## The Elements of Algebra Preliminary to the Differential Calculus: And Fit for the Higher Classes of Schools in which the Principles of Arithmetic are Taught |

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added addition algebraical altered answer appears applied approximate arithmetical becomes begin called common Consequently considered contains continued convergent correct cube cubic definition diminishes without limit divided division divisor equal equation evident example exponent expression feet figure fraction functions given gives greater half Hence impossible inches increase infinite instance less letters limit logarithm meaning method miles multiplied namely nearly necessary negative observe obtained operations positive possible preceding principle problem proceed proved quantity question rational reasoning reduced remainder represented respect result rules satisfy shew shillings side similar solution speaking square root stand student subtraction suppose supposition symbols taken theorem thing third true units weight whole number write yard

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Page 223 - The logarithm of a product is equal to the sum of the logarithms of its factors.

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 xxviii - Consider the fast terms as having the sign + ; multiply every term of the multiplicand by every term of the multiplier...

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 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 64 - 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...