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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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outbaoi
4C
PFTLOSODELE NATVRAEIS
Porro praecedentis propositionis ee corollariorum ejus benehcio,
collisitur etiam proporcio ris centripetae ad vim quamlibee notam,
qualis est ea Crraricatis. Nam si corpus in circulo Perrae concen-
erico vi graritatis sux revolratur, haec graritas est ipsius vis centri-
Deca. Datur autem, ex descentu grarium, ec tempus revolurionis
unius, et arcus dato quoris cempore descriptus, per hujus Corol.
2X. Fchujusmodi propositionibus Flucenius, in eximio suo Practa-
cu de Florolorio Oscillatorio, vim graritatis cum revolventium vi-
ribus centrituris contulit.
Demonstrari etiam possune praecedentia in hunc modum. In cir-
culo quoris describi intelligatur Polrgonum laterum quoccunque.
HC si corpus, in polygoni lateribus data cum velocitate movendo
ad ejus angulos singulos a circulo reflectatur; vis qua singulis re-
Rexionibus impinsie in circulum erit ut ejus relocitas: adeoque
Cumma ririum in dato tempore erit ut relocitas illa de numerus re-
dexionum conjunctim: hoc est (E polrgonum decur specie) uelongi-
cudo dato illo tempore descripta ex longitudo eadem applicara ad
Radium circuli; id est, uc quadratum longitudinis illius applicatum
ad Radium: adeoque, si polrgonum lateribus infinite diminuris co-
incidat cum circulo, ut quadratum arcus dato tempore descripti ap-
plicatum ad radium. Ilec est vis centrifugas qua corpus urget cir-
culum: ec huic aequalis est vis contraria, qua circulus continuo re-
Pellic corpus centrum rertus.
PROPOSITIO. V.
PROBLEMA L
Data quibuscunque in locis velocitate, qua corpus ficuram datam vi
ribus ad commune aliquod centrum tendentibus describit, centrum
illud invenire.
Figuram descriptam FAHBAnE reCtX treS DZ, TQV, VR in
punctis coridem P, Q R, Concurrentes in T et V. Ad tansentes
crisantur perpendicula P A, QB, RC, relociratibus corporis in
punctis illis F, Q. R a quibus criguntur reciproce proportionalia;
id est, ita ut siC P A ad QB ut relocitas in  ad velocitatem in
P, et QB ad RC ut relocitas in R ad relocitatem in Q. Per
Derpendiculorum terminos A, B, C ad angulos rectos cucantur AD
DBF, P C COnCUrrenteS in D _ F: EC actx VD, V F. concur-
RCHE IN CEHETO quaeSItO S.
LN d
DE MOrO