 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
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...Separate 12 into two pairs of factors which will form a proportion. PROPOSITION IV. THEOREM 331 If four quantities are in proportion, they are in proportion...term is to the third as the second is to the fourth. HYPOTHESIS, a : b = c : d. CONCLUSION, a : c = 6 : d. PROOF ad = be. § 328 .-. a: c = b:d. § 330... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...They will all be recognized as true proportions. 292. THEOREM. In any proportion the terms are also in proportion by alternation (that is, the first term is to the third as the second is to the fourth). Given : a:b = x:y. To Prove : a:x = b:y. Proof: a:b = x:y (Hyp.). .-. ay = br, (290). 293. THEOREM.... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...They will all be recognized as true proportions. 292. THEOREM. In any proportion the terms are also in proportion by alternation (that is, the first term is to the third as the second is to the fourth). Given : a : b = x : y. To Prove : a:x=b:y. Proof: a:b = x:y (Hyp.). .-. ay = bx (290). 293. THEOREM.... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...ac THEOREM IV 330. 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. The proof is left for the student. Notice that in taking a proportion by alternation, the quantities a, b, c, and d must... | |
 | Webster Wells - Geometry, Plane - 1908 - 206 pages
...manner, we may prove - = - ; - = - ; etc. caac PROP. III. THEOREM 219. 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. To Prove - = -. cd Proof. From (1), ad = bc. (§216) Then, - = -. (§218) cd... | |
 | Webster Wells - Geometry - 1908 - 336 pages
...manner, we may prove - = - ; - = - ; etc. cdac PROP. III. THEOREM '219. 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. Given the proportion - = -. (1) To Prove - = -. cd Proof. From (1), ad=bc. (§216)... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...to the third. 330. 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. 331. If four quantities are in proportion, they are in proportion by composition, ie the sum of the... | |
 | Edward Rutledge Robbins - Logarithms - 1909 - 184 pages
...245. A central angle is measured by its intercepted arc. 292. In any proportion the terms are also in proportion by alternation (that is, the first term is to the third as the second is to the fourth). 296. In any proportion the terms are also in proportion by composition and division (that is, the sum... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...4. 6 a PROPOSITION II. THEOREM 265. If four quantities are in proportion, they are in proportion % alternation • that is, the first term is to the third as the second term is to the fourth. Given a : b=c:d. To prove that a : c = b : d. Proof. ad — be. § 261 Dividing... | |
 | Fletcher Durell - 1911 - 234 pages
...product. 305. // the antecedents of a proportion are equal, the consequents are equal. 307. // four quantities are in proportion, they are in proportion...term is to the third as the second is to the fourth. 310. // four quantities are in proportion, they are in proportion by division ; that is, the difference... | |
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