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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from ...Show synopsisThis historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1863 Excerpt: ...by a: b. 232. The first term of a ratio is called the Antecedent, and the last term the Consequent. The antecedents in the preceding ratios are, therefore, 12, 19, and a, and the consequents 4, 9, and b. 233. Ratios may, therefore, be represented in the form of fractions, by making the antecedents the numerators, and the consequents the denominators; thus, 12 19, a-j.-g-, and-, express the ratios of 12 to 4, of 19 to 9, and of a to J. 234. A ratio is said to be of equality when the antecedent is equal to the consequent. Thus the ratio of 12: 12, or of a: a, is a ratio of equality. 235i A ratio is of greater inequality when the antecedent is greater than the consequent. Thus, The ratio of a+b: a, or of 12: 6, is a ratio of greater inequality. 236 A ratio of less inequality is when the antecedent is less than the consequent. Thus, The ratio of a: a--b, or of 6: 12, is a ratio of less inequality. Note.--It is evident that the ratio of equality may always be represented by unity. COMPARISON BY RATIOS. 237i If the terms of a ratio are both multiplied or both divided by the same quantity, the value of the ratio is not altered. The ratio of a: b is expressed by the fraction T. Let both b terms of this fraction be multiplied by n, and it becomes--. nb 4 The ratio of 4: 3 is expressed by the fraction-; and, if the o 12 4 terms of this fraction be multiplied by 3, it becomes-q-=k. Now, since the value of a fraction is not altered by multiplying both the numerator and denominator by the same quantity, a na T=-t, or the ratio a: b is the same as the ratio na: nb, and b nb the ratio of 12: 9 is the same as 4: 3. Thus the ratio of 16: 12, both terms being divided by 4, is the same as 4: 3. The ratio of 5: 7, both terms being multiplied by 3, is the same as the ratio of 1...Hide synopsis

Description:Good. Well-aged (hinge cracks, edgewear, spine cover heel...Good. Well-aged (hinge cracks, edgewear, spine cover heel missing 1/2"), but binding solid. Fading to part of front cover. P. O. name front and signature on back end papers. "John R. White, Berryville, Clark Co. Va. " Your purchase benefits world-wide relief efforts of Mennonite Central Committee.

Description:Good-/No Jacket. 8vo-over 7¾"-9¾" tall Cover has moderate wear,...Good-/No Jacket. 8vo-over 7¾"-9¾" tall Cover has moderate wear, chipping to corners. Missing front blank endpaper, hinge cracked and loose, foxing throughout. Tight and readable. Previous owner inscriptions. 360 pages. Black cover with black leather spine. An algebra text from the mid 19th century.

Title: A Practical Treatise on Algebra, Designed for the Use of Students in High Schools and Academies Author:Benjamin Greenleaf ISBN-13:9781175693938 ISBN:1175693936

Title: A Practical Treatise on Algebra: Designed for the Use of Students in High Schools and Academies... Author:Benjamin Greenleaf ISBN-13:9781247517322 ISBN:1247517322

Title: A Practical Treatise on Algebra: Designed for the Use of Students in High Schools and Academies Author:Benjamin Greenleaf ISBN-13:9781143506161 ISBN:1143506162

Title: A Practical Treatise on Algebra: Designed for the Use of Students in High Schools and Academies Author:Benjamin Greenleaf ISBN-13:9781144954626 ISBN:1144954622

Title: A Practical Treatise on Algebra: Designed for the Use of Students in High Schools and Academies Author:Benjamin Greenleaf ISBN-13:9781144005007 ISBN:1144005000

Title: A Practical Treatise on Algebra: Designed for the Use of Students in High Schools and Academies Author:Benjamin Greenleaf ISBN-13:9781144077929 ISBN:1144077923

Title: A Practical Treatise on Algebra: Designed for the Use of Students in High Schools and Academies... Author:Benjamin Greenleaf ISBN-13:9781247517322 ISBN:1247517322