| Elmer Adelbert Lyman, Albertus Darnell - 1917 - 520 σελίδες
...transforma4 6 tion is always possible, and is stated as follows : V. 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. PROOF. T^ ac & d ad = bc. (Why?) Transform - = — by alternation.... | |
| Claude Irwin Palmer, Daniel Pomeroy Taylor - 1918 - 460 σελίδες
...extremes, a and d the means, - = .. § 402 ac 406. Theorem. If four numbers form a proportion, they are in proportion by alternation; that is, the first term is to the third as the second is to the fourth. _. ac Given r=T bd To prove jj-jj. Proof. ad = bc. §398 .-•-A 406. Theorem. If... | |
| Claude Irwin Palmer - 1918 - 192 σελίδες
...td the first as the fourth is to the third. § 405. Theorem. If four numbers form a proportion, they are in proportion by alternation; that is, the first term is to the third as the second is to the fourth. § 406. Theorem. If four numbers form a proportion, they are in proportion by addition;... | |
| David Eugene Smith - 1923 - 314 σελίδες
...proportion in which the other two are made the means. 4. If four quantities are in proportion, they are in proportion by alternation ; that is, the first...to the third as the second term is to the fourth. 5. If four quantities are in proportion, they are in proportion by inversion ; that is, the second... | |
| Claude Irwin Palmer, Daniel Pomeroy Taylor, Eva Crane Farnum - 1924 - 360 σελίδες
...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.... | |
| Edward Ira Edgerton, Perry Amherst Carpenter - 1925 - 398 σελίδες
...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, they are in proportion... | |
| William Weller Strader, Lawrence D. Rhoads - 1927 - 434 σελίδες
...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... | |
| William Betz, Harrison Emmett Webb, Percey Franklyn Smith - 1912 - 356 σελίδες
...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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