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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. "
An Elementary Treatise on Algebra: Theoretical and Practical ... - Σελίδα 336
των James Ryan - 1826 - 383 σελίδες
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...therefore, as A is to B, so is E to F (5 Def. v.). Wherefore, ratios that, etc. QED PROPOSITION XII. THEOB. 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,...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1853 - 317 σελίδες
...and nB, »F any whatever of B and F ,• therefore A : B : : E : F (def. 5. 5.). PROP. XII. THEOR. ff any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so arc all the antecedents, taken together, to all the consequents. If A : B : C : D, and C . D : . E...

The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855
...therefore A : B :: E : F A _ C C _ E D ~ F ; .. , AE therefore - = -, PROPOSITION XII. 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...

The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...Therefore, A is to B .¿s E is to F (V. Def. 5). Wherefore, ratios that, &c. QED PROP. XII. THEOREM. If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so are all the antecedents taken together to au the consequents. Let any numbsr of magnitud« A, B, С,...

The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860
...E : F, C _ E D ~~ F! therefore — = ^, and therefore A : B :: E : F PROPOSITION XII. THEOREM. — If any number of magnitudes be proportionals, as one...consequent, so shall all the antecedents taken together he to all the consequents taken together. Let any number of magnitudes A, B, C, D, E, F, be proportionals...

Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...nB, riF any whatever of B and F ; therefore A : B : : E : F (V. Def. 10). PROPOSITION XII. THEOREM. If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so is the sum of all the antecedents to that of the consequents. Given A : B : : C : D, and C : D : :...

Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 σελίδες
...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...

Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...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...antecedents taken together be to all the consequents. Cos. Pst. 1, V. DEM. Def. 5, V. Definition of Proportion. 1, V. If any no. of Ms he equims of as many,...

The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ...

George Sturton Ward - 1862 - 79 σελίδες
...therefore - = -; о а and because с : d : : e : f, therefore - = - : therefore -¡ = 7, b Í PROPOSITION XII. If any number of magnitudes be proportionals,...antecedents taken together be to all the consequents. a, b ; c,d ; e, f. Let a : b ; ; с : d :: e :f. Then shall a : b ;: a + c+ e : b+ d+f. Because a :...

The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...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 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,...




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