## An introduction to the differential and integral Calculus1848 |

### Other editions - View all

An Introduction to the Differential and Integral Calculus: With an Appendix ... James Thomson, gen No preview available - 2016 |

An Introduction to the Differential and Integral Calculus: With an Appendix ... James Bates Thomson No preview available - 2018 |

### Common terms and phrases

according angle appears application assume axis becomes branches Calculus called circle common computation consequently consider constant quantity contain continually coordinates corresponding curve denominator denote derived described determine difference differential coefficient diminished dividing easy ellipse employed equal equation established evidently example expression factors foregoing formula fraction function give given greater Hence hyperbola increase infinite instance integral kind latter length less limit logarithms manner maximum means method multiplying nature nearly negative obtained origin parabola parallel passing perpendicular plain positive principles proposed Prove putting radius ratio readily reference regarding respectively result sides similar simply sine square straight line substituting successive taken taking tangent tend theorem third tion triangle TRIG variable whence zero

### Popular passages

Page 24 - The logarithm of a number is the index of the power to which the base of the system must be raised to equal a given number.

Page 277 - ... is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16. And this point is called the centre of the circle.

Page 109 - The surface of a sphere is equal to four times the area of a circle...

Page i - ELEMENTARY TREATISE ON ALGEBRA, Theoretical and Practical. By JAMES THOMSON, LL.D. Professor of Mathematics in the University of Glasgow.

Page 307 - ... 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 98 - Sometimes the curve after being convex to the axis suddenly changes its curvature, and becomes concave, the point at which the change takes place is called a point of inflexion, or of contrary flexure. If the tangent at this point be produced, one branch of the curve will be above, and the other below it, consequently on one side of the point in question — - -will be dx1 positive, and on the other side, negative.

Page 88 - To divide a given number a, into two parts, such that the product of the mth power of the one and the nth power of the other shall be the greatest possible. Let x be one part, then a — * is the other, and y = a...

Page 90 - What is the equation of the tangent to the curve at the point (2, -8)7 At the point (3, -9)?

Page 304 - ... and so on. But only a mind which has traced the consecutive deductions of the geometer is conscious of the necessary truth of the propositions, that circles are to one another as the squares of their diameters, and that spheres have to one another the triplicate ratio of that which their diameters have.

Page 252 - Calculus," which has been just published, relative to a subject of some interest in the history of science. " 394. Given the latitude of a place, and two circles parallel to the horizon ; to find the declination of a body which, in its apparent diurnal motion, will pass from one of them to the other in the shortest time possible.* " Let Z and P be the zenith and pole, and S and S' the required points on the given parallels, having equal polar distances, PS and P S'.