TAUTOCHROXIS IN VACVO. 6i 



\bi loco Q_qiuieciinquc funsftio impar, loco R vcro 

 qiuiecunque pnr lUbllitui pocert ipfuis v. Qiiia .v~ 

 QQ^: rt eric QzzVax , et uicirca f— R-f-V<Y.v. Ilic 

 R potcll :iccipi fundio par ipfius Q fcn l'<7.v, fuie 

 dunt;ix:it ipfuis y.v. 



§. 21. Ex hibce f.icile elicitnr curu:irum no- 

 ftro inllituto infcruientium conrtruclio. Circa axcm 

 vcrticulcm AP conllituatur parabola MAN , cujus 

 parametcr —a. Duda crgo ordinata ad axem or- 

 thogonaliMN, erit, fi fit APzr .v, PM— V^.v. In- 

 fra hanc parabolam circa cundcm axcm deicribatur 

 curuaqu accunque QAS, cujus axis AQ_fimul cll dui- 

 mcter. Ducantur vcrticalcs MR, NS, horizonta- 

 iem per A traufcuntcm fecantcs in T et V. Erit 

 AT— l^rt.v, et Ay—-'\'^ax; TR autcm et SV erunt 

 acqualcs, Qiiae , cnm fint ad eandem plagam fitac, 

 crunt fundlio par liiieac AI quac cll Trt.v, quarc IR 

 cxprimct fun(flioncm R. Tum noua coaihuatur 

 curua GAH, cujus applicata PG fit =LPM-f-TR , erit 

 altet a PH ob lcgcm continuitatis zz:PN-SV feu 

 PN-TR. Quarc erit PG=R-hV^/.v , ct PH=:-R 

 -{-Vax. Vode fequitur curuam GAH candcm cflc, 

 quac quacritur. 



§. 22. Hoc ergo modo inueniuntur curuac 

 infinitae, non quidem tautochronae , fcd tales ex 

 quibus tautochronae poffunt conflrui. Sic curua 

 AG prieccdcnti modo con(lru(fla , inde fi alia AM ^^5. '' 

 conllruatur, ut cjus arcus A.M ubiquc fa acqualis 

 refpondcnti appUcatac PG , crit hacc cuma tauto- 

 chrona (§. 17. ). Ex data vcro AG, rcquifita AM 



H 3 t'c- 



