Treatise on Natural Philosophy, Volume 1, Issue 1University Press, 1879 - Calculators |
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Page 2
... circle , and radii to the points of contact . The angle between the tangents is the change of direction required , and the rate of change is to be measured by the relation between this angle and the length of the circular arc . Let I be ...
... circle , and radii to the points of contact . The angle between the tangents is the change of direction required , and the rate of change is to be measured by the relation between this angle and the length of the circular arc . Let I be ...
Page 20
... circle . Let a be the velocity , and a the angle through which its direc- tion turns in unit of time ; then , by properly choosing the axes , we have dx dt == a sin at , dy dt = a cos at , Examples of accelera- tion . whence ( x − A ) ...
... circle . Let a be the velocity , and a the angle through which its direc- tion turns in unit of time ; then , by properly choosing the axes , we have dx dt == a sin at , dy dt = a cos at , Examples of accelera- tion . whence ( x − A ) ...
Page 22
... circle of radius r with uniform angular velocity ( about the centre ) , and let this circle move perpen- dicular to its plane with velocity V. The point describes a helix on a cylinder of radius r , and the inclination a is given by tan ...
... circle of radius r with uniform angular velocity ( about the centre ) , and let this circle move perpen- dicular to its plane with velocity V. The point describes a helix on a cylinder of radius r , and the inclination a is given by tan ...
Page 26
... circle , whatever be the form and dimensions of the orbit . duced from In the motion of a planet or comet , the acceleration is directed laws . towards the sun's centre . Hence ( § 36 , b ) the velocity is in- Kepler's of planet or ...
... circle , whatever be the form and dimensions of the orbit . duced from In the motion of a planet or comet , the acceleration is directed laws . towards the sun's centre . Hence ( § 36 , b ) the velocity is in- Kepler's of planet or ...
Page 27
... circle whose diameter is the major axis , if the orbit be an ellipse or hyper- bola ; in the tangent at the vertex if a parabola . Measure off on the perpendicular a third proportional to its own length and any constant line ; this ...
... circle whose diameter is the major axis , if the orbit be an ellipse or hyper- bola ; in the tangent at the vertex if a parabola . Measure off on the perpendicular a third proportional to its own length and any constant line ; this ...
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Common terms and phrases
acceleration action algebraic angular velocity anticlastic application arbitrary axis Cambridge centre of inertia circle co-ordinates coefficients component configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dt dy dx dy dy dy dy dz ellipsoid equal equations of motion equilibrium expression finite fixed force formula function give given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy Lagrange's linear mass measured momentum moving negative P₁ parallel particle path perpendicular polygon position principal axes principle quadratic quadratic function quantity radius rectangular resultant rigid body rolling roots rotation round simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values variable whole Y₁ αξ λ² аф
Popular passages
Page 510 - The Missing Fragment of the Latin Translation of the Fourth Book of Ezra, discovered, and edited with an Introduction and Notes, and a facsimile of the MS., by ROBERT L. BENSLY, MA, Sub-Librarian of the University Library, and Reader in Hebrew, Gonville and Caius College, Cambridge.
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