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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 209, page id 1041163592:0243
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PRIMCIPTA MATTIEMATICA.
Corol. 2. Si corpus in superticiem quamris CD. lecundum Ca LIBEK
rectam AD lege quaris ductam incidens, emergat secundum aliam enimos
quamvis rectam D K,
et a puncto C duci in-
celligantur Lincae currae
C F, C QIPAS  D, DR
semper pervendiculares:
erunt incrementa linea-
rum F D, _D, at9; 20-
colinexiplX PD, _D
incrementis iltis genitae,
ut sinus incidentia et
mersentia ad invicem:
dC COHETa.
PROPOSTTIOZEVIII. PROBLEMA XEVIII.
Tisdem positis, es circa axem AB descripta superficie quacunque
attractiva CD, reculari vel irreculari, per quam corpora de
loco dato a exeuntia transire debent: invenire superficiem se-
cundam attractivam P. F, qua corpora illa ad locum datum B
conversere faciat.
Juncta AB secet superticiem primam in C dx secundam in P,
puncto D uccunque astumpto. Ecpolto sinu incidentix in (uper-
siciem primam ad sinum emergentixe ex cadem, et sinu emersentixe
e superticie secunda ad sinum incidentix in candem, ut quantitas
aliqua data NI ad aliam datam NY; produe cum AB ad C UE AE BC
ad C F UEMI - NTadNY, cum A D ad TT AE AIE AFI equaliS AG, tum
etiam D S Zd R AE AE D R ad D EI uE DF ad NI. Junoe RB, eE
centro D interrallo D FY describe circulum OCCurrentem RLB prO-
ductae in L, ipsique D L. parallelam asc B F: ec punctum s tan-
set Lineam L F, quae circa axem AB revoluta describet Tuperk.
ciem quaesitam. d. F. F.
Nam concipe Lincas C P, C Q ipsis AD, D F respective, et Li-
neaS F R, FSipsS FB, F D ubique perpendiculares esse, ad coque
QS ips C F. semper aequalem; ec erie (per C Orol. 2. PrOP, XCVTI)
D ad AD uc M ad FV, adeoque ut D L ad D R vel F B ad FR:
E.C
O