Principles of the Differential and Integral Calculus ...J. Taylor, 1836 - 174 sivua |
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Principles of the Differential and Integral Calculus William Ritchie Esikatselu ei käytettävissä - 2019 |
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2adx 2xdx a²x² abscissa algebraic ax² b2 a² base becomes equal circle circumference constant quantity coversin cube curve cycloid cylinder d³u denominator denotes determine diameter differen Differential Calculus differential coefficient diminish DIONYSIUS LARDNER dividing dx² ellipse equation example EXERCISES ferential find the differential formly fraction function geometrical given Hence hyperbola ILLUSTRATION inch per second increase uni increase uniformly increment indefinitely small independent variable infinite Integral Calculus learner limit move uniformly multiplied Naperian logarithm number of terms ordinate parabola perpendicular principles pupil radius of curvature rate of increase rectangle Required the developement required the length right angles rule side solidity square straight line Substituting these values subtangent supposed surface tangent Taylor's Theorem triangle variable quantity vertex whilst
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Sivu iii - PRINCIPLES of GEOMETRY, familiarly Illustrated, and applied to a variety of useful purposes. Designed for the Instruction of Young Persons. Second Edition, revised...
Sivu vii - ... 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.
Sivu 80 - The surface of a sphere is equal to four times the area of a circle...
Sivu vi - ... 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...
Sivu 51 - 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.
Sivu 172 - ... 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.
Sivu 93 - 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.
Sivu 2 - 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.