4^4 
Oposcula s 
a-^b in fig» 4, CNrr:^, MN=:j, quac dux coordinan- 
tur ad tractoriam, CE=^, DE=:^, qux dux coordinan- 
tur ad fyntractoriam . RM radius circuli ofculantis tracto. 
riam in puncto M vocabitur = R, recta TR, jungens cen- 
tium ofculi , & punctum T,r=z>. Harum denominationum 
aiiqux espofitx funt in corol, 3. prop. primx: fed legen- 
tium commodo omnes hic coUectas placuit exhibere . 
Corollarium prtmHin » MN ordinata tractorix ad DE 
ordinatam fyatractorix tik in ratione conltante MT: DT. 
Quod quum de omnibus verum fit , confequitur , M^ dif- 
ferentiam duarum ordinatarum in tracroria efle ad D/ diffe- 
rentiam duarum ordinatarum in fyntractoria in eadem ratione. 
Corollaritim aherum , Ductis in tractoria duabus tangen- 
tibus MT, mt infinite proximis concurrentibus in puncto 
h t & fyntrac^oriam fecantibus in punctis D,</, diffcrentia 
rectarum /2D, hd^ five iineoia D/, qux abfcinditur ab arcu 
diy cujus centrum ft, radius hd^ lineola, inquam , D/ 
scquaiis eft arcui tractorix Mm: quod ea ratione probabis, 
qua in prima propofitione xquaiicas inter lineoiam T/, ar- 
cumque M.m elt demonftrata , 
FROFOSITIO TERTIA, 
NAturam fyntradorix analytica xquatione definire , 
Anaiyfim exercebo in fig. 2, qux fyntraftoriam cite. 
riorem inferam reprxfentat : poft quid in aiiis accidat in- 
dicabo . Conftat es Foienianis xquationem tradorix elTe 
dx := =^ — y . Perfpicuum item eft , eiTe 
TD:TM::DE:MN - 
b : a :: q : y : Ergo y :=z ltemTE=z\/bb — , 
z=z \/aa -—yy , Qyum autem fit CEr=CN-4-NT 
— TE, erit x \/aa — yy — \^^bb — qq . Pro x fubftitue 
S — ~-\/ aa ~ y y , & fiet =: S — Vaa — yy Vaa — y y 
— Vbb — qq . Pro y fubRitue ~ , & invenies = S — . 
\/bb — qq-\-^^\/bb — qq ^ & fumptis ditferentiis = 
__jtlAl±^, E. I. 
Eadem 
