ALTERVTER DATVS EST &c: ^9 



Devionftratio. Nam dcmiffis pcrpcndiculari- 

 buslll, HT ud rccflas PQ^ct SQ^, cruntHl— PX, ct 



HT=SY, jungantur BH, TH ct invenictur BH— BR 

 H-RIif^BRH-RX^Pl^RWH-PwVPl=PR-i-Pl* 



rzRl^, crgo BH—Rl , fimili argumcnto crit TH 

 — RT, atquiBH=:TH, crgoRIzrRT, adeoque pcr 

 prx-c. cafum crit Rl rcmi axis m.ijor, et BR fcmi 

 axis minor. Q. E. D. 



DE 



INNUMERABILIBUS CURUIS 



TAUTOCHROMS IN VACUO. 



Aiict;. Leonh. Eulero. 

 §. I. 



Quotics ego inngncm tautochronismi pro- Menr. Sept. 

 prictatem, quam Hugenius primus in cy- '^^^* 

 cloide incffe dcprchcndit, contemplatus Tab.v.5: 

 fum , fcmpcr dubitabam, an practer cy- ^'' 

 cloidcm aliuc curuac candem fortc habcant propri- 

 ctatcm. Hocque mihi eo probabilius vidcbatur, 

 quod ipfum Hugenium non ex tautochronismi con- 

 tcmplationc ad cycloidem perucniffe intcUigcbam: 

 fcd potius cycloidis proprictatcs fcrutantcm hanc 

 ipfum inter alias dctexiffe. Neu;tonus quidematque 

 licnn.innu< y qui deinccps candcm rcm tradarunt, 

 Tom. ly. G ana- 



