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a²+x² algebraic altitude angle Anthon's asymptotes axes axis of abscissas becomes chord circle circumference conjugate diameters conjugate hyperbola corresponding cosine cubical parabola cycloid described divided draw drawn dx² ellipse equal to zero exponent Find the integral formula Geom given point Hence hyperbola inch per second increase uniformly increment inscribed Integrate the expression logarithmic logarithmic spiral major axis maximum minimum multiplied negative obtain ordinate parabola parallel parenthesis perpendicular point of inflection polar curve Prop PROPOSITION I.-THEOREM radius of curvature radius vector ratio rectangle rectangular represent Required the differential required to determine required to find revolution SCHOLIUM secant line second differential coefficient Sheep extra side solidity spiral square straight line Substituting this value subtangent suppose surface tang tangent line Taylor's theorem theorem transverse axis unity versed sine vertex whence
Page 36 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.
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
Page 4 - Loomis's Elements of Plane and Spherical Trigonometry, with their Applications to Mensuration, Surveying, and Navigation. To which is added a full Series of Tables of Logarithms of Numbers, and of Sines and Tangents for every Ten Seconds of the Quadrant.
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...