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. Part I-[I]., Volume 1 |
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The Doctrine and Application of Fluxions, Vol. 1 of 2: Containing (Besides ... Thomas Simpson No preview available - 2018 |
The Doctrine and Application of Fluxions: Containing (Besides What Is Common ... Thomas Simpson No preview available - 2015 |
Common terms and phrases
a+cz Abfciffa affumed alfo alſo Angle Arch Area arifing Axis Bafe becauſe become Body Cafe Celerity Center centrifugal Force centripetal Force Circle Co-f Co-fine confequently conftant COROLLARY correfponding Curve defcend defcribed denoted determine Diſtance Ellipfis equal Equation EXAMPLE Exponent expreffed Expreffion faid fame Manner fecond fhall fimilar fince firft Term firſt Fluxion fome Force forefaid fubftituting fuch fuppofed given Gravity greateſt Hence Increaſe Infinite Series Interfection itſelf laft laſt leaft lefs likewife Logarithm logarithmic Spiral Meaſure Motion muft multiply'd muſt Number Ordinate perpendicular Plane poffible pofitive Point PROB propofed Quantity Ratio Refiftance refpectively reprefented Right-line SCHOLIUM Series ſhall Sine Spheroid Tangent thefe theſe thofe thoſe thro Triangle Unity Value variable Velocity Vinculum Whence whereof Whofe Fluent whofe Radius whole whoſe
Popular passages
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 498 - AB equal to c. From A as a centre, with a radius equal to b, describe an arc. From B as a centre, with a radius equal to a, describe an arc, intersecting the other arc at C.
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 1 - ... as a line by the motion of a point ; a surface by the motion of a line ; and a solid by the motion of a surface.
Page 241 - In like fort the Ratio of the Forces of Gravitation of the Moon, towards the Sun and Earth, may be computed. For...
Page 52 - C G. Now, seeing the motion of p, in the description of curves, must either be an accelerated or retarded one ; let it be first considered as an accelerated one, in which case the arch, CG, will fall wholly above the right line, CD, as in fig.
Page xi - An Explanation of Fluxions in a Short Essay on the Theory ; printed for W. Innys : wrote by a worthy friend of mine (who was too modest to put his name to that, his first attempt) whose manner of determining the fluxion of a rectangle, and illustrating the higher orders of fluxions, I have, in particular, followed, with little or no variation.
Page 128 - ... if n be greater than m ; therefore the fluent requires no correction in this case ; the area, AMRB, included between the asymptote, AM, and the ordinate BR, being truly defined by m+n n—m — -- —, as above. But if n be n — m less than m, then the fluent, when x = 0, the fluent is — a...
Page 54 - BCA, in a given point, C. Let CS be perpendicular to the diameter, AB, and put AB = a, BS = x, and SC = y. Then, by the property of the circle, ti...
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 •—