iE^3 
f z, continued;: but to contraQ: his Work into a little 
compafs, he auures us that.it is all, one, if inftead of the 
v/holc circumferences B b^E D d^ F/ he take the lines ^ 
each a third part of its correfpondent, and that 
in this cafe too^ the Circle whofe Center is Ljtakeri in the Di- 
arneter/;^ continued^ fhalLpals through the Pointsc?/^,^ and 
interfed the Tangent Ff in the Vo'mt my fib as to leave / m 
m to a third of the circumference of the Circle ; which iup- 
pofition being proved to be groundlefs and erroneous, all the 
confequenccs drawn from thence muft be fo too. If ,our 
Author had but confidered what the intermediate Points of 
the Curve between o & f , p & q^^q & f ought to exprefs , he 
could not but have difcovered the fallacy himfelf, for the 
lines o dy p q ^ are each proportione<I to fm^- as the fines )^/-, 
i Cyhd io their refpcftive .Arches k fy ify hf^ and fo of all 
the reft between (j andv^. vFhis^ould hav^ tMght him, that 
Aho^ Cufve he has oocafion ito ufe, did ur^iverfilly exprefs the 
Proportion of the Arches to their Sines, by that of thclinc 
fm to its refpeftive ordinatcs ; that it was a fort of Linex 
^jj^r^i^rijc, to be reckoned among the Lme£ Geometrice Ir- 
rMtiomlesy Ov fueh '•'whoie^ relation between tht partk of the 
Diameter and the^ Ordinates, are not generally expreflibic by 
any one Equation ; that this Curve did interfeft the Circle 
in the middle of the Arch k z,^ and continge it in the point 
z. This Ci^ri^^ will be better underfiood in Ftg. j, where it 
is drawn a^ it ought, and wherein the pj^opbrtion of tfte 
line/?^to the lines g'^^is as any Archl/is to its Siney&^. 
Tis evident, that this Curve is not the Circle mop qtirt 
Fig.^j yet 'tis not apparent but that a Circle pafling through 
the point «>^,may inter fc£t it in feveral points,as o^pyf : (but to 
fbppofe it to pafs through all the extremities of tlie Circutti^ 
fbrences of the infinite Polygons bet W-een the Circle and Tri- 
angle, or their thirds, is to make it coinddent with that 
Curve J It remains therefore to flic w, that the Circle pafling 
through P and whofc center is in the JLine f z^ does not 
jmiJi ^ /io ib'ih . - 
