 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
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...PROPOSITION IV. THEOREM 281. 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. Given a : b = c : d. To prove a : c = 6: d. Proof. 2 = £. (Hyp.) bd V Jl-V ad = be. (276) a:c=b:d.... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor, Eva Crane Farnum - Geometry, Modern - 1924 - 360 pages
...product of the extremes. 356. Transformations of a proportion. Any proportion can be transformed by: (1) Alternation; that is, the first term is to the third as the second is to the fourth. (2) Inversion; that is, the second term is to the first as the fourth is to the third. (3) Addition;... | |
 | Julius J. H. Hayn - Geometry, Plane - 1925 - 328 pages
...obtain — = —, or— = —. or m : a = c : r. ar ar ar Proposition IV. Theorem QED 192. // 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. Hyp.: Given that a : b = c : d. Det.: To prove that... | |
 | Edward Ira Edgerton, Perry Amherst Carpenter - Algebra - 1925 - 398 pages
...Let the pupil prove : 1 . // four quantities are in proportion, they are in proportion by alteration, that is, the first term is to the third as the second term is to the fourth. Ex., if a : b = c : d, then a : c = b : d. 2. If four quantities are in proportion,... | |
 | William Weller Strader, Lawrence D. Rhoads - Geometry, Plane - 1927 - 434 pages
...TRANSFORMATION THEOREMS Proposition 8 272. Theorem. Four quantities in proportion are in proportion also by alternation; that is, the first term is to the third as the second is to the fourth. Given: a : b = c : d. To prove: a : c = 6 : d. Proof: STATEMENTS FACTS 1. a:6 = c : d. 2. ad = 6e.... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 356 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? 363. If four numbers... | |
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