 | Euclides - 1840 - 192 pages
...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.... | |
 | Wales Christopher Hotson - 1842 - 306 pages
...reasoning it will follow, that if there be any number of equal ratios whatever, any one of the antecedents is to its consequent as the sum of all the antecedents to the sum of all t?ie consequents. 62. The relative magnitudes of the quantities which constitute any proportion are... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...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... | |
 | Admiralty - 1845 - 152 pages
...«'" : I."1 : : <•"' : 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... | |
 | Nathan Scholfield - 1845 - 894 pages
...PROPOSITION XVI. If any 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... | |
 | Scottish school-book assoc - 1845 - 444 pages
...113. Prop. 12. If there be any number of proportionals, as one antecedent is to its consequent, so is the sum of all the 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 - Algebra - 1845 - 442 pages
...248. 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. (Еисып, B. v. Prop, xn.) If a : b :: с : d :: e : /, &c. then a : b :: a + с + e + Sic. : b... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...proportional quantities, 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
...proportional quantities, 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)... | |
 | Dennis M'Curdy - Geometry - 1846 - 166 pages
...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... | |
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If any number of magnitudes are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. 
