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 Mathematics. BY Thomas Simpson...John Nourse, 1750 - Calculus |
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Page 2
... Bafe : For let the cur- vilineal Space Amn be generated by the continual , and parallel , Motion of the ( now ) variable Line mn , and let Rr be the Fluxion of the Base , or Abfciffa , Am ( as before ) ; then the Rectangle RrsS will ...
... Bafe : For let the cur- vilineal Space Amn be generated by the continual , and parallel , Motion of the ( now ) variable Line mn , and let Rr be the Fluxion of the Base , or Abfciffa , Am ( as before ) ; then the Rectangle RrsS will ...
Page 16
... Bafe AC of the gi- ven Triangle = b , and its Alti- tude BD = a ; and let the Al- titude ( BS ) of the infcribed Rectangle me C ( confidered as variable ) be de- noted by * : Then , because of the parallel Lines AC , and ac , it ba - bx ...
... Bafe AC of the gi- ven Triangle = b , and its Alti- tude BD = a ; and let the Al- titude ( BS ) of the infcribed Rectangle me C ( confidered as variable ) be de- noted by * : Then , because of the parallel Lines AC , and ac , it ba - bx ...
Page 19
... Bafe ; x = fg ( db ) the Diameter of the Cylinder , con- fidered as variable ; 3,14159 , & c . p = ( 3 4 6 ° c . ) the Area of the Circle whose Diameter is Unity . Then , the Areas of Circles being to one another as the Squares of their ...
... Bafe ; x = fg ( db ) the Diameter of the Cylinder , con- fidered as variable ; 3,14159 , & c . p = ( 3 4 6 ° c . ) the Area of the Circle whose Diameter is Unity . Then , the Areas of Circles being to one another as the Squares of their ...
Page 20
... Dia- meter is Unity , and let cbe the given Content of the Cylinder . Then it will be ::: * : ( px ) the Circumference of the Bafe ; which , multiplied by by the Altitude y , gives pxy for the concave 20 Solution of Problems.
... Dia- meter is Unity , and let cbe the given Content of the Cylinder . Then it will be ::: * : ( px ) the Circumference of the Bafe ; which , multiplied by by the Altitude y , gives pxy for the concave 20 Solution of Problems.
Page 21
... Bafe , by multiplying the fame Expreffion into of the Dia- meter x , will be found px2 4 ; which drawn into the pxzy 4 Altitude y , gives for the folid Content of the Cy- linder ; which being made c , the concave Surface pxy will be ...
... Bafe , by multiplying the fame Expreffion into of the Dia- meter x , will be found px2 4 ; which drawn into the pxzy 4 Altitude y , gives for the folid Content of the Cy- linder ; which being made c , the concave Surface pxy will be ...
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Common terms and phrases
a+cz Abfciffa affumed alfo let alſo Angle Arch Area Axis Bafe Baſe becauſe become Body Cafe Celerity Center Center of Gravity centripetal Force Circle confequently conftant COROLLARY correfponding Curve Cycloid decreaſe defcend defcribed denoted determine Diſtance Ellipfis equal Equation EXAMPLE expreffed Expreffion faid fame Manner fecond fhall fimilar fince firft Terms firſt fore fubftituted fuch fuppofed given Gravity Hence increaſe Infinite Series Interfection inverſely itſelf laft leaft lefs likewife Line Logarithm logarithmic Spiral Meaſure Motion muft multiply'd muſt Number obferve Ordinate otherwife Parabola parallel perpendicular poffible Pofition Point propofed Quantity Radius Ratio Rectangle refpectively reprefented Right-line Root ſhall Solid Sufpenfion Tangent thereof theſe thofe thro Triangle uniformly Unity Value variable Velocity Vertex Vinculum Whence whofe Fluent whofe Fluxion whoſe
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...