is often used in Dynamics. Article VIII. — When any number of quantities' are proportional, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of ail the consequents ; that is, if a : b : : c : d : : e : f &c., or -; = -r == -~, &c.» then will... | |
 | Euclid - 452 pages
...a„-! a1 we have, separando, whence, since, 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, [vn. 1 2] a„ + <*„_,+ ...-*-a! a, which gives al + <t( + ... H- an, or Sn. If, to compare the result... | |
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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. 
