Selections from Shaw's Appendix to the Second Part of the Instauration

The Author purposely left many Parts of his New Engine untouched, to go in quest of proper Materials whereon to employ it; and, being prevented by Death, did not return from prosecuting the latter design, to fmish the former. Whence tho' the Parts that are treated, appear perfect, as Parts; yet the Whole of this grand Engine wants much of being compleated. 1 The contrivance itself has, by the greatest Masters in science, been thought the best adapted, and most serviceable, of all those at any time proposed, for the Advancement of Philosophy and Arts; so that to perfect and fit it for general Use, may deserve more than ordinary Care and Concern. And tho' to bring it so forward as we fmd it, was the Labour of a Master-Builder; tho' the Work, in its own Nature, is difficult, and to vulgar philosophers, somewhat paradoxical; yet, perhaps, the Author has left such Instructions concernmg it, as may enable Workmen of a lower Class to fmish it, and render the Method of using it generally intelligible: which seems rather to reqUire sedulous Application, than any extraordinary Learning, or uncommon Abilities. In order, therefore, to promote the fmishing thereof, it may be proper to indicate the more considerable Attempts that have hitherto been made, with a View to something of the kind; and shew what farther remains to be done, with regard to the perfecting of this noble Invention, and bringing it into familiar Use. Aristotle has left us four book of Anafytics: the two first whereof, shew how to construct the Forms of Reasoning; and the two latter, deliver the Art of Discovering and Judging of Things. These Books of Anafytics appear to have been little understood, till they were illustrated and explain'd by Gunther; with the Addition of what is found to the same purpose in Plato2 and Galen.3 Gunther has Two Treaties upon the Subject: from whence many later Writers upon Methods, seem to have drawn their Doctrine; only illustrating it with Examples derived from Mathematics, Algebra, and Physics.4 7. This Work of Gunther was many Years after succeeded by another of the great mathematician Weigelius; wherein he endeavours to deduce the Art of Demonstration from mathematical Principles; and farther to explain, illustrate, and shew the use of Aristotle's Analytics.s 8. The celebrated M. des Cartes wrote an express Treatise de methodo; wherein he reduces the whole Art to four Rules, that seem contain'd in Aristotle's Anafytics; and will be found to coincide with the Medicina Mentis, mentioned below. This method of des Cartes, is deliver'd, with considerable Improvements, in the fourth Part of the Art of Penser; where the Author constitutes two Methods; t'tz. the Anafytical, and Syntheticaf, the former for Discovering, and the latter for Teaching. And he illustrates the Whole with a Variety of Examples, as well physical as mathematical. 9. Upon the same foundation, in the Year 1687, the excellent M. Tschirnhaus, a Member of the Royal Academy of Sciences at Paris, published an Essay towards a genuine Logic, or Method of discovering unknown Truths.6 This is an extraordinary Performance, that proceeds entirely upon the mathematical, or rather algebraical Method; and deserves to be read with Care and Attention. 10. Mr Tschirnhaus, reflecting that Mathematicians being the only Set of Men, who either maintain'd no controversies, or at least soon came to a Determination of them; hence apprehended, that Mathematicians alone were possessed of the right Method of Enquiry. Upon this, he applied himself to mathematical Studies; in order to see whether, by making the proper Alterations, the mathematical Method could not also be accommodated to other Subjects. 11. In particular, he applied himself to Algebra; and found that this Art performs even more than it promises; and with the highest Degree