PHYSICAL AND MATHEMATICAL SCIENCES. 121
that of a short-hand writing, or abbreviation of ordinarylanguage, to save trouble and repetition. This was thesimple principle which, being more and more improvedupon by each successive writer, was at length framedinto that refined and highly artificial system which wehave at present in use ; and which has in its turn provedthe means of indicating new relations of quantity ; and,from a machine to assist the labours of our hands, hasbecome a vehicle conveying us into new regions of truth.Thus, upon the whole, we may remark that up to theend of the fifteenth century, the advances made toemerge from the darkness of the preceding age were,with very few brilliant exceptions, confined to restorations of ancient science, and some immediate improve-ments which directly arose out of those restorations. Abeginning, however, was effected, and a foundation laid;and, in the next century, we shall find abundant proofsof its solidity in the substantial superstructure whichthen began to be raised upon it, and shall trace therapidity and success with which the work proceeded.
SECTION II.
SCIENCE IN THE SIXTEENTH CENTURY. -THE FIRST GREAT
MODERN IMPROVEMENTS. -THE DISCOVERIES OF COPERNICUS
The knowledge of algebra had hitherto been almostwholly confined to what was acquired from the intro-duction of the Oriental treatises, upon which, as wehave seen, some few improvements, rather in form thanin substance, were engrafted. The next age, however,exhibited a more busy scene of research, and in thisdepartment original enquiry now actively extended itself,and new investigations were continually made into the