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" 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. "
College Algebra - Σελίδα 521
των James Harrington Boyd - 1901 - 777 σελίδες
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

A Complete Course in Algebra for Academies and High Schools

Webster Wells - 1885 - 349 σελίδες
...may prove that : a : с = b : d, b : d = a : c, c: d = a: b, etc. 297. In any proportion t)ie terms are in proportion by Alternation; that is, the first...the third, as the second term is to the fourth. Let a : b = с : d. Then, by Art. 293, ad= 6e. Whence, by Art. 296, a : с = b : d. 298. In any proportion...

A Complete Course in Algebra

Webster Wells - 1885
...prove that : a : с = b : d, b : d = a : с, с : -d = a : b, etc. 297. In any proportion the terms are in proportion by Alternation; that is, the first...the third, as the second term is to the fourth. Let a : b = с :ß. Then, by Art. 293, ad = be. Whence, by Art. 296, a : с = b : d. 298. In any proportion...

A Complete Course in Algebra for Academies and High Schools

Webster Wells - 1885 - 349 σελίδες
...may prove that : a : c = b : d, b : d = a : c, с : d = a : b, etc. 297. In any proportion the terms are in proportion by Alternation; that is, the first...the third, as the second term is to the fourth. Let a : b = с : d. Then, by Art. 293, ad=bc. Whence, by Art. 296, a : с = b : d. 298. In any proportion...

The Elements of Geometry

Webster Wells - 1886 - 371 σελίδες
...manner it may be proved that a : c = b : d, PROPOSITION III. THEOREM. 245. In any proportion the terms are in proportion by ALTERNATION ; that is, the first...the third as the second term is to the fourth. Let a : 6 = c : d. Then by §242, ad = 6c. Whence by § 244, a : c = 6 : d. PROPOSITION IV. THEOREM. 246....

A Short Course in Higher Algebra: For Academies, High Schools, and Colleges

Webster Wells - 1889 - 426 σελίδες
...may prove that : a : с = b : d, b : d = a : c, с : d = a : b, etc. 313. In any proportion the terms are in proportion by Alternation ; that is, the first...the third, as the second term is to the fourth. Let a:b = c:d. Then by Art. 309, ad = be. Whence by Art. 312, a:r. = b:d. 314. In any proportion the terms...

College Algebra

Webster Wells - 1890 - 577 σελίδες
...d. In like manner we may prove that a : с = b : d, c:d = a:b, etc. 385. In any proportion the terms are in proportion by Alternation ; that is, the first...the third as the second term is to the fourth. Let a : b = с : d. Then by Art. 381, ad = be. Whence by Art. 384, a : с = b : d. 386. In any proportion...

The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - 1890 - 393 σελίδες
...= - , ac . • . I : a = d : c. QED Proposition 4. 286. 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. Hyp. Let a : b = c : d. To prove a : c — b : d. Proof. Since a : b = c : d, . • . ad = be. (281)...

The Elements of Geometry

Webster Wells - 1894 - 378 σελίδες
...= c:d. In like manner, a : c = b : d, ~ PROPOSITION III. THEOREM. 234. In any proportion, the terms are in proportion by ALTERNATION ; that is, the first...term is to the fourth. Let the proportion be a ; b = c-. d. (1) To prove a : c~ = b : d. We have from (1), ad = be. (§231.) Whence, a:c = b\d. (§ 233.)...

The Elements of Geometry

Webster Wells - 1894 - 378 σελίδες
...manner, a : c = b : d, b: a = d: c, etc. PROPOSITION III. THEOREM. 234. In any proportion, the terms are in proportion by ALTERNATION ; that is, the first...second term is to the fourth. Let the proportion be a:b = c : d. (1) To prove a : c = b : d. We have from (1), ad = be. (§231.) Whence, a:c = b:d. (§...

The Elements of Geometry

Webster Wells - 1894 - 378 σελίδες
...manner, a : c = b : d, b : a = d: c, etc. PROPOSITION III. THEOREM. 234. In any proportion, the terms are in proportion by ALTERNATION ; that is, the first term is to the third as the se.-ond term is to the fourth. Let the proportion be a: b = c:d. (1) To prove a : c = b : d. We have...




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