Page:Reflections upon ancient and modern learning (IA b3032449x).pdf/380

 some sort intire, and may be understood without the rest, so that there is no Harm done: But here that will by no means suffice, for the most verbose Mathematicians rarely ever said any thing for saying Sake, theirs being Subjects in which Figures of Rhetorick could have no sort of Place, but they made every Conclusion depend upon such a Chain of Premises already proved, that if one Link were broke, the whole Chain fell in Pieces; and therefore, he that would reduce those Demonstrations into a narrower Compass, must take the whole Proposition a new in Pieces, must turn it several Ways, must consider all the Relations which that Line, or that Solid has to other Lines or Solids, must carefully have considered how many several Ways it can be generated, before he can be able to demonstrate it by a shorter Method, and by other Arguments, than those by which it was proved before; in short, he must in a Manner be able to invent the Proposition of himself, before he can put it into this new Dress; for which Reason, Tacquet, Barrow, and De Witte, have been reckoned amongst the Principal Geometers of the