Proceedings of the Edinburgh Mathematical SocietyScottish Academic Press, 1899 |
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Página 13
... Principia ; this point should be specially noted , as one object of the introduction to the Quadratura is to show that the doctrine of fluxions is inde- pendent of infinitesimals , and the use of moments there would have endangered the ...
... Principia ; this point should be specially noted , as one object of the introduction to the Quadratura is to show that the doctrine of fluxions is inde- pendent of infinitesimals , and the use of moments there would have endangered the ...
Página 14
... Principia , Book II . , Lemma 2 . When the sides A , B are deficient by half their moments a , b respectively , the rectangle is AB - AaB + ‡ ab ; when the sides are greater by half their moments the rect- angle is AB + ¿ ¿ A + @ B + ...
... Principia , Book II . , Lemma 2 . When the sides A , B are deficient by half their moments a , b respectively , the rectangle is AB - AaB + ‡ ab ; when the sides are greater by half their moments the rect- angle is AB + ¿ ¿ A + @ B + ...
Página 17
... ( Principia , Book I. , Sect . 1 , Lemma 1 ) . Philalethes then turns to the criticism of the method of finding the fluxion of a " . He objects to Berkeley's translation of the phrase " evanescent jam augmenta illa et eorum ratio ultima ...
... ( Principia , Book I. , Sect . 1 , Lemma 1 ) . Philalethes then turns to the criticism of the method of finding the fluxion of a " . He objects to Berkeley's translation of the phrase " evanescent jam augmenta illa et eorum ratio ultima ...
Página 19
... Principia , Book I. , Sect . 1. , is characterised as an unquestionable proof of the matchless contempt which Philalethes has for truth . After referring to the use of infinites- imals by the Marquis de l'Hopital , he insists that the ...
... Principia , Book I. , Sect . 1. , is characterised as an unquestionable proof of the matchless contempt which Philalethes has for truth . After referring to the use of infinites- imals by the Marquis de l'Hopital , he insists that the ...
Página 20
... Principia , but he utterly misconceives that doctrine , interpreting it , it seems to me , exactly as Berkeley had done , so that an ultimate ratio is not the limit of a varying ratio , but the last value of a ratio . Berkeley very ...
... Principia , but he utterly misconceives that doctrine , interpreting it , it seems to me , exactly as Berkeley had done , so that an ultimate ratio is not the limit of a varying ratio , but the last value of a ratio . Berkeley very ...
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Proceedings of the Edinburgh Mathematical Society Edinburgh Mathematical Society Vista completa - 1966 |
Términos y frases comunes
a₁ Analyst angles arithmetic mean B.Sc b₁ Berkeley Berkeley's centroid circumcentre circumcircle circumscribed coaxal coaxaloid system College common measure conic coordinates corresponding cosb cosC cosh D.Sc determinant diagonal 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 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
Pasajes populares
Página 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.
Página 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.
Página 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...
Página 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.
Página 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.
Página 21 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means.
Página 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.
Página 24 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 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.