## The Differential Calculus: With Unusual and Particular Analysis of Its Elementary Principles, and Copius Illustrations of Its Practical Application |

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algebraic algebraic quantities amount becomes Binomial Theorem bushels cask cents coef common common logarithm compound interest condition constant construction curve denominator diameter differential calculus differential coefficient diminish distance Dock Square dx dy equal equation evident exponential function expression factor feet formula func given Hence increase independent variable inferred infinite leap length Maclaurin's Theorem maxima and minima maximum or minimum miles per hour modulus negative values notation number of dollars number of miles number of pounds numerical quantity ounces plane positive possible problem ratio reference Required the differential Required the number Required the value required to determine required to develop result root second dif SECTION straight line subtraction supposed Taylor's Theorem thrown body tion treatise vanishing fraction vary whole number

### Popular passages

Page 93 - A prism is a solid figure contained by plane figures, of which two that are opposite are equal, similar, and parallel to one another ; and the others parallelograms.

Page 64 - A single analytical formula," Playfair adds, " in the Method of Increments, has conferred a celebrity on its author which the most voluminous works have not often been able to bestow. It is known by the name of Taylor's Theorem, and expresses the value of any function of a variable quantity in terms of the successive orders of increments, whether finite or infinitely small. If any one proposition can be said to comprehend in it a whole science, it is this : for from it almost every truth and every...

Page 76 - B set out from two towns, which were distant 247 miles, and travelled the direct road till they met. A went 9 miles a day ; and the number of days, at the end of which they met, was greater by 3 than the number of miles which B went in a day. How many miles did each go ? 17.

Page 64 - ... has conferred a celebrity on its author, which the most voluminous works have not often been able to bestow. It is known by the name of Taylor's Theorem, and expresses the value of any function of a variable quantity in terms of the successive orders of increments, whether finite or infinitely small. If any one proposition can be said to comprehend in it a whole science it is this : for from it almost every truth and every method of the new analysis may be deduced. It is difficult to say, whether...

Page 93 - A dodecahedron is a solid figure contained by twelve equal pentagons which are equilateral and equiangular.

Page 149 - It was also shown in the same article, that the differential of the sum of any number of functions is equal to the sum of their...

Page iii - The Differential Calculus: with Unusual and Particular Analysis of its Elementary Principles, and Copious Illustrations of its Practical Application.

Page 12 - The quantity thus generated is called the fluent, or flowing quantity. 3. The velocities with which flowing quantities increase or decrease at any point of time, are called the fluxions of those quantities at that instant. Cor. 1. As the velocities are in proportion to the increments or decrements uniformly generated in a given time, such increments or decrements will represent the fluxionsf . * SIR I.

Page v - ... mathematical conception." The difficulties which this work is fitted to overcome are so idiosyncratic, that it will fail, we think, to meet the common needs of the student, who will find superadded to the difficulties of " pure mathematical conception " the perplexities of the author's practical problems. " The present treatise on the Differential Calculus is believed to be the first, of any character, that has been written and published in America as the special topic of a volume ; and the first,...

Page vi - The calculus being algebra, a strictly numerical science, the present treatise claims to have labored successfully in putting on the true character as such. No insinuation is allowed to prevail that it is any part whatever of analytical geometry or that it is other than the natural sequel and supplement of common algebra; useful, indeed, as an appliance, to borrow, in investigation of the few kinds of geometrical quantity.