( ) 
euht {motu forinfecus ajjumpo ) fer motuum quihus tranfigantur 
Icnyxt^vcov celeritatem, ( §}uippe idem efh , in 'Motu , Celeritoi ^ 
atque hicc, in Situ (^propter pofitionem obliquam [eu minus decli- 
vem) refpectiva Longitudo.) Aptiffime quidem in lineis a motu 
primhus oriundis^ {putd , Cycloide , Concboide ^ Spirali 5 ^adra» 
tricey (^c.) mc inepte in aliis ^ quce fingi faltem pojjunt iJHufmodi 
malibus defcribi^ 
Prcefumo autem (ex propyl 5» cap* 2» de Motu) eamejje curv£ 
in quovis puncto directionem, adeoque (3 declivitatem^ qtd£ efi rect<e 
ibidem tangentis : Item (ex prop. 6. cap. 10.) Motus compofiti dif 
rectionem ejje in Diagonio parallelogrammi ^ cujus later a ^ anguli 
exbibeant componenttum celeritates l3 directioues^ 
Intel ligatur jam (fig, 4.) j^a parabola, defcribi motu compoftto^ 
ex £quabili fecundum AT vel V<l 5 cujus itaque particulce )<rox^ovoi 
(per pr. 3. cap* 10. de Motu) /unt [eries Pnmanorumy qu£ ad fes 
riem totidem ultimee aqualium^ {hoc ejl^ ad rectam )<j^x^°^^v celeri* 
tate in^ acquijita tranfigendam,^ ejiut i ad 2y {per kr. Infin. pr. 
64. vel pr. I. cap. 5. de Motu») Adeoque^ [umpta KF= 2 VA^ 
^ compojito FFety par allelogr ammo 5 juncta -hlF efi Tana 
gens. 
Idem fmiliter obtinebitur in parahloidibus quibufcunque^ epe 
prop* 2, 5, 63 7, de Motu. 
Atque inde facile ( vel ex iifdem principiis^ oflenditur ; fiintel* 
ligatur Fig, ATv JIc confiitutay ut momenta ( refpectu AF ) erdi* 
natorum Tu^ y »^ fine ipfis T^ty y 0 , ordinatis proportionalia 3 es 
runt Celeritates acquijitce in a, 0^ feu (popta ATlineam(h 
tus £quabilis) rectis Ta^ju, proportionates : Et conjequenter ^ ut 
AuT (iQarum aggregatum^ ad AF v T {aggregatum totidem maxi: 
m£ (equalinm^) fie VA (aggregatum celeritatum /eu particularum 
erefpentium ) ad ( aggregatum totidem maxima aqualium ) 
TF. 
Spiralis As a (fig. 9.) punctum a defignatur motu compofitQ ex 
recto per A*, (3 circulari per VA^^equabtlibus utrifque W^?^*'*'^* 
Ergo, (umpta circuli tangente «tw=«t^ , completo AomF paralle* 
logrammo ; juncta a F Spiralem tanget, 
Vnde fiatim emergtt Archimedea qmdratura (five Circuli fve 
See torts cujufvis ) propter A F^^^^^^K 
sin motuum alter ^ puta A a^ fit acceleratus vel retardatus s pro 
