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The vector dr/cit expresses both the direction of motion and the rate. 2. In the time interval At, the particle moves along the path from P to P'. As At approaches zero, the point P' approaches P, and the direc- lion of the vector Ar/At approaches the direction of the tangent to the path at P. The velocity vector, therefore, is always tangent to the path of motion. The magnitude of the velocity is called the speed. 10 Position Vector of a Particle: Velocity and Acceleration 33 If we denote the cumulative scalar distance along the path with s, then we can express the speed alternatively as ds As .

5. 5. —sinO cosO 8Galileo demonstrated back in 1609 that the trajectory of such a projectile is a parabola. s Scientific Biography, Dover Publications, New York 1978. (2) Galileo Manuscripts, Folio 116v, vol. 72, Biblioteca Nationale Centrale, Florence, Italy. 9We also denote matrices in this text with boldface type symbols. Whether the symbol represents a vector or a matrix should be clear from the context. 2 Velocity of a moving particle referred to two different two-dimensional coordinate systems.

1 Newton's Laws of Motion: Historical Introduction 49 Aristotelian circles but in a straight line. Descartes came to this conclusion not by exper- iment but by pure thought. In contrast to belief in traditional authority (which at that time meant belief in the teachings of Aristotle), Descartes believed that only one's own thinking could be trusted. " For Descartes, pure reasoning served as the sole basis of certainty. Such a paradigm would aid the transition from an Aristotelian worldview to a Newtonian one, but it contained within itself the seeds of its own destruction.

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A Path to Coldness of Heart (Dread Empire 3) by Glen Cook


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