## A Treatise on Infinitesimal Calculus: Differential calculus. 1857 |

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### Common terms and phrases

algebraical angles asymptote axis Calculus change of sign changes sign circle coefficients conic constant coordinates corresponding critical values curvature cycloid decreases determine differential equation dimensions direction drawn dy dx elimination ellipse epitrochoid equa equal equicrescent equivalent examples expression factors finite quantity geometrical given point greater Hence homogeneous homogeneous function hyperbola hypotrochoid imaginary increases infinitesimal Infinitesimal Calculus infinity involved l)th let us suppose logarithmic maxima and minima maximum or minimum minimum value negative nth degree observed ordinate origin parabola partial derived-functions pass perpendicular plane curves plane of reference point of inflexion points of intersection polar positive primitive equation properties radius real roots replaced right-hand member shewn Similarly singular value straight line Sturm's Theorem substituting symbol tangent Theorem tion triangle vanish whence Witch of Agnesi zero

### Popular passages

Page 495 - When one medium is a vacuum, n is the ratio of the sine of the angle of incidence to the sine of the angle of refraction. retardation, S — optical path difference between two beams in an interferometer; also known as "optical path difference

Page 14 - It would, therefore, occupy 206265 times this interval or 3 years and 83 days to traverse the distance in question. Now as this is an inferior limit which it is already ascertained that even the brightest and therefore (in the absence of all other indications) the nearest stars exceed, what are we to allow for the distance of those innumerable stars of the smaller magnitudes which the telescope discloses to us ! What for the dimensions of the galaxy in whose remoter regions, as we have seen, the...

Page 315 - Find its equation. Show that the radius of curvature at each point of the curve is inversely proportional to the length of the normal intercepted between the point on the curve and the ?/-axis.

Page 12 - The powers, therefore, of our senses and mind place the limit to the finite ; but those magnitudes which severally transcend these limits, by reason of their being too great or too small, we call i...

Page 419 - Hyperbola, according as e is less than, equal to, or greater than unity.

Page 14 - It would, therefore, occupy 100000000 seconds, or upwards of three years, in such a journey, at the very lowest estimate. What, then, are we to allow for the distance of those innumerable stars of the smaller magnitudes which the telescope discloses to us ! If we admit the light of a star of each magnitude to be half that of the magnitude next above it, it will follow that a star of the first...

Page 316 - The Cycloid. The cycloid is traced out by a point in the circumference of a circle as the circle rolls along a straight line.

Page 526 - To find the general equation to cylindrical surfaces. A cylindrical surface is generated by a straight line which moves parallel to itself, and always passes through a given curve.

Page 278 - Find a point within a triangle such that the sum of the square of its distances from the three angular points is a minimum.

Page 479 - From a fixed point on the circumference of a circle chords are drawn, and on these as diameters circles are drawn.