 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...whatever of B, F; therefore, as A is to B, so is E to F. (v. def. 5.) Wherefore, ratios that, &c. QED PROPOSITION XII. THEOREM. If any number of magnitudes be proportionals, as one of the antecedents it to Us consequent, so shall all the antecedents taken together be to all the consequents. Let any... | |
 | Euclides - 1861 - 464 pages
...Thus also, if A : B > or < C : D, and C : D = E : F, then A : B > or < E : F. PROP. XII. — THEOB. If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents. Cos. Pst. 1, V.... | |
 | George Sturton Ward - Geometry, Algebraic - 1862 - 104 pages
...= -; о а and because с : d : : e : f, therefore - = - : therefore -¡ = 7, b Í PROPOSITION XII. If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents. a, b ; c,d ; e,... | |
 | Euclides - 1864 - 448 pages
...of B, F; therefore, as A is to B, so is E to F. (v. def. 5.) Wherefore, ratios that, &o. q. i;. i,. PROPOSITION XII. THEOREM. If any number of magnitudes...proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents. Let any number of... | |
 | Euclides - 1865 - 402 pages
...two. Prop. 1 1 . Ratios that are the same to the same ratio, are the same to one another. Prop. 12. If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents. Prop. 13. If the... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...which C has to A ; which is not the case. V. 7. .'. B is less than AQED PROPOSITION X. (Eucl. v. 12.) If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so must all the antecedents taken togetlw be to all the consequents. Let any number of... | |
 | Euclides - 1874 - 342 pages
...therefore 4. As A is to B, so is E to F (V. Def. 5). Wherefore, ratios that, &c. QED PROPOSITION 12. — Theorem. If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents. Let any number of... | |
 | Charles Lutwidge Dodgson - 1874 - 96 pages
...an instance of the Axiom " Things, that are equal to the same, are equal to one another." PROP. XII. If any number of magnitudes be proportionals : as one of the antecedents is to its consequent, so are all the antecedents to all the consequents. [Tf any number of magnitudes (a, b,... | |
 | Euclid, Lewis Carroll - Euclid's Elements - 1874 - 80 pages
...instance of the Axiom " Things, that are equal to the same, are equal to one another." ~" PROP. XII. If any number of magnitudes be proportionals : as one of the antecedents is to its consequent, so are all the antecedents to all the consequents. [If any number of magnitudes (a, b,... | |
 | Euclid - 1876 - 240 pages
...because C : D :: E : F, C _ E D ~ F; therefore - = ~, and therefore A : B :: E : F PROPOSITION XIL THEOREM. — If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents taken together. Let... | |
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IF any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents. 
