SECT. VI.
De inventione motmm in Orbibm datis. Prop. XXX. Prob. XXII.
Corporis in data .'TrajeSloria Parabolica movent is ^ invenire locum ad
tempm ajfignatum. SitS umbilicus & A vertex principalis Parabolae,M area Parabolica A P S, quae radio S P, yel poft exc effittuqm; 4co ArpSox
arips pduelf uvmer tiecjeu sd ealcdr ivpetart ifcueimt, vedle aicnrtie- * p - bteemndpao reef t.i pfiI npnrootpeolcrtitio anraelai. iliBa ifeex- Gca HA aSe iqnu Gale,' jeMrig,e q&; pcierrcpiielunsd icceunlutrmo PHa,r ainbotelarvma lilno loHco S qdueiac friitpot uPs. iecNaabmit edfetm Hiflà ad axem perpendiculari P 0, Gq.-\- GSq. ( = V\Sq~A<m
-Oq.2HGxP0- + H.G -VOq:)j-P0f. - Et GO deleto q.-f HGq u-
H AG0x?u- P.-O2+GPOA0*.+ fPe0ujj.0
trinq;HCj:. f-2GxP0(G0?.+JinCSi P0 . = j.-G GS^.0 1. - fcr . = H_)-
- A Oq. -f !P Oq.Pro A Oq. ibe A O x ?0(l
applicatis tcrmims omnibusadjPO, duöifq; in a A S , fief t C H x A S ( =
*A 0 x P O + iA 'S x P 0 = 3A s xP0Z 4J 0 - * S 0 p 0 =
6 6
at area; A PO S PO areae APS. Sed G /after 3 M, St inde
ì HG
fHGxAS eft q-ASxM, C EIr0go5 ]area A F S aequalis eft4 ASx M. Q^E.D.
Corol.fit arcum 1A. PH iandc tGemHp uesf tq audo cAoSrp,uust dteemfcpriupsf iqt uaorc ucmor piunst edre vfcerritpi-
cem A & perpendiculum ad axem ab umbilico S ere<ftum. Corol. 2.unte, veloci taEst pcuirncu&loil SAeSftP a pde rv ecloorcpituast emmo veqnusa mpe cropreptuuso thraabnufei-t iand vleinrteiacme Are, futat m3qauda 8m; caodrepouqsi tinem eap oerteia mm ortautsi ofnuei aebft A li nade aPG, eHa cum velocitate quam habuit in vertice A, defcribere poflet. Corol. 3. Hinc pus defcripfit arcuemti amqu veimcevvies rafall iginnvaetnimirii Apo Pt.e ftJ tuenmgpe uAs qPu o& c oard
min edium ejus punftum erige perpendiculum reftae G H occurrens H. Lemma XXVIII.
Nulla extatßgura Ovalis cujus area, reclispro lubitn abfciffa, pojfit per
éequationes numero terminorum ac dmenfionum fnitas generaliter
reviIonnlvvteranat iurOri. vpaelerpme tudoe tluinr epa urneffttuam, & q iunotedrveias ,i nc irrecaft aq uilolad ecxeeua tp poulunmc
tuutm mobile de polo, pergatq; femper ea cum velocitate, quae fit r e f t a ; illud defcilrliiubse t inStprair alOemva gleymris| loinnfginitiutids.o . JaHmo cf i amreoat uO upaulnisf tupmer fsienqiutaamtio sneeqmua dtiiofntaenmti ian vpeunnirfit ip oat epfot,l oi,n qvuean;i ehtuuirc eatrieaam; p proerp oeratniodnema- lvies neirfti , paocitieuonqt; :o mnia Spiralis punfta per aequationem finitam inSt.
feftio cum fpirali inpvroenpitreir eeat iaremft api octeufjtu fpveisr psoeqlmuaotnioen èdmat af;i niintatemr-. Amteqruo i inrefifntait ios,m&n iase qinufaintiiote,q upar óidnuteclrafe ffptiiora laelmiq ufae cdaut ainru mpu nlifnteisa rnuum
invenitur, exhibet earum interfeftiones omnes radicibus totidem, P ade