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" If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. "
Easy Introduction to Mathematics - Σελίδα 62
των Charles Butler - 1814
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

New Higher Algebra: An Analytical Course Designed for High Schools ...

Benjamin Greenleaf - 1864 - 420 σελίδες
...whence, a — b : b : : c — d : d. 317. If four quantities be in proportion, the sum of the Jirst and second is to their difference as the sum of the third and fourth is to their difference. If a : b : : c : d, then a -j- b : a — b : : c -\- d : c — d. By Art. 315,...

Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - 1865 - 474 σελίδες
...is to the difference between the third and fourth. THEOREM IX. If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. Let A, B, C, and D be the four magnitudes which give the proportion A : B :...

Algebra for the Use of Colleges and Schools: With Numerous Examples

Isaac Todhunter - 1866 - 614 σελίδες
...inversely, a : a — b :: с : c — d. This operation is called converlendo. 396. W/ten four quantities are proportionals, the sum of the first and second is...their difference as the sum of the third and fourth is to t/ieir difference. If a : b : : с : d, then a + b : a—I : : c + d : c — d. By Art. 393,...

Algebra for the Use of Colleges and Schools: With Numerous Examples

Isaac Todhunter - 1866 - 580 σελίδες
...inversely, a : a — b : : с : c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fowrtii is to tlieir difference. If a : b :: с : d, then a + b : a — b :: с +d : c — d. By Art....

The University Algebra

John Fair Stoddard, William Downs Henkle - 1866 - 546 σελίδες
...third. Let the student prove this. PROPOSITION (393.) 12. W/ien four quantities are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. DEMONSTRATION. Let a:b::e:d. We are to prove that a + b :a—b :: c + d : ca...

Navigation

James Pryde - 1867 - 506 σελίδες
...and therefore (29, e) a—bc—db — ad—c 41. THEOREM.. — If four quantities be proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. This change is called proportion by Mixing. /- • ii. *. ac i_ .. й + ^ c...

Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - 1868 - 276 σελίδες
...is to the difference between ihe third and fourth. THEOREM IX. If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. Let A, B, C, and D he the four magnitudes which give the proportion A : B ::...

A Treatise on Algebra

Elias Loomis - 1868 - 386 σελίδες
...b :: m:'n 9 m: U) c: d. n n c d : c : d. (i-) (2.) f f " 306." If four quantities are proportional, the sum of the first and second is to their difference, as the sum of the third and fourth is to their difference. Let a : b : : c : d. By composition, Art. 304, d+b : b :: c+d: d. By alternation,...

Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1868 - 340 σελίδες
...II., A:B::A+C + E:B + D + F. PROPOSITION XII. — THEOREM. 148. If four magnitudes are in proportion; the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. Let A : B : : C : D ; then will A + B:A — B : : C + D : C — D. For, from...

Annual Report of the Normal, Model, Grammar, and Common Schools in Ontario ...

Ontario Chief Superintendent of Education - 1869 - 450 σελίδες
...the ordinary rule for Equation of Payments. 3. Prove that if any four quantities are in proportion the sum of the first and second is to their difference as the sum of the third and fourtli is to their difference. 4. Define what is meant by " Compound Proportion." 5. Give and prove...




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