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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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First Public Examination in Literis Graecis Et Latinis

University of Oxford - 1879
...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...

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

Euclides, James Hamblin Smith - 1879
...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.....

The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 400 σελίδες
...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,...

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 400 σελίδες
...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,...

Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883
...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 :...

The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884
...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 =...

THE ELEMENTS OF GEOMETRY.

GEORGE BRUCE HALSTED - 1885
...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...

The Elements of Geometry

George Bruce Halsted - 1886 - 366 σελίδες
...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...

The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II ...

Association for the Improvement of Geometrical Teaching - 1888
...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...

Report of Her Majesty's Civil Service Commissioners: Together with ..., Τόμος 18

1874
...of square inscribed in the same circle. 5. Prove that if any numbers of magnitudes be proportional, as one of the antecedents is to its consequent so...antecedents taken together be to all the consequents. Assuming that similar polygons may be divided into the same number of similar triangles having the...




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