## The Doctrine and Application of Fluxions: Containing (besides what is Common on the Subject) a Number of New Improvements in the Theory. And the Solution of a Variety of New, and Very Interesting, Problems in Different Branches of the Mathematicks |

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Abſciſſa alſo let Angle Arch Area ariſing aſcend aſſumed Axis Baſe becauſe become Body Caſe Celerity Center centripetal Force Circle Circumſtance conſequently conſidered conſtant CoRoll correſponding Curve decreaſe denoted deſcend deſcribed determine Direétion Diſtance E X A M P L E Ellipſis equal Equation expreſſed Expreſſion firſt Terms fore Fraćtion given Gravity greateſt Hence increaſe Infinite Series inſtead inverſely itſelf laſt Laſtly leaſt leſs likewiſe Line Logarithm Meaſure Motion multiply'd muſt Number obſerved Ordinate otherwiſe Parabola parallel perpendicular Point Poſition poſſible propoſed Quantity Ratio Reaſon Rećtangle repreſented reſpectively reſt Right-line Root ſaid ſame Manner ſecond Sečtion ſee ſhall ſimilar ſince ſmall Solid ſome ſtill ſubſtituted ſuch ſufficient ſuppoſed Suſpenſion Tangent thereof theſe thoſe thro Triangle uniformly Unity univerſally Uſe Value variable Velocity Vertex Whence whoſe Fluent whoſe Fluxion

### Popular passages

Page 1 - As a line is generated by the motion of a point, a surface by the motion of a line, a solid by the motion of a surface, so a fourth-dimensional body may be generated by some motion of a solid.* 5.

Page 189 - ... of judges, when they pass such sentences. There is no certainty, except when it is physically or morally impossible that the thing can be otherwise. What ! is a strict demonstration necessary to enable us to assert that the surface of a sphere is equal to four times the area of its great circle ; and is not one required to warrant taking away the life of a citizen by a disgraceful punishment?

Page vii - Sir Isaac Newton defines fluxions to be the velocities of motions, yet he hath recourse to the increments, or moments, generated in equal particles of time, in order to determine those velocities ; which he afterwards teaches us to expound by finite magnitudes of other kinds : without which (as is already hinted above) we could have but very obscure ideas of the higher orders of fluxions...

Page 241 - Thus, also, the ratio of the forces of gravitation of the moon towards the sun and earth may be estimated. For...

Page 102 - Having thus shown the manner of finding such fluents as can be truly exhibited in algebraic terms, it remains now to say something with regard to those other forms of expressions involving one variable quantity only ; which yet are so affected by compound divisors and radical quantities, that their fluents cannot be accurately determined by any method whatsoever. The only method with regard to these, of which there are...

Page 52 - Q. in F. Now it is evident, that if the motion of p, along the line mg, was to become equable at C, the point...

Page 240 - Find the least velocity with which a body must be projected from the moon in the direction of a line joining the center of the earth and moon, so that it may reach the earth. Ex. 4. Given the velocity, distance, and direction...

Page 41 - The product of the sum and <Jie difference of any two quantities is equal to the difference of their squares. Conversely, the difference of the squares of any two quantities is equal to the product of the sum and the difference of the two quantities.

Page 1 - The magnitude by which any flowing quantity would be uniformly increased in a given time, with the generating celerity at any proposed position, or instant (was it from thence to continue invariable), is the fluxion of the said quantity at that position or instant." Substantially this definition of a fluxion was adopted later by Charles Hutton. Simpson dodges the word velocity, and remarks: "If motion in (or at) a point be so difficult to conceive that some have gone even so far as to dispute the...

Page v - In the preface the author offers this to the world as a new book rather than a second edition of that published in 1737; in which he acknowledges, that, besides errors of the press, there are several obscurities and defects, for want of experience, in his first attempt. This work is dedicated to George earl of Macclesfield. In 1752 appeared in 8vo, " Select Exercises for young proficients in Mathematics...