Analytical View of Sir Isaac Newton's PrincipiaLongman, Brown, Green & Longmans, 1855 - 442 pages |
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Page 31
... radius vector , or line drawn from the body to that centre , describes areas which are in the same fixed plane , and are always proportional to the times of the body's motion ; and conversely , if any body which moves in any curve ...
... radius vector , or line drawn from the body to that centre , describes areas which are in the same fixed plane , and are always proportional to the times of the body's motion ; and conversely , if any body which moves in any curve ...
Page 43
... radius vector SP ; that is , we can find the proportion which the force must bear to the distance , in order to retain the body in the given orbit or trajectory ; and conversely , the force being given , we can determine the ...
... radius vector SP ; that is , we can find the proportion which the force must bear to the distance , in order to retain the body in the given orbit or trajectory ; and conversely , the force being given , we can determine the ...
Page 45
... radius vector r , and SY = p , we have PV = 2pdr dp and F is as dp 2 p3 dri and 3 also F is as v2dp . In these formulas , substituting for 2 dr p and r their values in terms of x and y , we obtain a mean of estimating the force as ...
... radius vector r , and SY = p , we have PV = 2pdr dp and F is as dp 2 p3 dri and 3 also F is as v2dp . In these formulas , substituting for 2 dr p and r their values in terms of x and y , we obtain a mean of estimating the force as ...
Page 46
... radius is known . But its general expression involves second diffe- rentials ... radius of curvature is d $ 2 √ ( d2 y ) 2 + ( d2 x ) 2 ' ther is dr dp " and this is ... vector coincide , that is , the case of the circle , in which the ...
... radius is known . But its general expression involves second diffe- rentials ... radius of curvature is d $ 2 √ ( d2 y ) 2 + ( d2 x ) 2 ' ther is dr dp " and this is ... vector coincide , that is , the case of the circle , in which the ...
Page 49
... radius vector , we have abdr √r ( 2 a − r ) a− r ) 3 ; therefore p = b A and d p = 2a - r the formula d p p3.dr abdr a becomes 3 = or b2 √r × 1a × dr b2 2 the force is inversely as the square of the distance . * This result ...
... radius vector , we have abdr √r ( 2 a − r ) a− r ) 3 ; therefore p = b A and d p = 2a - r the formula d p p3.dr abdr a becomes 3 = or b2 √r × 1a × dr b2 2 the force is inversely as the square of the distance . * This result ...
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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.