( 74S ) 
II. Nouvtlle Methode en Geometrie pm le$ Se0mt des Su- 
perficies Coniqties & CyHndriqt4es ; qui ont pour Bdji des 
Cercles^ou des faraboles^des EUipfes, des Hyperboles 5 Par 
Ph.de la Hirc^Parifie^, J, Paris, 16 7 3, in quarto. 
THis Authofj (who came but very lately to my hands) in- 
forms his Reader, in his Preface^ that he would not have 
publilht this Book, if he had not been perfwaded , that the 
fimplicity and plainnefs of the New Optical or Projeftive 
Method, by him found our, after the brontllon projt^ ot rough- 
draught of M.Des jirgueSy would be of great ufe to the ftudi- 
ousof this fubjeft, and if he had not been aware, that no 
Writer had as yet taken this way by him infilled on. For, he 
faith , that in his firft Propofition he demonflrates all the pro- 
portions of the Lines, which coming from one pointy or being 
parallel among themfelves , and meeting the Seftion?, arc cue 
by thefeSedions, or by the lines that joyn thecontafts, or by 
other Tangents ; which he affirms doth comprehend a great 
part of the Propoficions of j^poDonius'-i and many others alfo 
of which he hath not fpoken: Which feems to him very eafie 
to underftand , forafmuch as it is nothing elfe but a continual 
repetition of the application of one only line cut in three 
parts, which Line he calls cut^4m^»/^4//^; not that the parts 
taken feparately are in harmonical proportion, but that, by 
taking one of the extreams for one , and the fame with that of 
the middle for another , and the whole for the lafl: , thefe three 
lines iQiall be in harmonical proportion. 
After he had difpafched thss Propofition , he faith , that he 
was refolved to have concluded his Book with the Power, 
Relation, or Habitudes of the Ordimtes by comparing them 
to the Reflanglesof the parts of their diameters ; but that he 
found himfelf infenfibly engaged to add to it fomeother Pro- 
pofitions of a more ufeful kind , and which might eafily be 
demonftrated by the Firft; and then, thePropofitionsof the 
Ancients about the or pup^ffa comparationis'^^nd thedemon- 
ftrations by him given of them he affirms to be different from 
thofe of others, thatfo this work of his might not only be en- 
tire, but new. 
5 E 2 He 
