 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. Let...  The Elements of Geometry - Page 80by Henry W. Keigwin - 1897 - 227 pagesFull view - About this book
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...If four quantities are in proportion, they are in proportion ly alternation; that is, the first term is to the third as the second is to the fourth. Let a : b = c : d. To prove that a:c = b:d. Now ad = bc. § 327 i Divide each member of the equation by cd. Then 2-J.... | |
 | Euclid - Euclid's Elements - 1904 - 488 pages
...than, equal to, or less than the third, according as the second is greater than, equal to, or less than the fourth. Let A, B, C, D be four magnitudes of the same kind such that A :B::C:D; then A >, = , or < C according as B >, = , or < D. If B > D, then A : B < A :... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...a proportion in as many different ways as possible. PROPOSITION IV. THEOREM 807. If four quantities are in proportion, they are in proportion by alternation ; that is, the first term is to the third as the second is to the fourth. Given the proportion a : b=c -. d. To prove a... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...two pairs of factors which will form a proportion. PROPOSITION IV. . THEOREM 331 If four quantities are in proportion, they are in proportion by alternation ; that is, the first term is to the third as the second is to the fourth. HYPOTHESIS. a : b = c : d. CONCLUSION. a : c =... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...into two pairs of factors which will form a proportion. PROPOSITION IV. THEOREM 331 If four quantities are in proportion, they are in proportion by alternation ; that is, the first term is to the third as the second is to the fourth. HYPOTHESIS, a : b = c : d. CONCLUSION, a : c =... | |
 | Joseph Victor Collins - Algebra - 1908 - 442 pages
...the Terms of a Proportion. 1. Alternation. If four like quantities taken in order are in proportion, the first is to the third as the second is to the fourth. If«=c,then a = -- f By Mult. Ax. Multiply through by - -^ bdcd \ c / 2. Inversion. If four quantities... | |
 | James William Nicholson - Algebra - 1909 - 332 pages
...с. Then, 62 = ac. ... 6=Vac. 301. Principle of alternation. If four numbers are in proportion, then the first is to the third as the second is to the fourth. Let a : b = с : d. rpi a С Then, - = -. bd Multiply by -, = - ; or a : с = b : d. 302. Principle of inversion.... | |
 | Fletcher Durell - 1911 - 234 pages
...305. // the antecedents of a proportion are equal, the consequents are equal. 307. // four quantities are in proportion, they are in proportion by alternation ; that is, the first term is to the third as the second is to the fourth. 310. // four quantities are in proportion, they... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...ad = be. QED REASONS 1. By hyp. 2. § 388. 3. § 393. PROPOSITION IV. THEOREM 396. If four numbers are in proportion, they are in proportion by alternation; that is, the first term is to the third as the second is to the fourth. 1. 2. & Given a: b = c: d. To prove <i:c — 7i:<l.... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...principles stated above lead at once to these additional properties of proportions : 362. If four numbers are in proportion, they are in proportion by alternation ; that is, the first term is to the third term as the second is to the fourth. Thus if a:b = c:d, then a. : c = b : d. Why?... | |
| |
