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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 395, page id 1066518432:0423
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P
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I X.
XI. Capite XZ. Lib. II. exposui generalem theoriam graritatis
rariabilis, cum scilicet corpora Colicitantur secundum directiones
quascunque unitormi tamen lese procedentes, propterea considera-
ri has directiones continsere curram quamlibet, vel, quod ecodem
recidit, suppolui casdem directiones currae cuicunque pro libitu
assumexe normales esse, ad id ut lex continuitatis in hisce obserrare-
tur. Sed, quia Colutio problematis in propositione L. XXVI. cvoluti
cacs, in quam primum incidi, ideo, quod plerumque accidere (o-
let, ejus analrsis geometrica paulo longior atque difticilior crasE.
Verum posteaquam hoc opusculum jam sub praelo esset, Faciliorem
Daulo ex, ni Fallor, elegantiorem ejusdem problematis nactus sum l0-
lutionem, quam cum analrsi ipla vel potius demonstratione cum
Benerolo Lectore hoc loco communicare placet. EHo curra quae- Fis. 258.
cunque AMIse mobili describenda, ac solicicationum graritatis MIX
directiones MNI ubique normales sint curre cuicunque AYy delcri-
Peae crolutione BN, quam proinde directiones MN ubique contin-
sent. Tangenti AB Cursum productae in a currae BN in B, 29atur
Per A perpendicularis indefinita CAV, ex in quadrante CR∞ cen
Ero A et radio quocunque descripto ductis AI e AK radiis cum
AC angulos CAI, CAK continentibus aequales angulis BAa, NMP.
in quibus lincx AB, MN CUIEVE AMIB OCCurrunE, agantur rectxe
Ta, IO Parallelae AC e producantur usque ad occursum in d et I
cum hrverbola OaT inter asmptotas aA, AV descripta. Circa
axem rerO AB delcripea sIt curra quaedam DF. hac lege, ut ablcisa
ejus AF aequet ubique homologam interceptam YM inter curram
AY et datam curram AMI mobili describendam, OrdinatA VerO F F
ordinatam a0 in hyperbola abscista ejus AA POSIta === MINY. FF, Si mO-
bile incedat in medio resistente, cujus relistentix sine in composi-
ta ratione densitatum ex duplicatae celeritatum, fat in hrperbola
quadrilincum aDST vel dD20 aequale superficiei crlindrica, cujus
balis arcuS AMI currae describendae, quae crlindrica superticies oritur,
Si in cingulis punctis arcus AM ad ejus planum perpendiculares cri-
santur proportionales densitati medii D, in respectiris currx pun-
atis, interrietque quadrilincum aS delcentui mobilis Cx A in NI, al-
terumque dE acentui ejusdem mobilis ex M in A. Ilisce praeparatis,
Dico velocitatem mobili in M acquisitam post descensum per arcum
AM fore ad celeritatem initialem in A in composita ratione, ex hisce
tribus Aa ad AC seu reciproca sinus anguli NMP ad sinum anculi
BA, ex A2 ad AC, seu abscissae minoris ad majorem quadrilinei hyper-
boliet