== (4) = 



Euolutio prima geometrica. 



§. 2. Primo iginir hanc formulam pcr qiiadratiiras cx- 

 liibcamus, confuicrando lineam curuam , cuius abfciflac x rc- 

 fpondcat applicata j = -j— ^ -|- J- , tum vcro cius arca fj d x 

 jibfciflae .v infillcns ipfum valorem quacfitum repracfcnrabit , 

 quamobrem formam luiius curuac accuratius pcrpcndam.us. Ac 

 priiT.o ciuidem euidens eft , hanc curuam neuri(|uam in regio- 

 nem abfciflhrum negariuarum porrigi, fcd a rermino .v zzi o in- 

 cipere. Pofito autcm .v :rz o manifclto fitj^zzii, ob /.vroo; 

 at cxiftcntc x infinite paruo fiet j = i -f- a- -f- — , \bi ficile 

 perfpicitur polbemum membrum -1- eflc ncgatiuum et quafi in- 

 finitics maius quam .v, ita vt fiat ;■ =: i — / .v, exiflente / nu- 

 mero maximo; vnde patct , fi curuam ad axem AO rcfcra- 

 mus in coquc abfci(fas .v a puncto A capiamus, in ipfo punclo 

 Tab. I. A applicatam forc A C = i , ct curuam in C hanc applicatam 

 Fig. •!• A C tangcre, proptcrea quod dccrcmcntnm applicatac infinities 

 fupcrat incremcntum abfciflae. Curua igitur originem ducet 

 ab iplb punclo C, hincquc continuo propius ad axem infiede- 

 tur, quem tandem in dirtanria infinita atringcr. Pofito enim 

 jfzrioo fit >'=z: — -1--I-/-L; vbi notetur prius mcmbrum — 



'^ OO OO ^ oo 



prae altero euancfccre, ita vt ifte valor fit pofitiuus, vndc pa- 

 tet, hanc curuum a pundo C ad axcm conrinuo propius cfle 

 accefliiram. 



§. 3. Confidcrcmus nunc abfciflam AB=:z i, vbi fum- 

 to x—i fit yzz:i-)-o, vndc nihil planc concludcre h'ccret, 

 hanc ob caufliim flatuamus x :rz i — 0:, vt fiatj' zn ^ 

 lam /(i — w) in fcricm euoluendo fict 



l( l— u) 





I I J-4-3t'' 



0» a)-H»w"-|-iW H- ctc. i-f-fiW-f-sw" 



FiaC 



