Analytical View of Sir Isaac Newton's PrincipiaLongman, Brown, Green & Longmans, 1855 - 442 pages |
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Page vi
... integrals ) , ib . Method of drawing tangents , 26. — Normals , ib . — Exemplified in the conic sections , 27.- Problems of maxima and minima , Quadrature of curves , 28. Example : ib . - - Example , ib . - - - ―― -- Parabola , ib ...
... integrals ) , ib . Method of drawing tangents , 26. — Normals , ib . — Exemplified in the conic sections , 27.- Problems of maxima and minima , Quadrature of curves , 28. Example : ib . - - Example , ib . - - - ―― -- Parabola , ib ...
Page 22
... integrals . The two systems , therefore , in no one respect whatever differ except in their origin and language ; their rules , principles , applications , and results , are the same . A different symbol has been used in the two systems ...
... integrals . The two systems , therefore , in no one respect whatever differ except in their origin and language ; their rules , principles , applications , and results , are the same . A different symbol has been used in the two systems ...
Page 23
... integral , and ƒ by the former for the fluent . Although the continental method of notation is now generally used , and is on the whole most convenient , yet it has its inconve- nience , as the d is sometimes confounded with co ...
... integral , and ƒ by the former for the fluent . Although the continental method of notation is now generally used , and is on the whole most convenient , yet it has its inconve- nience , as the d is sometimes confounded with co ...
Page 24
... integrals of fluxional or differential expressions . A rectangle AM being generated by the side P M moving along A P while the side N M moves along A N , the movement or fluxion or differential of AM , or of AP × PM , is PS + MO , part ...
... integrals of fluxional or differential expressions . A rectangle AM being generated by the side P M moving along A P while the side N M moves along A N , the movement or fluxion or differential of AM , or of AP × PM , is PS + MO , part ...
Page 25
... integral is a quan- tity such that , by taking its fluxion or according to the foregoing principles , you given fluxional or differential expression . have to integrate any quantity as " dx , we divide by m + 1 , and increase the ...
... integral is a quan- tity such that , by taking its fluxion or according to the foregoing principles , you given fluxional or differential expression . have to integrate any quantity as " dx , we divide by m + 1 , and increase the ...
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angle applied apsides attraction axis Bernouilli body moves calculus central force centre of forces centre of gravity centrifugal force centripetal force circle comet conic sections corollaries curve cycloid demonstration density described diameter differential differential calculus direction discoveries distance disturbing force earth eccentricity ellipse equal equation evanescent expression fluid fluxion focus force acting force is inversely geometrical given points Hence hyperbola infinitely integral investigation Laplace masses method moon moon's move round observed orbit osculating circle parabola particle pendulum perpendicular planets Principia problem proportion proposition quadrature quantity radii radius of curvature radius vector ratio rectangle resistance respecting revolve round satellites Scholium Sir Isaac Newton solution space sphere square straight line supposed surface syzygy tangent theory tide tion trajectory triangles velocity wave whole
Popular passages
Page 37 - ... the squares of the periodic times are as the cubes of the distances from the common centre, the centripetal forces will be inversely as the squares of the distances.