 | James Maurice Wilson - 1878 - 450 pages
...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... | |
 | University of Oxford - Greek language - 1879 - 414 pages
...Describe an isosceles triangle, having each of the • angles at the base double of the third angle. 6. If any number of magnitudes be proportionals, as one...is to its consequent, so shall all the antecedents be to all the consequents. 7. If four straight lines be proportionals, the rectangle contained by the... | |
 | Euclides, James Hamblin Smith - 1879 - 376 pages
...to A ; which is not the V. 7. .'. B is less than A. o. ED PROPOSITION X. (EucL v. 12.) If any nwnber of magnitudes be proportionals, as one of the antecedents is to its consequent, so must all the antecedents taken together be to all the consequents. Let any number of magnitudes A,B,C,D,E,F..... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...as E is to F. [V- Definition 5. Wherefore, ratios that are the same &c. QKD PROPOSITION 12. THEOREM. If any number of magnitudes be proportionals, as one...is to its consequent, so shall all the antecedents be to all the consequents. Let any number of magnitudes A, B, C, D, E, F be proportionals ; namely,... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...is to F. [V. Definition 5. PROPOSITION 12. THEOREM. If any number of magnitude* be proportionals, at one of the antecedents is to its consequent, so shall all the antecedents be to all the consequents. Let any number of magnitudes A, B, C, D, E, F be proportionals ; namely,... | |
 | Mathematical association - 1883 - 86 pages
...for all values of »i 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 B + D+F. F, then A :... | |
 | Euclides - 1884 - 434 pages
...nF, and if mA be less than nB, mE is less than nF; .-. A : B = E : FV Def. 5 PROPOSITION 12. THEOREM. If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so is the sum of all Hie antecedents to the sum of all the consequents. it is required to prove A: B =... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...If A : C>B : C, or if T : A < T : B, /. A > B. If A : C<B : C, or if T : A > T : B, THEOREM VI. 492. If any number of magnitudes be proportionals, as one of the antecedents is to its consequent ', so will all the antecedents taken together be to all the consequents. Let A : B : : C : D : : E : F, then... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...A : C> B : C, or if T : A < T : B, .: A > B. If A : C<B : C, or if T : A > T : B, THEOREM VI. 499. If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so will all the antecedents taken together be to all the consequents. Let A : B : : C : D : : E : F, then... | |
 | Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888 - 208 pages
...Mults. 3. Hence A :B : : A + C + E : BID + F. £>'/• 5or, if any number of magnitudes of the same kind be proportionals, as one of the antecedents is to its consequent, so is the sum of the antecedents to the sum of the consequents. QED COR. If A : B : : C : D (A being greater... | |
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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. 
