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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 476, page id 1041163592:0512
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176
PHTLOSOPHLA NATORALIS
De Monni pradictis eribus Comerae locis observatis, invenianeur in hoc novo
plano loca eria vera (uE Supra:) deinde eriam Orbis per loca
illa cransiens, e ejuldem areae duxe inter obserrationes descripex.
qux SInE d CE es REC NON tempUS EOcum t quo arca toca d F e de-
Ceribi debeat.
Oper. 2. Servetur Congicudo Nodorum in opcratione prima, et
augeatur inclinatio Plani Prajectoriae ad planum Fcliprica, addi-
eis ad inclinationem illam 20 vel 303 quxe dicantur O. Deinde
ex obserratis praedictis tribus Comctae locis apparentibus, inve
niantur in hoc novo Plano loca eria vera, Orbisque per loca
ilsa cransiens, ut ex ejusdem arex duxe incer obserrationes de
(CripE, qu_e (INE det es e tempuS totum F quo area tota d + e
describi debeat.
Tam AIE C ad Z uE A ad B, _ G 2d Y uE D ad F, ex Z 2d Z VF
a 2d es ex Y 2d Y UE dad c; Sicque S tempus verum inter obserra
tionem primam ac cerriam; et signis F dc = probe observatis
quaerantur numeri m de n, ea lesc, ut sIE 2C7 - 2C = m C = me +
nC = n Y, ec 2T = 26 aequalC mT = mt + nT = nF. RE S1, in
operatione prima, I desionet inclinationem plani Trajectorix ad
planum Feliprica, e K longicudinem Nodi alcerurrius, erie
l. FnO vera inclinatio Plani Prajectoria ad Planum Relipticae, e
KE + mP vera longitudo Nodi. AC denique A in operatione
primas secunda aC tertia, quanEITaTOS R, r dc G desiGMenE LaTeTZ
recta Trajectorixe, ee quantitates 7,  = ejusdem Latera trans
verta respectire: erit R Fmr = m R +nS =nR verum Latus re-
Etum, e
L F mI = m L + n 2 = n
verum Latus eransrersum Tra-
jectorix quam Cometa describit. Dato aurem Latera cran(verso
datur etiam tempus periodicum C OmCtx. d. F. l.
Cxterum Cometarum revolventium tempora periodica, ee Or-
bium lacera transversa, haud latis accurare decerminabuntur, nisi
per collationem Comctarum inter le, qui diversis temporibus ap.
Darenc. Si plures Cometx, post aequalia temporum interralla,
eundem Orbem descripsisse reperiantur, concludendum erie hos
omnes esse unum ex eundem Cometam, in eodem Orbe revolven-
tem. EF cum demum ex revolutionum temporibus, dabuntur Or.
bium lacera transrersa, ec ex his laceribus dererminabuneur Or-
bes F Iliprici.
SXSTEMAF