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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 208, page id 1041163592:0242
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PHTTLOSOPHTE NATDRALIS
PROPOSITIO ZOVII PROBLEMA ZIVII.
Posito quod sinus incidentiae in superficiem aliquam sit ad sinum e
mergentiae in data ratione, quodque incurvatio viae corporum
juxta superficiem illam fiat in spatio brevissimo, quod ut pun-
ctum considerari possit; determinare superficiem quae corpuscula
omnia de loco dato successive manantia converrere faciat ad
alium locum datum.
Sic Locus à gue corpunema curigus soldo quem con-
versere debent; CD P curra linea quae circa axem AB revoluta
deleribat superticiem quaeltam; D, F. currae illius puncta duo quae-
vis; ex P F, F. C perpendicula in corporis rias AD, DB demissa.
Accedat punctum D ad punctum F, ee linex D S qua AD au-
setur, ad lincam DC qua D B diminuitur, ratio ultima crit ca-
dem quae linus incidentix ad sinum emergentiae. Datur ergo ratio
6d
DDE MOTV
LiORPORVHE
transire debet d Caplucur IuS LIC MICTCMEMCUI C M. ad ipsius
BC decrememum CIl in data illa latione; ceninque cu
cervallis ALL BN d
finicum, nunc mioree ad alletdo Palles vantels es habebumut L1
Cucae illae omnes quas Cartesius lapilea a CComcuia de lcta
ctiones expoluit. Ouarum inventionem cum Cartesus maximi
Fecerie ex Audiose celarerie, visum fuit hac propolicione expo-
MCFO.
incrementi linexe AD ad decrementum linexe DB; _E PFOPECrCA
curra CC
s in aXC AB Cumatur ubirisi punctum C, per que
aum encur ctoe mucce eeo in
D: punctum illud D cangec curram quaelitam C D F, candemque
ubiris tansendo determinabit. 9. F. I.
Corol. T. L’aciendo aucem ut punceum vel D tane abcat in 1
COrot