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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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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1813
...XI. Theor. Ratios that are the same to thr same ratio, are the same to one onother. Prop XII. Theor. If any number of magnitudes be proportionals, as one of the antecedents is to it? consequent, so shall all the antecedents taken together he to all the consequents. Prop. XIII....

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 σελίδες
...of B, F : Therefore, as A is to B, so is E to Fa. Wherefore, ratios that, &c. QED PROP. XII. THEOIl. IF any number of magnitudes be proportionals, as....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 ...

John Playfair - 1819 - 317 σελίδες
...whatever of B and F ; therefore A : B : : E : F (def. 5. 5.). Therefore, &c. QED PROP. XII. THEOR. If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so are all the antecedents, taken together, to all the consequents. If A : B : : C : D, and C : D : :...

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1819
...Prop. XII. Tli*or. If any number of magnitudes he proportional.-, as one of the antecedents is 10 it; consequent, so shall all the antecedents taken together be to all the consequents. Prop. XUI.Theor. If the 6rst has to the second th». same ratio which the third ha« to the fourth,...

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

John Playfair - 1819 - 333 σελίδες
...whatever of B andF ; therefore A : B : : E : F (def. 5. 5.). Therefore, &c. Q, ED . x PROP. XII. THEOR. If any number of magnitudes be proportionals, as one of the antecedents ii to its consequent, so are all the antecedents, taken together, to all the consequents. If A : B...

An Elementary Treatise on Algebra, Theoretical and Practical ...

James Ryan, Robert Adrain - 1824 - 516 σελίδες
...A is to B as C to D, therefore-g=jj, EC for the same therefore g-=-, that is, A : B : : E : F. QED PROP. XII. If any number of magnitudes be proportionals,...the antecedents, and A, B, C, the consequents ; and we are to prove that as rA is to A, so is rA+rB+rC to A+B+C. rA The ratio of rA to A is expressed by-r-=r,...

Solutions of the Cambridge Problems: From 1800 to 1820, Τόμος 2

John Martin Frederick Wright - 1825
...the segments of the other. 4. Inscribe an equilateral and equiangular hexagon in a gives circle. 5. If any number of magnitudes be proportionals, as one...antecedents taken together be to all the consequents. 6. If magnitudes taken jointly be proportionals, they shall also be proportionals when taken separately....

A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 σελίδες
...Wherefore, ratios that, &c. QED PROP. XII. THEOR. У any number of magnitudes be proportionals, a» one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequent». Let any number ef magnitudes A, B, C, D, E, F, be proportionals : that is, as A is to...

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 σελίδες
...therefore * * 5 Def. 5. as A is to B, so is E to F. Wherefore, ratios that, &c. «. ED PROP. XII. THEOR. 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,...

The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 324 σελίδες
...This proposition is to ratios what Axiom I. Book I. is to magnitudes. PROPOSITION XII. THEOREM. (489) If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so are all the antecedents taken together to all the consequents. Let any number of magnitudes A, B, C,...




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