 If four quantities are in proportion, they are in proportion by Inversion; that is, the second term is to the first as the fourth term is to the third.  Grammar School Algebra - Page 236by George Edward Atwood - 1900 - 253 pagesFull view - About this book
 | 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...term is to the third as the second is to the fourth. Given the proportion a : b=c -. d. To prove a . • c — b : d. Proof. a : 6 = c : d. Hyp. .-. ad=bc,... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...different ways as possible. PROPOSITION IV. THEOREM 307, If four quantities are in proportion , tlicy 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 . c = b : d. Proof. a : b = c : d. Hyp. .-. ad^~bc,... | |
 | Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...proportion are equal, the consequents are equal. 307. // four quantities are in proportion, they arc 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 are in proportion by division ; that is, the difference... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...\-'v PROPOSITION IV. THEOREM. 330. 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... | |
 | 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...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 QED... | |
 | 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...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.... | |
 | 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)... | |
 | 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... | |
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