Books Books 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. An Easy Introduction to the Mathematics: In which the Theory and Practice ... - Page 66
by Charles Butler - 1814 ## New Elementary Algebra: In which the First Principles of Analysis are ...

Benjamin Greenleaf - Algebra - 1864 - 336 pages
...6 : b : : c — d : d. THEOREM Vin. 322. 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. Let a : b : : c : d; Then, a + b : a — b : : c + d : c — d ByTheo.VL, and... ## Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Conic sections - 1865 - 472 pages
...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 - Algebra - 1866 - 614 pages
...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,... ## The University Algebra

John Fair Stoddard, William Downs Henkle - Algebra - 1866 - 546 pages
...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... ## Algebra for the Use of Colleges and Schools: With Numerous Examples

Isaac Todhunter - Algebra - 1866 - 576 pages
...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.... James Pryde - Navigation - 1867 - 506 pages
...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 - Geometry - 1868 - 276 pages
...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 - Algebra - 1868 - 386 pages
...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 - Geometry - 1868 - 338 pages
...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... 