Ch8] 
Equation is ^ — 2 d e'-e^'\-l?^=c^. Fourthly; To infcribc 
Polygones in a continual double Progreflion within a Circle, 
many different Rules may be given: the following will ferve, 
which is the fame with that, how to find the fubtenfc of an 
Arch, out of the fubtenfc of a double Arch. The Rule is 
thus ; 2 R*~ V 4 R^~A' R' ; Suppofihg A to be the 
Chord of a double Arch , and B-of a fingle Arch . From hence- 
itis eafily deduced , that V jR* being the fide of an equilate- 
ral Triangle infcribed^the fide of a Hexagon will be R :of tlie 
Dodecagon V un iR"" — V iR* : and fofor the refl . Now re- 
ducing according to thefe Equations the Lines to Numbers , it- 
will be found that in F^g. 2 Td. 2 
173205,08 4^ = 5#ooo,co 
epz=z 2oooco,oo ei = 36602,54 fm = ^9^S9,^i 
207055,25 rfr= 9990,04 
But fuppofing, as our Authour will hav^ it, that </«>ftandsin- 
the fame Circle with^ j aad e f , itfoUows that the ^Jquare of. 
^ a— 422638679 whereas it iliould have been equall to 
4287 1 8707 d'f. ^iquare of d 0 iri tlie Tabjle . The Aquare of 
the Tangent fm is alio a grcat.dcal tQ fmall, ^ and the whole , 
(^adrature to little : All whicft thakd it appear, that the 
Glory of Len^is the Gr«it is not (as this Book pretends) much 
advanced by the Atchivcments of this Author ; ^ who 
would have done well, in a Matter th^t lb little needed it, t<^ 
haveforbornto makcufcof thcfacred Words of our Sa^yioiir, 
Math. iuh. 2$rh. 
