 If four quantities are in proportion, they are in proportion by alternation, ie the first term is to the third as the second is to the fourth.  Plane and Solid Geometry - Page 156by Arthur Schultze, Frank Louis Sevenoak - 1925 - 480 pagesFull view - About this book
 | Thomas Keith - Arithmetic - 1822 - 354 pages
...16 shillings, Answer. Variation 1. The third term is to the fourth as the first is to the second. 2. The second term is to the first as the fourth is to the third. 3. The fourth term is to the third as tke second is to the first. Examples. (1.) If 2cwt.3qrs.14lb.... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...VH.-THEOREM. The terms of any proportion form also a proportion when they are taken INVERSEI/T ; that is, the second term is to the first as the fourth is to the third, or the second has the same ratio to the first that the fourth has to the third. Let the proportion... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...the fourth, the proportion is taken by alternation, as in the second case, Article 18. When we say the second term is to the first as the fourth is to the third, the proportion is taken inversely, as in the third case. 21. Proposition — Ratios which are equal... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...the fourth, the proportion is taken by alternation, as in the second case, Article 18. When we say the second term is to the first as the fourth is to the third, the proportion is taken inversely, as in the third case. 21. Proposition. — Ratios which are equal... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...the fourth, the proportion is taken by alternation, as in the second case, Article 18. When we say the second term is to the first as the fourth is to the third, the proportion is taken inversely, as in the third case. 21. Proposition. — Ratios which are equal... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...= — =-• bd Multiply both members by — Then fL=A• ca or a : c :: b : d. QED THEOREM VI. 161. If four quantities are in proportion, they are in proportion by inversion. Let a : b :: c : d. To prove that b : a :: d : c. dc Take the form -- — — • bd Divide 1 by each... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...used for brevity, meaning the product of the numbers which represent those lines. Proposition 3. 285. If four quantities are in proportion, they are in proportion by inversion; that is, the second term is to the first as the fourth term is to the third. Hyp. Let a : b = c : d.... | |
 | Seth Thayer Stewart - Geometry - 1891 - 426 pages
...means. PROP. II. If four quantities are in proportion, they are in proportion by alternation. PROP. III. If four quantities are in proportion, they are in proportion by inversion. PROP. IV. If four quantities are in proportion, they are in proportion by composition. PROP. V. If... | |
 | William Freeland - Algebra - 1895 - 328 pages
...Multiplying both members by -> we have, с а& _ bc bc cd «Ц. с d .-. a : с = b : d. 288. V. Inversion. If four quantities are in proportion, they are in proportion by inversion. Let a:b = c:d. mi. ac Then - = -. bd Taking the reciprocals of both members, we have, u_d а с .-.... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...second is to the fourth. a: b=c:d ad = be [?] PROPOSITION IV 190. Theorem. In a proportion the terms are in proportion by Inversion; ie the second term is to the first as the fourth is to the third. a:b = c: d ad = be [?] d = b c . a or 6 : a = d : c f divide by what ?1 PROPOSITION V 191. Theorem.... | |
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