Principles of the Differential and Integral Calculus: Familiarly Illustrated, and Applied to a Variety of Useful Purposes. Designed for the Instruction of Youth

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J. Taylor, 1836 - 174 lappuses

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iii. lappuse - PRINCIPLES of GEOMETRY, familiarly Illustrated, and applied to a variety of useful purposes. Designed for the Instruction of Young Persons. Second Edition, revised...
vii. lappuse - ... of analytical operations, acquired by dint of practice and experience, is a mere common species of labour, often merely mechanical; whilst a distinct apprehension of the specific object and meaning of the operations, and a contemplation of the clearness and beauty of the various arguments employed, constitute the intellectual lore that gratifies and enriches the mind, and stimulates its energies with an ardour after the investigation of truth.
80. lappuse - The surface of a sphere is equal to four times the area of a circle...
vi. lappuse - ... conclusion is geometrically in close connexion with the first cause, is very different from that which it receives from putting in play the long train of machinery in a profound analytical process. The degrees of conviction in the two cases are very different. It is known to every one who has been engaged in the instruction of students at our Universities, that the results of the differential calculus are received by many, rather with the doubts of imperfect faith than with the confidence of...
51. lappuse - When is this possible? 4. Divide a given straight line into two parts, so that the rectangle contained by the parts may be equal to a given rectangle.
172. lappuse - ... as a line by the motion of a point ; a surface by the motion of a line ; and a solid by the motion of a surface.
93. lappuse - Y, and x+y is the sum of their logarithms; from which it follows that the sum of the logarithms of two numbers is equal to the logarithm of their product. Hence, To multiply two or more numbers by using logarithms: Rule.
2. lappuse - By continuing to double the number of sides, the area of the polygon will approach nearer and nearer to that of the circle, and- may be made to differ from it by a quantity less than any finite quantity.

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