A Survey Course in Mathematics |
Common terms and phrases
abscissa algebra altitude analytic geometry approaches zero ax² ax³ axis calculus called circle x² computing cone Construct the graph coördinate axes coördinates cosine course cubical parabola CUMULATIVE REVIEW definition derivative is zero differential ellipse Example EXERCISES falling body feet per second figure Find the derivative Find the equation find the length Find the volume frustum geometric series geometry given Greeks Hence horizontal hyperbola integral latitude mathematics maxima and minima maximum means measured method minimum multiplied negative obtained ordinate parabola plane plane geometry positive PROBLEMS FOR INVESTIGATION quadrant radius represents right triangle shown sides sine Sketch the curve slope SOLUTION solved sphere square straight line student Substituting surface tangent theorems tion triangle ABC trigonometric functions trigonometry variable velocity volume inclosed x-axis x₁ y-axis y₁
Popular passages
Page 102 - Some people hate the very name of statistics, but I find them full of beauty and interest. Whenever they are not brutalized, but delicately handled by the higher methods, and are warily interpreted, their power of dealing with complicated phenomena is extraordinary. They are the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of those who pursue the Science of man (pp.
Page 113 - Newton generalized the law of attraction into a statement that every particle of matter in the universe attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them; and he thence deduced the law of attraction for spherical shells of constant density.
Page 12 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.
Page 46 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Page 12 - Two triangles are congruent if two angles and the included side of one are equal respectively to two angles and the included side of the other.
Page 103 - I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the "Law of Frequency of Error." The Law would have been personified by the Greeks and deified, if they had known of it. It reigns with serenity and in complete self-effacement amidst the wildest confusion. The huger the mob and the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of unreason.
Page 38 - The horizontal line is called the x-axis and the vertical line the y-axis, and these two lines together are called the coordinate axes.
Page 74 - Hyperbola is the locus of a point which moves so that its distance from a fixed point, called the focus, bears a constant ratio, which is greater than unity, to its distance from a fixed straight line, called the directrix.
Page 46 - In any triangle the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon it.
Page 74 - The mathematical definition of an ellipse is: A plane curve such that the sum of the distances from any point on the curve to two fixed points is a constant.