OpUSCULA, I2J 
ut formula evadat fif^^.v/i — ff, in qua eft quia 
du^'^>dy''. Ergo quas in Theoremate Bernoulliano eit , nunc 
fit r= v^i — f ^ . Ergo qq:z=.i — ;7f, quae pofitiva ell , nam 
ponitur efTe p;; > i , qu^ vero in Theoremate Bsrnou!liano 
ell: ;v hic elt «; quae vero ibi eft j , hic vocetur ^z; quare 
in eas formulas introduc^is his valoribus habebis du :=z 
.. ^^^^ pio dx^sdp; & pro coordinatis curvarum habe- 
\/^—qi . 
zq\ zq"- . \ i qq — u y & demum pro arcu c urv^ ha - 
bebis h — zq^ ~ fdu ^ i - q q^ five zq^ -1»^ fdu\li-qq'^ 
^ \/ dti' — dy^ , quod numero fjperiori demonftravi ^quale 
s . pp — I "h fp d X ; ergo zq'^ — h:=^ s . p p • — i f p d x , 
five f p dx ^ z q^ — s . p p — I — L, quam jn hypothefi p p 
> 1 imaginaria nulla tui"bare poillint . Hoc modo patefjcluni 
cir fi'ie dubitatione quamlibet fbrmulam diiferentiaiem per 
reCl;incaiionem curvae algebraicse conftrui po ife . 
§. 1$. Haec omnia oportet exeraplis illufirare . Sit prlmo 
conftruenda formula - t/L—^ - Theoremate Bernoulliano uti 
non licet , quia pofita —^— —p, fieret i — p p ^ 
y/ X —'a X — a 
quantitas negativa ; nam x accipi femper debet maior a alio- 
quin formula propofita effet imaginaria . Qiiare confugicndum 
eft ad noftram methcdum ; erit itaque pp — i ~ , & 
gp =z : , Ck j- = ;~ — " . hreo s .v v i 
2 — 3 
1 .X . X a 
= 2\/.v.v^.v — a. Prxtere^ coordinat^ corvsc adhibendo: io- 
veniuntur elTe i x — y ^ — ^ rr: , five x u . Ergo_ 
Theoremate noftro habebimus 2 sj ^ . %} x — a -\- f — ^-^— — 
\/x — a 
fyjdu"- — dy^ . Huic radici calculus iiidicabit fignum ~h ede 
apponendum . 
§. i6. jara vero per ea , qux d i i^a fan t numero 14, con^ 
ftruamus formulam ^/j^' — - r/j' reiliflcato arcu curv^ alge^ 
brai- 
