Gregory St Vincent, a Flemish mathematician, held a respectable place among the geometers of his day. The main object of his researches was the quadrature of the circle, which he sought with the most persevering indus try through all the difficulties of the geometry of his time. He even believed he had succeeded ; but in this he was wrong : his researches, however, procured him a rich har vest of other geometrical truths.
Andrew Tacquet, another Flemish mathematician, was a respectable geometer. He endeavoured to extend the boundaries of the science by a treatise on the mensuration of the surface and solidity of bodies formed by cutting a cylinder in different ways by a plane, and of different solids formed by the revolution of segments of circles and conic sections. In treating of these, he has affected the rigorous style of the ancient demonstration, a thing not entitled to commendation, considering that it was by adopting a more brief style, and new views, that the science was then re ceiving great improvement.
The celebrated Huygens was one of the brightest orna ments of that period. At an early age, he published his Theoremata de Circuli et hyfi. quad. He completed what Snellius had done concerning approximations to the circle, in his work De Cirodi Itragnitudine inventa ; these were the labours of his youth : afterwards he found the surface of conoids and spheroids, a problem which, on account of its difficulty, had not been attempted before his time. He determined the measure of the cissoid; he sheaved how to reduce the problem of the rectification of curve lines to that of quadratures; and he invented the theory of invo lutes and evolutes. His treatise De Horologio Oscillatorio, is the finest specimen that has ever been given of the ap plication of the most profound geometry to mechanics. In short, his name is associated in the history of geometry with some of the most brilliant discoveries that have been made in the science.
Our countryman, James Gregory, also stands in the very highest class as a geometer. He treated of the quadrature of the circle, and gave better methods of approximating to it than were known before his time. He attempted to shew that the complete solution of the problem was a thing im possible ; but the correctness of his reasoning was ques tioned by Huygens. In 1668, Gregory published his Geo
metrhe pars Universalie, which gave the first idea of the logarithmic curve, and contained many curious theorems, useful for the transformation and quadrature of curvilineal figures, for the rectification of curves, and for the measure of their solids of revolution, &c. He wrote various other works, some of which belong rather to the modern analysis than to the ancient geometry. The excellence of his wri tings, and their rareness, has induced Mr Baron Maseres to reprint them at his sole expellee, as a testimony of his estimation of the author's merit, and to make the elegance of his views, and the extent of his claims as a discoverer, better known. Our mathematical readers will readily re collect, that this is not the only obligation of the kind that this worthy man has conferred upon science. See GRE. cony.
Dr Barrow next claims our attention by his admirable geometrical writings ; his geometrical lectures are com posed partly in the style of the ancient, and partly in that of the modern geometry. He had the high honour of be ing the geometrical tutor of Newton, to whom he resigned his mathematical professorship, with a view to dedicate his time to theological studies ; but seduced from his purpose by his favourite science, he did homage to it, by giving an edition of the writings of Archimedes, Apollonius, and Theodosius. Such was this excellent man's estimation of geometry, that he considered the contemplation of it as not unworthy of the Deity. The beginning of his Apollonius was inscribed with the words, 0Eas yto,tErfEr, Tit autem Domine, quantus es geometra," God himself geomet•izes ; 0 Lord, how great a geometer thou art !" In Italy, Torricelli, the disciple of Galileo, cultivated geometry : with such a master, it is easy to conceive any degree of excellence in the scholar. Among other geo metrical enquiries, he treated of the solid formed by the rotation of a hyperbola about its asymptote; and he slimed that it had a finite magnitude, a thing which may appear paradoxical, when it is considered that the generating sur face is infinitely great.