1Et per punctum Eagatur (per hujus Lem. VII.) recta AEC,
cujus partes AE, ECad rectas TA& τCterminatæ, ſint ad
invicem ut tempora V & W: & erunt A& Cloca Cometæ in
plano Eclipticæ in obſervatione prima ac tertia quamproxime, ſi
modo Bſit locus ejus recte aſſumptus in obſervatione ſecunda.
cujus partes AE, ECad rectas TA& τCterminatæ, ſint ad
invicem ut tempora V & W: & erunt A& Cloca Cometæ in
plano Eclipticæ in obſervatione prima ac tertia quamproxime, ſi
modo Bſit locus ejus recte aſſumptus in obſervatione ſecunda.
LIBER
TERTIUS.
TERTIUS.
Ad ACbiſectam in Ierige perpendiculum Ii.Per punctum B
age occultam Biipſi ACparallelam. Junge occultam Siſecan
tem ACin λ, & comple parallelogrammum iIλμ. Cape Iσ æqua
lem 3Iλ, & per Solem Sage occultam σξ æqualem 3Sσ+3iλ,
Et deletis jam literis A, E, C, I,a puncto Bverſus punctum ξ
duc occultam novam BE,quæ ſit ad priorem BEin duplicata
ratione diſtantiæ BSad quantitatem Sμ+1/3iλ. Et per punctum
Eiterum duc rectam AECeadem lege ac prius, id eſt, ita ut ejus
partes AE& ECſint ad invicem, ut tempora inter obſervationes
V & W. Et erunt A& Cloca Cometæ magis accurate.
age occultam Biipſi ACparallelam. Junge occultam Siſecan
tem ACin λ, & comple parallelogrammum iIλμ. Cape Iσ æqua
lem 3Iλ, & per Solem Sage occultam σξ æqualem 3Sσ+3iλ,
Et deletis jam literis A, E, C, I,a puncto Bverſus punctum ξ
duc occultam novam BE,quæ ſit ad priorem BEin duplicata
ratione diſtantiæ BSad quantitatem Sμ+1/3iλ. Et per punctum
Eiterum duc rectam AECeadem lege ac prius, id eſt, ita ut ejus
partes AE& ECſint ad invicem, ut tempora inter obſervationes
V & W. Et erunt A& Cloca Cometæ magis accurate.
Ad ACbiſectam in 1erigantur perpendicula AM, CN, IO,
quarum AM& CNſint tangentes latitudinum in obſervatione
prima ac tertia ad radios TA& τC.Jungatur MNſecans IO
in O.Conſtituatur rectangulum iIλμ ut prius. In IApro
ducta capiatur IDæqualis Sμ+2/3iλ, & agatur occulta OD.
Deinde in MNverſus Ncapiatur MP,quæ ſit ad longitudinem
ſupra inventam X, in ſubduplicata ratione mediocris diſtantiæ Tel
luris a Sole (ſeu ſemidiametri Orbis magni) ad diſtantiam OD.
Si punctum Pincidat in punctum N; erunt A, B, Ctria loca Co
metæ, per quæ Orbis ejus in plano Eclipticæ deſcribi debet. Sin
punctum Pnon incidat in punctum N; in recta ACcapiatur
CGipſi NPæqualis, ita ut puncta G& Pad eaſdem partes
rectæ NCjaceant.
quarum AM& CNſint tangentes latitudinum in obſervatione
prima ac tertia ad radios TA& τC.Jungatur MNſecans IO
in O.Conſtituatur rectangulum iIλμ ut prius. In IApro
ducta capiatur IDæqualis Sμ+2/3iλ, & agatur occulta OD.
Deinde in MNverſus Ncapiatur MP,quæ ſit ad longitudinem
ſupra inventam X, in ſubduplicata ratione mediocris diſtantiæ Tel
luris a Sole (ſeu ſemidiametri Orbis magni) ad diſtantiam OD.
Si punctum Pincidat in punctum N; erunt A, B, Ctria loca Co
metæ, per quæ Orbis ejus in plano Eclipticæ deſcribi debet. Sin
punctum Pnon incidat in punctum N; in recta ACcapiatur
CGipſi NPæqualis, ita ut puncta G& Pad eaſdem partes
rectæ NCjaceant.
Eadem methodo qua puncta E, A, C, G,ex aſſumpto puncto
Binventa ſunt, inveniantur ex aſſumptis utcunque punctis aliis
b& β puncta nova e, a, c, g,& ε, α, χ, γ. Deinde ſi per G, g,γ
ducatur circumferentia circuli Ggγ, ſecans rectam τCin Z: erit
Zlocus Cometæ in plano Eclipticæ. Et ſi in AC, ac,αχ capi
antur AF, af,αφ ipſis CG, eg,χγ reſpective æquales, & per
puncta F, f,φ ducatur circumferentia circuli Ffφ, ſecans rectam
ATin X;erit punctum Xalius Cometæ locus in plano Eclipticæ.
Ad puncta X& Zerigantur tangentes latitudinum Cometæ ad ra
dios TX& τZ; & habebuntur loca duo Cometæ in Orbe proprio.
Denique (per Prop. XIX. Lib. I.) umbilico S,per loca illa duo de
ſcribatur Parabola, & hæc erit Trajectoria Cometæ. Q.E.I.
Binventa ſunt, inveniantur ex aſſumptis utcunque punctis aliis
b& β puncta nova e, a, c, g,& ε, α, χ, γ. Deinde ſi per G, g,γ
ducatur circumferentia circuli Ggγ, ſecans rectam τCin Z: erit
Zlocus Cometæ in plano Eclipticæ. Et ſi in AC, ac,αχ capi
antur AF, af,αφ ipſis CG, eg,χγ reſpective æquales, & per
puncta F, f,φ ducatur circumferentia circuli Ffφ, ſecans rectam
ATin X;erit punctum Xalius Cometæ locus in plano Eclipticæ.
Ad puncta X& Zerigantur tangentes latitudinum Cometæ ad ra
dios TX& τZ; & habebuntur loca duo Cometæ in Orbe proprio.
Denique (per Prop. XIX. Lib. I.) umbilico S,per loca illa duo de
ſcribatur Parabola, & hæc erit Trajectoria Cometæ. Q.E.I.
zoom in
zoom out
zoom area
full page
page width
set mark
remove mark
get reference
digilib