## Proceedings of the Edinburgh Mathematical Society, Volumes 17-18 |

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angles axes B.Sc begin Berkeley Book called centre circle coaxaloid system College common conic conjugate connected considered constant contain coordinates corresponding cosC cosh definition Demonstration determinant direction Edinburgh envelope equal equation expression figure fluxions four function geometrical George Gergonne point given gives Glasgow greater Hence hyperbola II-points imaginary increments infinite infinity integral isotomic conjugate joining Lemma less limit magnitudes Mathematics mean measure meet method Newton noted obtained pairs parallel passes Philalethes planes positive potential principles problem Proceedings Professor proof proportion proved quantities ratio rectangle referred respectively Robins School sides similar Similarly sinh Society solutions space square supposed taken tangents theorem third touches triangle ultimate ratios University values vanishes variable varying write zeros

### Popular passages

Page 24 - 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.

Page 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.

Page 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...

Page 5 - 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.

Page 15 - And as one of the antecedents is to its consequent, so is the sum of the antecedents to the sum of the consequents; [V.

Page 21 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means.

Page 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.

Page 24 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Page 6 - 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.