## 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 alſo let Angle anſwering Arch Area ariſing aſſumed Axis Baſe becauſe become Body Caſe Celerity Center centripetal Force Circumſtance Co-fine Co-ſ conſequently conſidered conſtant CoRoll CoRollary correſponding Curve denoted deſcend deſcribed Direétion Diſtance E X A M P L E Ellipſis equal Equation expreſſed Expreſſion firſt Term Fluxion Force foreſaid given Gravity greateſt Hence increaſe Infinite Series inſtead inverſely itſelf laſt leaſt leſs likewiſe Logarithm Meaſure muſt Number obſerved Ordinate otherwiſe P R O Parabola perpendicular Point poſitive poſſible propoſed Quantity Ratio repreſented Reſiſtance reſpectively Right-line ſaid ſame Manner ſecond Sečtion ſee Series ſeveral ſhall ſimilar ſince Sine ſmall ſome ſought Spheroid ſubſtituting ſuch ſuppoſed Tangent theſe thoſe Triangle Unity Uſe Value Velocity Whence whereof whole whoſe Fluent whoſe Radius

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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 241 - Earth, will give 2360000, or 27 . 3 nearly, for the periodic Time at that Diftance. In like fort the Ratio of the Forces of Gravitation of the Moon, towards the Sun and Earth, may be computed. For, the centrifugal Forces in Circles, being univerfally as the Radii...

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 9 - To find the fluxion of any given power of a variable quantity, multiply the fluxion of the root by the exponent of the power, and the product by that power of the same root, whose exponent is less by unity than the given exponent. This rule is expressed more briefly, in algebraical characters, by •—

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...