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PRINTED FOR J. DEIGHTON AND SONS, CAMBRIDGE,

AND G, AND W.B. WHITTAKER, AVE-MARIA-LANE.

1819.

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The propositions contained in the following compilation are either obvious deductions from those of Euclid, or such as exhibit some remarkable properties of lines, angles, or figures, which are not to be found in Euclid's work; or, lastly, they are the geometrical solutions of many well-known problems in the different branches of Natural Philosophy. But although the propositions, which have here been collected for the use of the academical student, are of these three kinds, it has not been thought advisable to class them according to that threefold division. Designed as a supplement to the Elements of Euclid, they have been disposed according to Euclid's arrangement. And

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