 If four quantities are in proportion, they are in proportion by inversion ; that is, the second term is to the first as the fourth is to the third.  Plane and Solid Geometry - Page 134by Walter Burton Ford, Charles Ammerman - 1913 - 321 pagesFull view - About this book
 | Charles Guilford Burnham - Arithmetic - 1837 - 266 pages
...multiply the third term by the ratio of the first to the second, we shall obtain the fourth term. Again : the first term is to the third as the second is to the fourth; for^=3 and f$=3, therefore, whether we multiply 10 by 3, the ratio of 5 to 15, or 15 by 2, the ratio... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...(18), a and d may be taken as either the extremes or the means of a new proportion. 20. When we say the first term is to the third as the second is to the fourth, the proportion is taken by alternation, as in the second case, Article 18. When we say the second term... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...(18), a and d may be taken as either the extremes or the means of a new proportion. 20. When we say the first term is to the third as the second is to the fourth, the proportion is taken by alternation, as in the second case, Article 18. When we say the second term... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...(18), a and d may be taken as either the extremes or the means of a new proportion. 20. When we say the first term is to the third as the second is to the fourth, the proportion is taken by alternation, as in the second case, Article 18. When we say the second term... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...—; Si C bd .-. ad = cb. But a and d are extremes; b and c, means. THEOREM II. In any proportion, the first term is to the third as the second is to the fourth. a:b = c:d; then, — = —- Multiply by —> and bdc ab be ab — — —> or — = —> or a: c =... | |
 | Webster Wells - Algebra - 1885 - 324 pages
...may prove that : a : c = b : d, b : d = a : c, с : d = a : b, etc. 297. In any proportion the terms are in proportion by Alternation; that is, the first term is to the third, as the second term is to the fourth. Let a : b = с : d. Then, by Art. 293, ad=bc. Whence, by Art. 296, a : с =... | |
 | Webster Wells - 1885 - 368 pages
...prove that : a : с = b : d, b : d = a : с, с : -d = a : b, etc. 297. In any proportion the terms are in proportion by Alternation; that is, the first term is to the third, as the second term is to the fourth. Let a : b = с :ß. Then, by Art. 293, ad = be. Whence, by Art. 296, a : с... | |
 | Webster Wells - Algebra - 1885 - 370 pages
...may prove that : a : с = b : d, b : d = a : c, c: d = a: b, etc. 297. In any proportion t)ie terms are in proportion by Alternation; that is, the first term is to the third, as the second term is to the fourth. Let a : b = с : d. Then, by Art. 293, ad= 6e. Whence, by Art. 296, a : с =... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...manner it may be proved that a : c = b : d, PROPOSITION III. THEOREM. 245. In any proportion the terms are in proportion by ALTERNATION ; that is, the first term is to the third as the second term is to the fourth. Let a : 6 = c : d. Then by §242, ad = 6c. Whence by § 244, a : c = 6 : d.... | |
 | Webster Wells - Algebra - 1889 - 584 pages
...may prove that : a : с = b : d, b : d = a : c, с : d = a : b, etc. 313. In any proportion the terms are in proportion by Alternation ; that is, the first term is to the third, as the second term is to the fourth. Let a:b = c:d. Then by Art. 309, ad = be. Whence by Art. 312, a:r. = b:d. 314.... | |
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