Elements of Analytical Geometry and of the Differential and Integral Calculus
Harper & Brothers, 1851 - Calculus - 278 pages
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algebraic angle asymptotes axes axis of abscissas base becomes binomial called chord circle circumference co-ordinates conjugate consequently constant containing corresponding curvature curve cycloid described determine diameter difference diminish distance divided draw drawn ellipse equal equal to zero equation exponent expression feet formula function give half Hence hyperbola inch per second increase increment independent infinite integral length less limit logarithmic maximum measuring multiplied negative normal obtain ordinate origin parabola parallel passing perpendicular positive preceding Prop PROPOSITION quantity radius radius vector ratio rectangle reduces referred represent required to find result side sine solidity spiral square straight line Substituting this value subtangent suppose surface tang tangent tangent line theorem triangle unity variable whence
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Page 106 - The Cycloid. The cycloid is the curve described by a point in the circumference of a circle rolling in a straight line.
Page 4 - First Book in Greek. Containing a full View of the Forms of Words, with Vocabularies and copious Exercises, on the Method of constant Imitation and Repetition.
Page 230 - To free the equation of fractional exponents, substitute for the unknown quantity a new unknown quantity with an exponent equal to the least common multiple of the denominators of the exponents in the equation. Thus, in (1) put y = z", whence y * — z"", y ' = e", and y
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Page 113 - As the body falls, the distance d and the time s are variables, and 16 is a constant. Again, time measured from a past date is a variable, while time measured between two fixed dates is a constant. 2. The constants in a mathematical investigation are, as a rule, general numbers, and are represented by the first letters of the alphabet, a, b, c, etc. ; variables are usually represented by the last letters, x, y, z, etc. 3. A variable which has a definite value, or set of values, corresponding to a...
Page 2 - Grammar of the Greek Language. For the use of Schools and Colleges. 12mo, Sheep extra, 75 cents.
Page 36 - A radius of a circle is a straight line drawn from the centre to the circumference.
Page 205 - O = slope of the indifference curve on A or B = —— It is thus clear from above that if we have to find out the MRS^ at a point on the indifference curve we can do so by drawing tangent at the point on the indifference curve and then measuring the slope by estimating the value of the tangent of the angle which the tangent line makes with the X-axis. Principle of Diminishing Marginal Rate of Substitution An important principle of economic theory is that marginal rate of substitution of X for Y...