## Elements of the Differential and Integral Calculus |

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Algebra altitude angle apply asymptote auxiliaries axes Binomial Theorem Calculus centre of gravity co-ordinates concave constant convex cusp cycloid cylinder d²y d³y derived determine Differential Calculus distance dx dx² dx dy dx² dx³ dy dx dy² equal evolute expression find the differential Find the integral Find the value finite force formula infinitely small intersects the axis logarithmic manner maxima and minima maximum or minimum multiple point multiplied negative obtain ordinate osculatory circle parabola perpendicular plane curve point of inflexion polar curves positive problem proposed radius of curvature radius vector reducing render the function required to find right line second differential coefficient solid solids of revolution solution sought spiral subtangent suppose surface Taylor's Theorem theorem tion vary velocity vertex whence by substitution x²)³

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Page 224 - The squares of the periods of revolution of any two planets are proportional to the cubes of their mean distances from the sun.

Page 205 - ... base; the one of the air of the external atmosphere, and the other column of the air in the chimney, of the same height when hot, but reduced by cooling to the temperature of the atmosphere. Now, according...

Page 92 - ... the tangent of the angle which the line makes with the axis of abscissae), was lately employed by M. Crova* for the discussion of experiments relating to the degree of constancy possessed by so-called

Page 132 - Art. 255); and the equation will become id \ i du a(lu) = le — , tv that is, the differential of the logarithm of a quantity is equal to the modulus of the system into the differential of the quantity divided by the quantity itself. 57. If we suppose a = e the base of the Naperian system, and employ the usual characteristic I...

Page 231 - A magnitude is said to be ultimately equal to its Limit; and the two are said to be ultimately in a ratio of equality. 4. A line or figure ultimately coincides with the line or figure which is its Limit.

Page 171 - Curve is ono whose equation contains transcendental functions. Many of the higher plane curves possess historical interest, from the labor bestowed on them by ancient mathematicians. We shall consider only a few of them. THE CISSOID OF DIOCLES. 148. This curve was invented by Diocles, a Greek geometer who lived about the sixth century of the Christian era; the purpose of its invention was the solution of the problem of finding two mean proportionals. It may be defined as follows : If pairs of equal...

Page 239 - What is the length of the axis of the maximum parabola that can be cut from a given right cone ? Ans.

Page 40 - To divide a number a into two parts such that the sum of the squares of the parts shall be the least possible.

Page 176 - Ex. 2. The axes of two equal right circular cylinders intersect at right angles. Required the volume common to the cylinders. Let OA and OB (fig.

Page 238 - This curve is traced by a point in the circumference of a circle which rolls upon a straight line as a directrix, as the curve oa2as (Fig.