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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 453, page id 1041163592:0487
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PRINOIPTA MATHEMATICA.
453
RE Per punctum P aBREUT (per hujuS LCM. VIT.) recta AF. C, LIBen
cujus parres AF, PC ad rectas T A _C TC terminatX, (INE 24 TEK1
invicem ut tempora V ec WV: et crunc A e C. loca Cometae in
plano Felipricae in obferratione prima ac certia quamproxime, II
modo B AE locus ejus recte assumpeus in obserratione secunda.
Ad AC bilectam in Perise perpendiculum Ti. Per punctum B
asc occultam Bi ipsi AC Parallelam. Junse occultam Si secan
tem AC in n, et comple parallelogrammum i ln u. C apc 10 aequa-
lem 3In, ex per Solem Sagc occultam 0E aequalem 355 = 3i N.
Ec deleris jam liceris , P, C3 I, a puncto B verlus punctum E
duc occultam novam BF, quxe sic ad priorem BF in duplicaca
ratione distantia BS ad quancitacem Su F 3in. EE per punctum
F icerum duc rectam FC cadem legc ac prius, id ctt, ita uE ejus
DArEeS AF eC FC Ent ad invicem, ut cempora inter obterrationes
Y _ WY. FECrunt A e C loca Cometae magis accurate.
Ad AC bisectam in I crigantur perpendicula AM, CiNV, IO,
quarum AM ec CN Unc tangentes lacicudinum in observatione
prima ac certia ad radios T A e TC. Jungatur M N (CCanS IO
in O. Constiruatur rectangulum iIn u ue prius. In PA prO-
ducta capiatur ID aequalis Su + Zin, e agatur occulta OD.
Deinde in MN versus Ncapiacur MF, quae sic ad longicudinem
suxra inventam X, in subduplicata ratione medioeris distantiae Tel-
luris a Sole (Peu semidiametri Orbis magni) ad distanciam O D.
Si punctum F incidat in punctum N; erunE A, B, C tria locaC0-
mecae, per qua Orbis ejus in plano Fclipricae describi debet. Sin
punctum F non incidat in punctum N; in recta AC capiatur
CO ipSI NF aequalis, ita uc puncta C ec P ad caldem partes
rectae WVC jaceanE.
Fadem methodo qua puncta L, A, C, G CX alTumpeo puncco
B inventa sunc, inveniantur ex alsumpeis uccunque punctis aliis
b Sc B puncta nOra e, a C, 5, eE, a, X, V. Deinde (i Per C, 5, 3
ducatur circumferentia circuli GQ V. secans rectam + C in Z: Crie
Z locus Comerx in plano FclipEICR. EF SI in AC, aC, ax capi-
anCur AF, af, a  ipsIS CG, c8, x Y respective aequales, ec per
puncta F, f p ducatur circumferentia circuli F fa, lecans rectam
AT in X; erit punctum X alius Cometae locus in plano Relipricae.
Ad puncta X ec Z crigantur tansentes lacitudinum Cometxe ad ra-
diosT X X FZ; ee habebuntur loca duo Comcexe in Orbe proprio.
Denique (Per PrOP. XIX. Lib. L.) umbilico S, per loca illa duo de-
seribatur Parabolas et haec erit Trajectoria COmerx. Q. L. L.
Con-
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