 | Robert Potts - 1865 - 528 σελίδες
...PROPOSITION XII. THEOREM. lf any number of magnitudes be proportionals, as one of (lie antecedent» is to its consequent, so shall all the antecedents taken together be to all the consequents. Let any number of magnitudes A, B, C, D, I?, F, be proportionals :. that is, as A is to B, so C to... | |
 | Euclides - 1865 - 402 σελίδες
...ratio are equal to one another . . . . . . . . . V. 11. 2. If any number of magnitudes of the same kind be proportionals, as one of the antecedents is to its consequent, so are all the antecedents taken together to all the consequents . . .V. 12. 3. Magnitudes have the same... | |
 | Robert Potts - 1868 - 434 σελίδες
...Wherefore, ratios that, &c. QED PROPOSITION XII. THEOREM. If any number of magnitude* he proportionals, at one of the antecedents is to its consequent, so shall all the antecedent* taken together be to all the consequents. Let any number of magnitudes A, B, C, D, E, F,... | |
 | Euclides, James Hamblin Smith - 1872 - 376 σελίδες
...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 magnitudes A,B,C,D,E,F...}}e... | |
 | Euclides - 1874 - 342 σελίδες
...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...antecedents taken together be to all the consequents. Let any number of magnitudes A, B, C, D, E, F, be proportionals ; that is, as A is to B, so C to D,... | |
 | Charles Lutwidge Dodgson - 1874 - 96 σελίδες
.... This is 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, c, d, e, f, <fcc.)... | |
 | Euclid, Lewis Carroll - 1874 - 80 σελίδες
...This is 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. [If any number of magnitudes (a, b, c, d, e,f, &c.}... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 σελίδες
...as A is to B BO is E to F. (V. 2, com: ) QED PBOP. VIII.— THEOREM. {Euc. V. 12.) In any number of proportionals, as one of the antecedents is to its consequent, so shall all the antecedents be to all the consequents. IfA:B::C:D::E:F; then it is reqmred to shew that asA:B::A + C + E: - ~ ~... | |
 | Euclid - 1876 - 240 σελίδες
...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...antecedents taken together be to all the consequents taken together. Let any number of magnitudes A, B, C, D, E, F, be proportionals ; that is, as A is... | |
 | Association for the improvement of geometrical teaching - 1876 - 66 σελίδες
...for all values of m and ;¿, A :C ::B : D.] THEOR. 9. If any number of magnitudes of the same kind be proportionals, as one of the antecedents is to its consequent, so shall the sum of the antecedents be to the sum of the consequents. . [Let A : B :: C : D :: E : F, then A... | |
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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. 
