## A Treatise on the Differential Calculus: And Its Applications to Algebra and Geometry, Founded on the Method of Infinitesimals |

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### Other editions - View all

A Treatise on the Differential Calculus: And Its Applications to Algebra and ... Bartholomew Price No preview available - 2015 |

### Common terms and phrases

algebraical asymptote becomes branches calculated change of sign changes sign Chapter circle coefficients consider constant convex coordinates corresponding critical values curvature Curve whose Equation cusp cycloid decreases denominator derived-functions determine dimensions direction drawn in fig dx dy dy dx eliminated ellipse epitrochoid equa equal Evaluate expression factor finite quantity fraction func geometrical given greater Hence homogeneous function hyperbola hypocycloid hypotrochoid implicit function increases increments indeterminate form infinite infinitesimal Infinitesimal Calculus infinity involved length limit logarithmic maxima and minima maximum or minimum means minimum value negative ordinate origin parabola perpendicular plane curve plane of reference point of inflexion polar positive radius vector real roots result shewn side Similarly straight line substituted subtangent suppose symbol tangent Taylor's Series tesimal tion Tractory triangle vanish variations of signs whence Witch of Agnesi

### Popular passages

Page 429 - but varies for different media; that is, the sine of the angle of incidence bears a constant ratio to the sine of the angle of refraction. The envelope of all the refracted rays is called the caustic by refraction of the given surface*.

Page 283 - cycloid is the curve traced out by a point in the circumference of a circle, as the circle rolls along a fixed straight line. (a) Let the given straight line (fig. 39) be taken as the axis of x, and the radius of the

Page 276 - and y have already preoccupied the two directions at right angles to each other in the plane of the paper, which is (and conveniently so) called the plane of reference, we must seek for some other course by which a line,

Page 303 - when x = a, a line parallel to the axis of y, at a distance a from it, is an asymptote ; and if x = oo , when y = b, a line parallel to the axis of x, at a distance

Page 44 - (fig. 4) be the circle, of which let the radius be a; take o the centre, and let the angle AOC be the rath part of four right angles, and AC be the side of a regular polygon of n sides inscribed in the circle ; and make

Page 335 - it is plain that the curve is symmetrical with respect to the axis of x, and since the curve passes through the origin, the

Page 283 - a curve, such that FT, the length of the tangent intercepted between the point of contact and the axis of x, is always equal to OA, then the locus of P is the equitangential curve. Let OM = x, MP = y, OA = PT = a; then the definition of the curve above given leads, as will be seen in the next Chapter, to an equation of the form

Page 246 - Ex. 7. To find a point within a triangle, such that the sum of the lines drawn from it to the angular points may be a minimum.

Page 390 - the length of the evolute is equal to the difference of the radii of curvature of the involute corresponding to its two extremities. Of this we subjoin some examples

Page 358 - the equation represents an ellipse, parabola, or hyperbola, according as e is less than, equal to, or greater than unity. Hence the equation to the parabola