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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 college Euclid: comprising the first six and the parts of the eleventh ...

Euclides - 1865
...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...

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

Robert Potts - 1868 - 410 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,...

## Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 349 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...

## The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...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,...

## Euclid, Book V Proved Algebraically So Far as it Relates to Commensurable ...

Charles Lutwidge Dodgson - 1874
.... 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, Book V. Proved Algebraically, So Far as it Relates to Commensurable ...

Euclid, Lewis Carroll - 1874 - 62 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.}...

## Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...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: - ~ ~...

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

Euclides - 1876
...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...

## SYLLABUS OF PLANE GEOMETRY

1876
...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...

## Elementary geometry

James Maurice Wilson - 1878
...C : D; therefore *»A : »/B :: «C : «D, THEOREM 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. Proof. Let A : B :: C : D :: E : F, then...