 Proposition 7. 289. ff four quantities are in proportion, they are in proportion by composition and division; that is, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.  Plane and Solid Geometry: Inductive Method - Page 126by Arthur A. Dodd, B. Thomas Chace - 1898 - 406 pagesFull view - About this book
 | 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...sum of the third and fourth is to their difference. This change is called proportion by Mixing. /- • ii. *. ac i_ .. й + ^ c + d Given that -т = ->... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 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...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 the given proportion,... | |
 | 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,...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, Art, 301, a + b :... | |
 | 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...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 : D; we are then to... | |
 | Horatio Nelson Robinson - 1868 - 430 pages
...PROPOSITION VII. — If four quantities be in proportion, the sum of thejirst and second is to (heir difference, as the sum of the third and fourth is to their difference. If a : b = с : d, we are to prove that a-\-b : a — b = c-\-d : с — d. By Prop. VI, a : a+b =... | |
 | Ontario Chief Superintendent of Education - Education - 1869 - 450 pages
...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... | |
 | Horatio Nelson Robinson - 1869 - 276 pages
...between the third and fourth. THEOREM IX. If four magnitudes are proportional, the sum ojthe^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 :: Q : D; we are then to... | |
 | Isaac Todhunter - Algebra - 1870 - 626 pages
...This operation is called convertendo. 396. When four quantities are proportionals, the sum of tlie first and second is to their difference as the sum of the third and fourth is to their difference. If a : b :: с : d, then a + b : ab :: c + d : c — d. By Art. 393, "v-^, and by Art. 394, ^=^J ,,... | |
 | Isaac Todhunter - 1870 - 818 pages
...This operation is called convertendo. 396. When four quantities are proportionals, the sum of tJte first and second is to their difference as the sum of the third and fourth is to their difference. If a : b :: с : d, then a + b : ab :: c + d : cd. a + bc + d By Art. 393, -y- = —j- , and by Art.... | |
 | Horatio Nelson Robinson - Algebra - 1872 - 436 pages
...— c-\-d : d, a — 6 : b = с — d : d. PROPOSITION VU. — If four quantities be in proportion, the sum of the first and second is to their difference, as the sum of the third and fourth ù to their difference. If a : Ъ = с : d, we are to prove that a-\-b : a — b = c-\-d : с — d.... | |
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