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Elements of Algebra Preliminary to the Differential Calculus
Augustus De Morgan
No preview available - 2012
abbreviations algebraical quantities altered Anomaly answer applied arithmetical arithmetical meaning AUGUSTUS DE MORGAN called coefficient common Consequently contains convergent convergent series correct cube root cubic feet cubic foot denote differential calculus diminishes without limit divergent series divided division divisor equal numbers example exceeds exponent functions given gives greater Hence impossible subtraction inches increases without limit infinite number instance Lemma less letters logarithm mantissa meaning method metical miles multiplied nearly equal negative quantity number of terms number or fraction numerator and denominator polynomial preceding equation problem proceed proved question rational rational polynomials remainder result rules shew shewn shillings a yard solution specific gravity square root suppose supposition symbols taken tion true twelfth root unknown quantities Verification weight whence whole number word
Page 251 - ... contained in this treatise, and those, for the most part, in so imperfect a way, that he is not fit to encounter any question unless he sees the head of the book under which it falls. On a very moderate computation of the time thus bestowed, the pupil would be in no respect worse off, though he spent five hours on every page of this work. The method of proceeding which I should recommend, would be as follows '. Let the pupils be taught in classes, the master explaining the article as it stands...
Page 228 - If the curiosity of any gentleman that has leisure, would prompt him to undertake to do the logarithms of all prime numbers under 100,000 to 25 or 30 figures, I dare assure him that the facility of this method will invite him thereto ; nor can anything more easy be desired. And to encourage him, I here give the logarithms of the first prime numbers under 20 to 60 places.
Page v - The operation of division is also indicated by writing the divisor under the dividend with a line between them ; thus 14 by 2 is also frequently denoted thus y.
Page 255 - PRINCIPLES OF GEOMETRY, familiarly Illustrated, and applied to a variety of useful purposes. Designed for the Instruction of Young Persons.
Page 27 - ... gravity but the percentage of voids. The specific gravity of any material is the quotient found by dividing its weight by the weight of an equal bulk of water. Water, therefore, has a specific gravity of 1 ; a cubic foot of any substance like granite, having a specific gravity of 2.65, weighs 2.65 times as much as a cubic foot of water. A cubic foot of water weighs 62.355 Ibs., or practically 62.4 Ibs. ; hence a cubic foot of solid granite weighs, 2.65 X 62.4 = 165.3 Ibs.
Page 251 - ... otherwise. All who have been engaged in the education of youth are aware that it is a hard thing to make them think ; so hard, indeed, that masters had, within the last few years, almost universally abandoned the attempt, and taught them rules instead of principles, by authority instead of demonstration. This system is now passing away, and many preceptors may be found who are of opinion that, whatever may be the additional trouble to themselves, their pupils should always be induced to reflect...
Page 62 - It follows that any four numbers are proportionals, when the first divided by the second is equal to the third divided by the fourth.
Page xxxix - I hope it never will be any ether ; were it only for this reason, that so much has been written on Euclid, and all the difficulties of geometry have so uniformly been considered with reference to the form in which they appear in Euclid, that Euclid is a better key to a great quantity of useful reading than any other.
Page xxxix - ... [students, the majority of which were not distinguished for mathematical taste and power] were subjected. TODHUNTER, I. Essay on Elementary Geometry; Conflict of Studies and other Essays (London, 1873), p. 167. 1819. In England the geometry studied is that of Euclid, and I hope it never will be any other; for this reason, that so much has been written on Euclid, and all the difficulties of geometry have so uniformly been considered with reference to the form in which they appear in Euclid, that...