Namq; ex demonftratione fuperiorb. Propofitionis,quibus arcus quivis fimiles tempora P Qj k p q diata ratione diftantiarum defcribuntur:,. funt in dimi- C P Sc SP ta ratione corporis velrp, hoc eft, indimidia- S nendo, fummse tempoardu mfu mqumibamus caorrepuos roummn Ses - ff-iPm. iles, Et compodfcerficbruibnutunrt,
u rf,u hnot ci ne fet atdemempdorima itdoitaat aq uriabtuiosn fei.g uCrEa;E. .t oDta.e fPim Qil eSsc dpe *q
Prop. LX. Theor. XXIII.
Si corpora duo S & P, viribus quadrato diftantia fua reciproce proportionalemfe
mutuo trahentia, revoluntur circa gravitatis centrimi
commune : dico quod Ellipfeos, quam corpm alterutrum P hoc
motu circa alt er um S defcribit, Axis tranfverfm eritad axemtranf-
verfuik Ellipfeos, .quam corpm idem P circa alterum quiefcens S
eodem tempore periodico defcribere poffet, ut fumma corporum du-
fpNuemarmmio orum adfmiic S f da e P.fpc recirpo ad rtTspehm primam eE oillrllieupmdfe duarum aas liteuefirpfueemnrti medie i proportionalem int er hanc
ncoer ra tpeomripsu Ss apde &,rfiuomdimcuamm uSfsi.b, foinrevnicte min dsiemquidailaetsa,eav aVdeIIn.t maeinquuaeltiuar, iEn llriaptfieoonse icno Erplloiprufim acuutjeums p o5*fì4e-haaxics rPio.re,efttr M afneffvqeurifpulsic &in uteamtupr oirna hpaec treamtiopnoe
riroadtiirceam
in ratione, em tranfverfum cujus Ellipfeos ratio -t aptear, Tidh eeoft
verfus portionalium Ellipfeos inter circa Sfi S adal tVer ad ifui sP, uetf ptrrimipali cdautaa r;u mad corpus , emoqejd iaed p arox-- dveier lupmro pdoerftciroipntasleiu cmirc ain itmerm PSc 5ofbiiPle,S mobilef ut SSfiP id Pef.c ripEtste ad primam ienrvite raide axaexmis ttrraannff-- Q. E. D.
duarum meSe
S. Prop.
Prop. LXI. Theor. XXIV.
Si corpora duo virìbm quibufvis fe mutuo trahentia, neq\ alias agitata
vel impedita, quomodocunq\moveantur} motm eorumperinde
fe habebmt ac fi non traherent fe mutuo, fed utrUmq\ a corpore
tertio in communi gravitatis centro conflituto viribus iifdem tra-
heretur : Et Virìum trahentium eadem erit Eex refpeSlu diitan-
tia corporum a centro ilio communi atq\ refpeSlu diftantia totius incorNtperao
mrcao ,r vptioerrneasd. uillnate ,a dq uciboums mcournpeo rgar faev mitauttisu oc etrnathruumnt ,i ntetenrdmeneddiou mad, adeEotq jq eusoendieamm f udnatia a ce ffti ar actoior pdoifrtea nintitseer mcoerdpioor ims auntarriuenfvti.s Qa _ceEn. tDro, ibliitou rc ormatmiou cnuij uafdv idsi fptaontetifatamti sc odripftoanritsi seej uufndieums aad c oerapnodreem al tpeorote, fdtaa-- tem diftantise alterius j ut Scdiftantia & quantitatibus d artaist iout equunaqn-,t idtaetriisv actuujru,f vaidsq, uquasnet ietxa tuenma aliam, quse ex altera diftantia Seillam diftantiarum rationem ad q uparniotirteast ibhuasb etonttiidbeums f dimatiilsi tdeart admerqi-j vdairtuefrt.e vPelr oininvedrèi ef i uvti sd, iftqaunat icao croprupso urunmum a ba bin vailcteemio trahitur, fit jlibet hujus diftantise poteftas j vel deniqj ut quantita sv eqlu usetv qisu seex- hac diftantia 8ceadem vis, qua cqourpanutsi tiadteibmu sa dd actoism mquuonme ogdraovciutantiqsj .cdeenrtirvuamta t. i aehrii—t tturor, ilidoi rceoftme mìtuidnei,m v veel lumt veeardieem u td cifotarpnotirsies hauttjurasc pbo dtieffttaanst,i av ea l cdene
niqj ut quantitas ex hac diftantia Setis fimiliter derivata. Hoc eft Vis tr aahneanltoigs isé adqeuman teirtaitt iLbuesx rdeafi*
peftu diftantise utriufqj. Q. E. D.
Prop.