Proceedings of the Edinburgh Mathematical Society

Scottish Academic Press, 1899

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Σελίδα 22 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 13 - These are said not to be moments, but quantities generated from moments, which last are only the nascent principles of finite quantities. It is said that the minutest errors are not to be neglected in mathematics : that the fluxions are celerities, not proportional to the finite increments, though ever so small ; but only to the moments or nascent increments, whereof the proportion alone, and not the magnitude, is considered.
Σελίδα 14 - If with a view to demonstrate any proposition, a certain point is supposed, by virtue of which certain other points are attained; and such supposed point be...
Σελίδα 3 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Σελίδα 13 - And as one of the antecedents is to its consequent, so is the sum of the antecedents to the sum of the consequents; [V.
Σελίδα 19 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means.
Σελίδα 17 - If you should say, it is a mere limit ; be pleased to reconcile this with what we find in the first case of the second lemma in the second book of his Principles : Ubi de lateribus A et B deerant momentorum dimidia, $c. — where the moments are supposed to be divided.
Σελίδα 22 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 4 - AC so related that =- is greater than .=- it is evident that the ratio of A to B is greater than the ratio of C to D ; or that the ratio of C to D is less than the ratio of A to B.

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