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a₁ Analyst angles arithmetic mean B.Sc Berkeley Berkeley's C₁ centroid circumcentre circumcircle circumscribed coaxal coaxaloid system College common measure conic coordinates corresponding cosC cosh D.Sc determinant droites Edinburgh ellipse envelope equal equation finite fluxions geometrical George Watson's College Gergonne point given Glasgow Green's function harmonics Hence hyperbola II-points II(m imaginary increments indivisibles infinite inscribed integral isogonal isotomic conjugate K-transformations Lemma limit line at infinity line of centres magnitudes Mathematical Society meet method mid-point Newton nine-point nine-point circle obtained orthocentre pairs parabola parallel perpendicular Philalethes planes positive prime and ultimate Principia proof proportion proved Quadratura quantities rectangle respectively Robins S-point system sides of ABC sinh solutions Space bounded symmedian point system of circles tangents theorem triangle ABC trilinear coordinates ultimate ratios vanishes variable zeros αλ
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.