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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 346, page id 1041163592:0380
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340
PHTLOSOPHTS NATVRALIS
DE MOTV MINOE Ex Parte concara quam ex parte convexa; praevalebie im-
prestio forcior, et motum Orbis vel accelerabie vel recardabies
proue in eandem resionem cum iplius motu vel in concrariam di-
rigitur. Proinde uc Orbis unulquilque in motu suo uniformiter
persereret, debene impressiones ex parce utraque sibi inricem aequa-
ri, ec feri in regiones contrarias. Inde cum imprestiones TunE uE
contiguae superticies de harum translationes ab inViCeM, CrUNE Eran-
Pationes inverse ue superticies, hoc est, inverle ut superticierum di-
stanciae ab axc. Sunt autem ditterentiae motuum angularium circa
axem ut lx cranclationes applicatae ad dictantias, sire ut transtaci-
ones directe ex distantie inverse; hoc est (conjunctis racionibus)
ut quadrata distantiarum inverse. Ouare s ad infinitae rectae
SABC D F E ParECS CIn-
sulas crigantur perpendicula
Aan Bb, CC, D d. L e, XC.
ipsarum S, SB, SC, SD.
SF, ecc. Quadratis reciproce
proxortionalia, et per ter-
minos perpendicularium du-
ci intelligatur linea curva
Fyperbolica; crunt summae
difterentiarum, hoc cA, mo-
tuS toti angulares, UE rC
(pondentes summae linearum
Aa Bb, CC, D d. F C: id
est, Ei ad constituendum MC-
dium unisormiter Ruidum, Orbium numerus augeatur de latitudo
minuatur in infinicum, ut areae Irperbolicae his Cummis analoqa
AaQ, Bbd, C69 D dD F e G, _C. Ft tempora motibus an-
gularibus reciproce proportionalia, erunt etiam his areis reciproce
proxortionalia. FC igitur tempus periodicum particulae cujulris
D reCIprOCC UE arca D d B hoc CA, (per nOtaS Curvarum qua-
draturas) directe ut distantia S D. Q. F. D.
Corol. T. Tlinc motus angulares parcicularum. Ruidi sunt reci-
proce ut iptarum distantiae ab axc colindri, e relocitates ab(0-
lutae Tune aequales.
Corol. 2. Si Auidum in rase cxlindrieo longicudinis infinitx con-
tincatur, et cylindrum alium interiorem contincat, revolvatur
autem cplindrus aterque circa axem communem, sineque revolu-
tionum
act
EORPORDN