SEV OSCILLATORUS. i 1 % 



Demonflratio. 



Quum medium eft tenuiflimum, fit valor lit- 

 terae n minimus-,. vt vero appareat quid db hac 

 poiltione refultet notari debet , effe c~ 2nf — i — 



Anntt 8n z t 3 . i6n + t + . r ... „„« 



2W *-r-TTz — 1X1+ 1.2.3 4- ~~ etc * fimiliterqne c ns 



, A.nnss i 8n J s J i i 6n*s* . T 



— I -4-2WJ-H T^-^-T^l^r-TTzTi^ -+" etc - I flm 



vero fi vtamur aequatione differentiali paragraphi 

 tertii, quae eft c~~ 2nt tdtzz.c 2ns s ds, fufficiet ex iitis- 

 feriebus infinitis duos primos accipere terminos y 

 (quia nempe valor n minimus eit) atque fic po- 

 nere c~ 2nt zzi — znt er c 2nr zz i -j^zns , hosquc 

 valores in aequatione fubflituere y quae fie trans- 

 mutatur in hanc tdt—inttdtzzsds-\-inssds, cuius- 

 inregralis eft ^tt — ^nt^zz^ss-^-^ns^. Quod 11 

 vero vtamur acquatione tertii paragraphi inte- 

 grata,. nempe ini — 2nt t-\-c— -***—- — mc 2ns 's ~\-c 2n * 

 noti amplius fufiiciunr duo" termini ex feriebus- 

 praememoratis fumendi, quin imo quatuor requi- 

 runtur ita vt ponendum fir c~ 2nt zz i — mt-\- 



1.2 1.2.3 C X- -1- - /O -t- i , 2 .^l.2. 3? P U1V 



quorum vaiorum fubltitionem [oritur iam znt — 

 i 4 ««//-{- 4 n 3: / * -^n + t 4 --h i — 2 « / -j- 2 nntt— 

 \n^t % ~~ — ins—^nns s—^n 3 " j 3 — |«*j4- -+- r 

 + 2«; + ?«^^+^» 3 J" 3 5 <: ] uae recte dispofitis> 

 terminis reiectisque — ^n*t + et |«fj^ atque fac"taj 

 diuifione per —4«« transit in hanc ±tt — jnt?zz 

 *s s -\-^n s 2 ", vt antea. Diuifa autem autem iftai 

 aeqnatio per s-\-t redujci poteft ad hanc fbrmair» 

 $—szzfyi(tt—st-\-ss)> vei quoniam arcus- s et / no*- 



tabili- 



