## New Mathematical Tables Containing the Factors, Squares, Cubes, Square Roots, Cube Roots, Reciprocals, and Hyperbolic Logarithms: Of All Numbers from 1 to 10000; Tables of Powers and Prime Numbers; an Extensive Table of Formulæ, Or General Synopsis of the Most Important Particulars Relating to the Doctrines of Equations, Series, Fluxions, Fluents, &c. &c. &c |

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### Common terms and phrases

4th Power 5th Power absciss angle sought approximate root Assume axis biquadratic equation brº change of sign circular sector CIRCULAR SEGMENTS co-efficients computation cube root cubic equation decametre denote diameter diff difference ditto Factors feet Fluxions formula fraction frustrum given angle given leg given side hyperbolic logarithm imaginary roots integral irreducible least less limits multiplying Myriogramme nearest nearly negative Newton's method Numb obtained obvious odd number original equation places of decimals places of figures positive roots preceding terms prime number proposed equation proposed number radius real roots Reciprocals represent Required the square rule segment sine Solidity solution square and cube square root substitute toises unknown quantity Whence zero

### Popular passages

Page 319 - Gramme, which is the weight of a cubic centimetre of distilled water, is the element for all weights.

Page liv - ... 17, &c. These numbers have formed a subject of investigation and inquiry from the earliest date down to the present day ; and a rule for finding them is still amongst the desiderata of mathematicians. The method of finding a prime number beyond a certain limit, by a direct process, is considered one of the most difficult problems in the theory of numbers, which, like the quadrature of the circle, the trisection of an angle, and the duplication of the cube, have engaged the attention of many able...

Page xxxi - Every equation of an even degree, involving only real coefficients of which the last term is negative, has at least two real roots, one positive and the other negative.

Page 319 - ... the unity of length, called a metre. In order to express decimal proportions in this new system, the following terms have been adopted. The term Deçà prefixed, denotes 10 times ; Heca, 100 times ; ('Kilo, 1000 times ; and Myrio, 10,000 times. On the other hand, Deci expresses the 10th part ; Centi the 100th part ; and Milli the 1000th part : so that Decametre signifies 10 metres ; the Decimetre the 10th part of a metre ; &c. The Metre is the element of long measures ; Arc, that of square measures...

Page xxxviii - Transform an equation into one whose roots shall be the squares of the differences of the roots of the original equation...

Page 300 - G, the distance of the centre of gyration from the axis of motion, t, the time the force acts, v the velocity acquired by the revolving body in that time.

Page 171 - ... and of the fourth and fifth powers of all numbers from 100 to 1000. Tables of Multiplication to a still greater extent have been published in France. In...

Page liii - ... saw, for the first time since leaving Panama, a luxuriant vegetation, but which however was far from being comparable with that of the last-mentioned country. To what difficulties such journeys are subject, may be generally known from the accounts of travellers in the pursuit of natural history ; but it may not be uninteresting to the reader to be informed of Mr. Hasskarl's experience in that respect. The roads over the mountains of Peru are bad, mostly not broader than a bridle-path, and there...

Page xxx - The coefficient of the third term is equal to the sum of all the products that can be formed by taking the roots two at a time.