## An Expository Sketch of a New Theory of the Calculus |

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### Other editions - View all

An Expository Sketch of a New Theory of the Calculus William Batchelder Greene No preview available - 2009 |

An Expository Sketch of a New Theory of the Calculus (Classic Reprint) William Batchelder Greene No preview available - 2018 |

An Expository Sketch of a New Theory of the Calculus (Classic Reprint) William Batchelder Greene No preview available - 2017 |

### Common terms and phrases

a'de abscissa actual analogy angle assumed axis of x becomes calculus called centimetre common concave conceive conception consequently consideration considered constant contained continuously convex coordinates correlative corresponding curvature curve cuts the axis decreasing definition determination differential direction distance drawn element equal equation evident exact example existence expression extremity fact follows give given greater identical increase increasing function infinitely small integral length logarithmic manner maximum means measured mind Moreover nate nature negative notion Observations obtain ordi ordinate origin parallel particular point of tangency positive possess present primitive Putting quantity rate of increase reader reason receives regarded relation remains represented right line secant second derived line side space special value Substituting taken takes tangent term theorem theory things tion truth unity variable variation vary x and y zero

### Popular passages

Page 75 - If, with a view to demonstrate any proposition, a certain point is supposed, by virtue of which certain other points are attained ; and such supposed point be itself afterwards destroyed or rejected by a contrary supposition ; in that case, all the other points attained thereby, and consequent thereupon, must also be destroyed and rejected, so as from thenceforward to be no more supposed or applied in the demonstration.

Page 34 - Hamlet with the part of the Prince of Denmark omitted, for so far I have said nothing whatever about technical education.

Page 10 - From (3) p b9 b tan0'= 2~b = 2Tb=2l but this is the trigonometrical tangent of the angle which the tangent to the curve at (a, b) makes with the axis of x. Hence the new axis of y ' is a tangent to the curve at the origm.

Page 85 - *=!* and by simply changing the axes, we have hence, the sub-tangent is equal to the modulus of the system of logarithms from which the curve is constructed. In the Naperian system M=l, and hence the sub-tangent will be equal to 1 = AE.

Page 29 - ... when referred to the same pole and initial line. Show that the radius of curvature at any point of this locus is J of the length of the radius vector to the corresponding point on the original curve. for a plane curve, the upper or lower sign being taken according as the curve is convex or concave to the axis of x, The normal at the point P of the conic Zabx = Ьхг + ay1 meets the axis of x at G.

Page 5 - ... Measures to the farm, the household, the mechanic arts, etc., are so extensive that we now present a distinct treatment of the subject. 333. These Practical Measurements include Measures of Surface, Measures of Volume, Measures of Capacity, and Comparison of Weights and of Money. MEASURES OF SURFACE. 334. A Surface is that which has length and breadth without thickness. THE EECTANGLE.

Page 56 - Further, it is to be known that it is man by means of whom the natural world is conjoined with the spiritual...

Page 48 - ... the three components (two horizontal and one vertical) of the movement under investigation. In what follows we shall consider only the horizontal movements; the same arguments, however, may be applied to the case of vertical movements. Let us suppose a small horizontal platform to be moving parallel to the axis of X, and let it be required to determine the acceleration of this motion. On this platform an apparatus is mounted which can oscillate parallel to the same axis with a natural period,...

Page 1 - A more general definition of function is : // two or more variables are so related that to any given set of values comprising one and but one value for each of the variables except one of them there corresponds at least one value of the latter variable, each of the variables is said to be a function of all the others. Thus, if v be the volume of a parallelepiped, say a slab, and if /, b and / be respectively its length, breadth, and thickness, each of the four variables is a function of the remaining...

Page 84 - The value m, which depends upon the value of the base a, of the system of logarithms employed, is called the modulus of the system.