130 Opuscula * 
draUini elevatis , atqiie in iinam fummam colle(?i:is ; extracla- 
que inae radice quadrata exurgit — : — . d?c jcquale 
_^ J3 -!i_lLf_ . ^ ^ — ^ . quod indicat lignum radicis 
elTe politive accipiendum , 
§. 20. Exemplum tertium doceat reducere ad rec1:ificatio- 
nem curvse algebraicss formulam differentialem dx \!jLidli-i: . 
facla coliatione cum formula generali pdpc habebis = 
\/(Za-r~xx , aa-4-rx ^ —xx 
titatem negativam , & per confequens ordinatam s.i-pp^^ 
y imaginariam ; m.ethodo BernouIIiana , tamquam inutili 
fepofita , adhibe noftram , pro qua invenies pp — j -^z — 
quantitatem pofitivam , & cum fit dp^- — , atque 
a aa -\- x X 
. , dx aJaa-^-xx , x / ; ■ 
mde j — ~ — , reperies s . p p - 1 ^ - sj a a -\- x 
quantitatem algebraicam f \l du" - dy jungendam ; erit itaque 
. „ d X y a a -4- x x y~ i ~, — 7 
^ .sj a a -^.sc X -V f — ^ ^ \/du~ay^ ut no- 
Itrum prsscipit Theorema; coordinatse vero curvae adhibendae 
3 __________ 
erunt s , p y a a •■r- x x ^ y ^ & /7^ — w^-A' 
r= z:z u , Si defideras rationera , qua f d if^ — dy" 
a 
affirmativajn accepimus , fume diiferentialia coordinatarum y , 
^xdx ixx-^iaa , ^ ^ ^ 
u ; fcilicet . ■■ y , & — d:K ^ du^ 
■^J aa x x a 
dy X XX o , 
ex quo eru.es ^ ™ — = - — f f ? — ; — ~ * ^ ^ ~ f f 
-+- X X 
s atque \/i — =r ^ cum itaque fit 
= '^''j^^* — i/j-, ex nofcro Theoremate , erit debita 
fubflitutione pera(fia ^/du^ — dy^ ^ -^^ "^ ".I r ^/^^ = D ~ 
