 | American School (Chicago, Ill.) - Engineering - 1903 - 426 pages
...b = c:d III. In any proportion the terms are in proportion by Alternation; that is, the first term is to the third as the second is to the fourth. Let a : b = с : d By I, ad = be By П, a : с = b : d IV. In any proportion the terms are in proportion by Inversion;... | |
 | American School (Chicago, Ill.) - Engineering - 1903 - 390 pages
...THEOREH III. 131. In any proportion the terms are in proportion by Alternation ; that is, the first term is to the third as the second is to the fourth. Let a : 6 = c : d By (128) ad = be By (130) a:c = b:d THEOREn IV. 132. In any proportion the terms are in... | |
 | Robert Judson Aley, David Andrew Rothrock - Algebra - 1904 - 344 pages
...Theorem I. THEOREM IV. If four numbers be in proportion, they will be in proportion by alternation; that is, the first is to the third as the second is to the fourth. Algebraically, if A : Б = С : D, then is A : C= Б : D. See (2) under Theorem II. THEOREM V. If four... | |
 | 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... | |
 | 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. If four... | |
 | Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...inversion. 199. Theorem HI. // four quantities are in proportion, they are in proportion by alternation, that is, the first is to the third as the second is to the fourth. Geometric proof: Taking the figure and notation of Theorem I, by the same plan of proof, show that... | |
 | Edith Long, William Charles Brenke - Geometry, Plane - 1916 - 292 pages
...inversion. 199. Theorem HI. // four quantities are in proportion, they are in proportion by alternation, that is, the first is to the third as the second is to the fourth. Geometric proof: Taking the figure and notation of Theorem I, by the same plan of proof , show that... | |
 | Mabel Sykes, Clarence Elmer Comstock - Geometry, Modern - 1918 - 576 pages
...terms of another proportion, the fourth terms are equal. THEOREM 93. If four numbers are in proportion, the first is to the third as the second is to the fourth; that is, they are in proportion by mean alternation. THEOREM 95. If four numbers arc in proportion,... | |
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Permutando, or alternando, by permutation or alternately; when there are four proportionals, and it is inferred that the first is to the third, as the second is to the fourth. 
