## 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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2adx 2xdx abscissa arc ae base becomes equal called circle circumference constant quantity cosecant coversin cube curve cycloid cylinder denominator denotes determine diameter differen Differential and Integral Differential Calculus differential coefficient diminish Dionysius Lardner dividing ellipse example EXERCISES ferential find the differential formly fraction function geometrical given Hence hyperbola illustrate inch per second increase uni increase uniformly increment increment read indefinitely small independent variable infinite Integral Calculus learner limit move uniformly multiplied Naperian logarithm number of terms obtain ordinate parabola perpendicular principles pupil radius of curvature rate of increase ratio of equality rectangle Required the developement required the length right angles rule secant SECTION side solidity square straight line Substituting these values subtangent supposed surface tangent Taylor's Theorem tion transverse axis triangle variable quantity vertex whilst x'dx

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Page iii - PRINCIPLES of GEOMETRY, familiarly Illustrated, and applied to a variety of useful purposes. Designed for the Instruction of Young Persons. Second Edition, revised...

Page 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.

Page 80 - The surface of a sphere is equal to four times the area of a circle...

Page 175 - Dr. Ritchie's little elementary work is excellently well adapted to its object. It is brief, plain, and full of all that is necessary : curious and useful in its application ; and beyond any other of the kind now existent in its familiar and distinct explanation of some of the instruments required in the practical application of the principles laid down and demonstrated.

Page 175 - LL.DFRS 12mo. with 150 Woodcuts. 3s. 6d. cloth. " The practical applications which are added must render the study very delightful to the young, since the Exercises on the Principles will be found as amusing as the ordinary sports of childhood.

Page 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...

Page 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.

Page 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.

Page 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.

Page 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.