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'Let PQR be a spiral that cuts all the radii...', 1687.

Newton, Isaac, Sir

'Let PQR be a spiral that cuts all the radii...', 1687.
4 0 c m
actual image size: 24cm x 32cm


Lemma 3, on the revolving motion of bodies in resisting mediums, from Newton's 'Principia Mathematica' (1687): 'Let PQR be a spiral that cuts all the radii SP, SQ, SR, equal angles. Draw the straight line PT touching the spiral in any point P and cutting the radius SQ in T; erect PO and QO perpendicular to the spiral and meeting in O, and join SO. I say that if points P and Q approach each other and coincide, angle PSO will come out a right angle, and the ultimate ratio of rectangle TQ x 2PS to PQ2 [PQ squared] will be the ratio of equality'. The discoveries of English physicist and mathematician Isaac Newton (1642-1727) were prolific and hugely influential on science and thought.

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