 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.  The student's algebra - Page 13by John Darby (teacher of mathematics.) - 1829Full view - About this book
 | 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 by... | |
 | Benjamin Greenleaf - Algebra - 1864 - 420 pages
...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, ±±*... | |
 | Horatio Nelson Robinson - Conic sections - 1865 - 474 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 : : C :... | |
 | Isaac Todhunter - Algebra - 1866 - 618 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...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, = 0 Cv... | |
 | 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 By Prop.... | |
 | Isaac Todhunter - Algebra - 1866 - 580 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.... | |
 | Joseph Ray - Algebra - 1866 - 420 pages
...275. Proposition IX. — If four quantities are in proportion, the sum of the first and second will be to their difference as the sum of the third and fourth is to their difference. Let a : b : : C : d (I), Then will .... a+6 : a— 6 : : c-\-d : c — d. From (1),... | |
 | Joseph Ray - Algebra - 1866 - 250 pages
...2«>2. Proposition IX. — If four quantities are in proportion, the sum of the first and second will be to their difference, as the sum of the third and fourth is to their difference. Let a: b: : C: d. (1) Then will a-\-b • a — 6 : : c+ d : c—d. From (1), by... | |
 | 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 + d Given... | |
 | 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 :: C :... | |
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