cit, ita vt fit ^zro, ac motiis totiis coiuincbi:ur iii h:ic CiiV' 

 plicillima acqiuuioiic: ?-^ — o, liinc ^ =: conil. hoc crt ccle- 

 ritas angiihiris erit conltans, qiiae, qnoniam angulus $ continuo 

 iT;innitur, ponatur y^ — — /, vnde fit a 6 = k — f t. Hinc fi 

 ponamus initio, vbi ; — o, filnm tcnuiffe fitum AC norma- 

 Icm ad axcm, ita vt tum fucrit ^ =: 90", crit /: r df . 90°, iolco- 

 quc ^—90 — ^ . r. Dcnotabit ergo ^- ccrtum angulum, 

 qui fit =a, ita vt habeamus ^1=90°— ar, quo inuento lia- 

 bebimr.s x — c t — a fin. a t ct j ziz a cof. a t , hincque por- 

 ro ff-rzf — <7 a cof. a ; ct ^-i' n: — a a fin. a /. Vndc fi init.io 

 corpufculum in C quieuifTc fnmamus, tam "^- quam ''^ ibi 

 cuanuide necenc cft, cui conditioni fatisfit fi fumatur a ~ -£. , 

 ita vt fit $=2^0° — ^-, hincque 



X ziz it — a fin. -.- et r := a cof. — . 



a ^ a 



Ex pofieriorc fit '^^' nr A cof. ^- , quo valorc fubflituto fiet 

 x = a A cof. X — >/(« a — jtjO , 



Vnde patct hanc curuam fore cycloidcm inucrfam, a circulo, 

 cuius radins =fl, fub recfta CD axi paralJcla, volucntc dc- 

 fcriptam, cuius cufpis in ipfo pudo C fit fita. 



§. 44. Contcmplcmur ctiam cafnm oppofirum, quo fridio 

 effet infinita, idcoqne Z^roo, ct in noflra acquationc primum 

 n cmbrum prae altero cuancfcct, eritque a d ^ h- c d t {in.$ - o^ 

 vntie fit cdt z=z —J^^ et intcgrando c t =1 ~ a i tang. iQ-\~C. 

 Vnde fi pro / — o fuerit ^ zr 90°, erit C -— o idcoque r/zr:- 

 •i-alcot.{&^ idcoquc jf = a / cot. i ^ — <7Cof. ^, cxilknte. 

 rrrafin. 5, cx quibus formulis manifcfio dcducirur Tra(^'oria 

 vulgaris. Cum cnim ob cdt-~~. fit r) v zr — li-i£2(iil et 



■ J<n.t»' ' Jin.$ 



d^^fla^cof. O, crit l^rr — tang. i), vndc patct ipfum fi- 

 Noua Acla Acad. Imp. Sc. T. II, D Jum 



