PHYSICAL AND MATHEMATICAL SCIENCES. 113

Italy, not only enriched by the traffic, but also instructedin the science of those countries; he brought with hima knowledge of algebra, and two works of his, on thatscience, bear the dates of 1202 and 1228. The sub-ject is pursued only as far as quadratic equations ; thetechnical language is very imperfect, and as yet unformed,the quantities and operations being expressed in wordsat length, with the help of only a few abbreviations.The rule for solving quadratics by completing thesquare is demonstrated by a geometrical construction.

The polarity of the magnetic needle is described insome lines attributed to Guyot, a French poet, wholived about 1180; but some authors are of opinion thatthis description was actually written by Hugo Bertiusin the middle of the succeeding century : and it isgenerally believed that the compass was first employedin navigation by Flavio Gioja of Amalfi , about 1260.He is said to have marked the north with a fleur-de-lis,in compliment to the branch of the royal family of, France then reigning in Naples.

The poet Dante, who flourished at the close of thethirteenth century, distinguished himself also in philo-sophical pursuits: and we find among his numerousworks an essay on the nature of the elements.

Vitello, a Polish philosopher, commented on Alhazen ;and improved on his writings in a treatise published in1270. He examined largely the refraction in glass andwater, and gave a table of the deviations at differentincidences, but without any perception of the law whichconnects them. He conceived refraction to arise froma sort of impediment or retardation which the lightundergoes in entering the denser medium ; and reasonedupon an obscure idea of the resolution of force. Hetreated imperfectly of the rainbow, and of the eye, andshowed, as indeed Alhazen had done, that vision is notperformed, as the peripatetic philosophy taught, byemission from the eye to the object. He also gave a ,sort of vague theory of parhelia and halos.