Proceedings of the Edinburgh Mathematical Society, Volum 11

Scottish Academic Press, 1893

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Pàgina 11 - Find an expression for the area of a triangle in terms of the coordinates of its angular points.
Pàgina 126 - Renew is to be conducted, and it may be of interest to the members of the Society to have these presented in outline.
Pàgina 50 - must be ranked as one of the retarders of quaternion progress, in virtue of his pamphlet on Vector Analysis; a sort of hermaphrodite monster, compounded of the notations of Hamilton and Grassmann.
Pàgina 14 - The circle which passes through the middle points of the sides of a triangle touches the four circles which touch the three sides.
Pàgina 57 - Va/3 than any which depend on the definition of a quaternion, will appear in a strong light if we try to extend our formulae to space of four or more dimensions. It will not be claimed that the notions of quaternions will apply to such a space, except indeed in such a limited and artificial manner as to rob them of their value as a system of geometrical algebra.
Pàgina 51 - ... which hold good for any number of vectors. In the first equation the manipulation is as in common algebra, in all respects. In the second, in all respects save one ; for the reversal of the order of the vectors in a vector product negatives it, thus, Vac = - Vca.
Pàgina 74 - where the reader may be puzzled to find out why the usual simple notion of differentials is departed from, although the departure is said to be obligatory.
Pàgina 75 - The question arises whether the quaternionic product can claim a prominent and fundamental place in a system of vector analysis. It certainly does not hold any such place among the fundamental geometrical conceptions as the geometrical sum, the scalar product, or the vector product. The geometrical sum a + ,? represents the third side of a triangle as determined by the sides a and ;5.
Pàgina 51 - Sa/8 represent the sine and the cosine of the angle included between a and ft, combined in each case with certain other simple notions. But the sine and cosine combined with these auxiliary notions are incomparably more amenable to analytical transformation than the simple sine and cosine of trigonometry, exactly as numerical quantities combined (as in algebra) with the notion of positive or negative quality are incomparably more amenable to analytical transformation than the simple numerical quantities...

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