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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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P R A F A F IO
EX iis quae hactenus dicta sune, constat Planetas in Orbicis suis
recineri per Vim aliquam in ipsos perpetuo agentem: constat
Vim illam dirigi semper vertus Orbitarum cenera: constat hujus
efficaciam augeri in accessu ad cenerum, diminui in recessu ab co-
dem: ex augeri quidem in eadem proportione qua dimiruitur qua-
dratum distantia, diminui in eadem proxortione qua dictantie
quadratum augetur. Videamus jam, comparatione insticura inter
Planetarum Vires centripetas ec Vim Gravitatis, annon ejusdem
Forre sinc generis. Ejuldem vero generis crunt, si deprehendan-
cur hinc ec inde leges caedem caedemque affectiones. Primo ica-
que Lunae, quae nobis proxima est, Vim ceneripetam expendamus.
Sparia rectilinea, quae a corporibus e quiere demissis dato cem-
pore sub ipso mocus initio describuneur, ubi a viribus quibuscun-
que urgentur, proportionalia sune ipsis riribus: Iloc utique con-
sequitur ex rariociniis Machematicis. Pric isieur Vis centripeta
Lunae in Orbica Cua revolreneis, ad Vim Graricaris in uxerkicie
Terra, uc spacium quod tempore quam minimo describeret l. una
descendendo per Vim centripetam versus Terram, si circulari om-
ni motu prirari Anscretur, adt spacium quod eodem tempore quam
minimo deseribit grare corpus in vicinia Terrae, per Vim gravita-
eis suae cadendo. Elorum spatiorum prius aequale est arcus a Luna
per idem cempus descripei sinui rerlo, quippe qui Lunae cransta
tionem de Tangente, Factam a Vi ceneripeta, meticur; atque adeo
computari porelt ex dacis cum Luna tempore periodico cum di-
Hantia ejus a CentrO Perre. Sparium posterius invenitUE Per R. X-
verimenta Pendulorum, quemadmodum docuie fugenius. Inito
itaque calculo, sparium prius ad sparium polterius, seu vis cen
trivera lunae in Orbica sua revolventis ad vim Gravicatis in su-
perticie Terra, erie ur quadratum semidiamerri Perrx ad Oebitx
Cemidiameeri quadrarum. Randem habet rationem, per ca qur
superius octenduncur, vis centripeta Lunxe in Orbita sua revol-
veneis ad rim Lunae centripetam prope Perrae superficiem. Vis
itaque ceneripera prope Terrae superticiem aequalis est vi Gravica
tis. Non ergo diversae sune vires, sed una acque eadem: si enim
divertae essene, corpora viribus conjunctis duplo celerius in Ter-
ram caderene quam ex vi sola Graviratis. Constat isitur Vim
illam ceneripetam, qua Luna perpetuo de Tansente vel trahieur
vel impellitur ex in Orbita retinetur, ipsam esse rim Gravicaris
cerrestris ad Lunam ulque pertingentem. Rc rationi quidem con-
sentancum est uc ad ingentes distantias illa selc Virtus extendat,
Cum
I HHBS HIII HIIBMIHII