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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
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

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

John Playfair - 1832 - 333 σελίδες
...any 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, no are all the antecedents, taken together, to all the consequents. If A:B: : C: D, and C: D: : E:...

The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...ratios that, &c. QED PROPOSITION XII. t. THEOR. — If any number of magnitudes be proportionals, af v one of the antecedents is to its consequent, so shall...all the . / antecedents taken together, be to all lhe consequents. Let any number of magnitudes A, B, C, D, E, F be proportionals ; that is, as A is...

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

Euclid - 1835 - 513 σελίδες
...B, F : Therefore, as A is to B, so is E to F'. Wherefore, " ratios that," &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. Let any number of magnitudes A, B,...

The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - 1835 - 513 σελίδες
...B, F : Therefore, as A is to B, so is E to F". Wherefore, « ratios that," &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. Let any number of magnitudes A, B,...

The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 σελίδες
...magnitude, is the least of the two. XI. Ratios that are equal to the same ratio are equal to one another. XII. 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. XIII. If the first have to the second...

Solutions of the Cambridge Problems, from 1800 to 1820, Τόμος 2

John Martin Frederick Wright - 1836
...the segments of the other. 4. Inscribe an equilateral and equiangular hexagon in a given circle. 5. If any number of magnitudes be proportionals, as one...of the antecedents is to its consequent, so shall au the antecedents taken together be to all the conséquents. 6. If magnitudes taken jointly be proportionals,...

Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 σελίδες
...nB, nF, 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. If A:B::C:D,andC:D::E:F;A:B:':A + C +...

Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...E ; and wB, nF any whatever of B and F ; therefore, A : B : : E : F (v. Def. 5). 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 : :...

The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - 1841 - 98 σελίδες
...D — E : F, because A £ В — D V _ 1 • • D — F and .-. С : D — E : F. PROP. XII. THEO. If any number of magnitudes be proportionals, as one...antecedents taken together be to all the consequents. then will For if M с- м ' then м and мОс-mÇ, MO ET- »и л, also M А с- т «. (5 def. v.)...

The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 σελίδες
...B, F: therefore, as A is to B, so is E to F.* Where5 ' fore, ratios that, &c. QED 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,...




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