118 SCIENTIFIC SURVEY OF ABERDEEN AND DISTRICT 
by Vieta, but Anderson supplied the proofs and gave additional theorems. 
One of the propositions deals with the problem propounded by Van 
Roomen, a Dutch mathematician, to Vieta, in which it is required to solve 
a certain equation of the forty-fifth degree. Vieta solved it in a few 
minutes, having recognised from the coefficients occurring in it that it 
merely involved the division of an angle into forty-five equal parts. 
Anderson wrote seven pamphlets or tracts, all between the years 1612 
and 1619. He was apparently his own publisher, and in one of his pre- 
faces he tells that many copies of his books were still on his hands. 
Probably they never got into circulation, a fact which may account for the 
extreme scarcity of his writings now. It is doubtful if there are half a 
dozen complete sets of his writings in Great Britain to-day, and no 
complete account of them has as yet appeared in our language. 
Tue Grecory Famiry—This family occupied an unusually dis 
tinguished place in the history of science in Scotland. In the course of 
three generations no fewer than sixteen members of the family occupied 
chairs in British universities, their allegiance being divided between 
mathematics and medicine. For almost a century they practically 
monopolised the teaching of these subjects in Scotland. The only parallel 
that exists in the history of mathematics is that of the Bernouillis in 
Switzerland and Germany. The first and probably the ablest of the 
Gregories, James Gregory, was the son of the Rev. John Gregory, minister 
of the parish of Drumoak in Aberdeenshire, and he was born at Aberdeen 
in 1638. His mathematical ability may have been inherited from his 
mother’s people, she, as has already been stated, being one of the Anderson 
family, of which Alexander Anderson was a member. 
James Gregory studied at Marischal College, and soon gave evidence of 
great inventive and mathematical skill. At the early age of twenty-four, 
he published his Optica Promota, in which he showed that a reflecting 
telescope could be constructed, which would be a considerable improve- 
ment over the hitherto employed Galilean type. At that time the 
University of Padua was at the height of its fame, and, attracted by the 
brilliance of its teaching, Gregory spent several years there, and published 
the first of his geometrical writings, Vera Circuliet Hyperbolae Quadratura, 
during his residence at the Italian University. In this tract he showed 
from geometrical considerations that the area between the asymptotes of 
a hyperbola and the curve could be expressed as a convergent series and 
also as a logarithm, thus establishing the first logarithmic expansion. It 
will come as a surprise to many persons, even to mathematicians, to hear 
that the logarithmic series was known for some years before Newton made 
known the binomial expansion. At this time Gregory produced original 
papers on the quadrature of curves, and on the inverse method of tangents 
or the integral calculus, as we would now call it, which attracted the 
attention of Newton, Huygens, Wallis, and other leading mathematicians 
of the period. In 1668 he followed up his previous activities by publishing 
his Exercitationes Geometricae, which firmly established his reputation as 
one of the foremost mathematicians in the country. On the Chair of 
Mathematics at St Andrews becoming vacant in this year, Gregory was 
