Disputatio astronomica de motu vertiginis lunæ quam ... præside ... Erico Burman, ... Publice exhibet stipendiarius stieglerianus, Andreas Celsius, Upsaliensis. In aud. Gust. maj. ante meridiem 12 Decembr. a. 1727

t£s Disputatio Astronomica De

MOTU

VERT1

ginis

lüne

j4b

_Amplisp

_Facult;

_Philof.

_Regi&

Acad,

_Vpfalienjis

_adprobatam

Ρ R /E S I D Ε

VIRO AMPL JSSIMO,

Mag.

AA/CO

BURMAN)

Astron. Prof. Ordin.

Publice cxhibet

Stipendiarius Stieglerianus,

Andreas

_Celsius,

12 Ρ SJ L IEN,S IS,

In Auch Guft. _{Maj. anre meridiern}

pR/EFATIO

Oflqitam

ges Mechanicas rtvocare _coepe·

runt

Philofophi,

illorum

_eaujfis

ac

ve-hementiores

_{confitflationes}

dos _{& Garqmantas profcribere}

jujfite-videntifjima

demonftran-dt ratio. Gerte

_nobilisjima

& jucundi_firma

_Philojophia

Bionis

_fafiigium

eft,ut cer*

titudine _& evidentia _{demonflratiomim}

vix

_ipji

_{Dijputationem}

die _{infiltnere velie}

, vamimfortevi¬

debitur _{& infuljum. Verum}

enim ve* ro _,

qvum adhuc nön _{pauca fuperftnt^} qua ad

_liquidum

_defiderant

,

fipecimmis equidem loco·» motum ver* ttginis Lima , quem etiamnum Viro$

magni nominis _{negare conßat, demon*}

ftrare conabor,

AXI-Μί MjM«üsMiΜΜΜΜ ΜΜΜJ» Mtiåfa Ώϋϊ^&οί rr*^f

ΐίΐ^

§,

ft

Orptis

ΐή

fimpiici

VJ

_mipulfmn,

unu

formiter

dire&mn.

CORO LIAR1U Μ.

§. 2. Totum ergo mobile pun-di inftar _{coni\deratum, vel ejus}

centrum _{gravitatis , invariata}

ce-leritate fecundum unicam redarn

progreditur.

CORO LLARIHM,

§.

püftAum,

in _{corpore üc moto relative} qui-efcens, eadem velocitate _äqualem

te&am _percurrit.

4/

LEMMA.

§. 4. Si mobile per retlam

_tmpulfit

muco_{progrediatur,queelibet in}

_ifio

cor-pore

linea fitum

Demorißratio.

Moveatur _{corpus , v. gr. fpha>}

ricum , per re&am ΛΊ> : dico ra¬

dium AC in fitu BD iibi _paralle¬

lem _{efTe. DuÖis enim reöis CD Sc} CB , erit _, in

Triangulis ACB Sc BCD, CD s _{y/Z>, quoniam pun&a}

β^ί Sc C _{äquales delcribunt lineas} (

$·

o y

( §. 3. )^6> ρ BD(per

bypotbefm),

j&B -z angulo CBD (Prop. g Elem.

•i.Evcl.), ac

confequenreryiCå

Z>Ö

parallell (Prop. 28

Élerrt.t.

)&ü;

CORO L L AR 111 Μt

§. 5. Si

mobile,

ubi

perve-nerit, novo _{impulfu pergar}

fecün-dum dire&ionem _{ßß, ad prioremt;}

AB _{inciinatam, patet AC in (itu EF} Tibi manere _paralleiarn

(Pfip>t

Ekm f.); immo _generalirh , corpus

per re&as quotvis . inclinafas. &

contiguas progrediens iinearuro..

fervare

_{parallelifrniim.}

CO ROLL AR IIIΜ.

§. 6. Qvum autem curv^e ex re-&is inclinatis &. _{contiguis infini¬}

te _{exiguis componantur,}

_mobile-»

per curvam quoq.ue incedens.

ll-tum iinearum fuarum _{conilsr.teiL«,} retinet

_parallelum.

DEFI-6 _4M o

<H§*-DEFINITIO.

§. 7. _{Si corporis pun&um} quod-vis circa axem _peripheriam

circu-larem _{defcribat, dicitur ha?c cor¬}

poris revolutio _ejus motus verti·

ginis,

CORO LL AR IUM.

§. 8.Hinc _fequimr, il mobile _per

curvam lacum iimul _vertiginis

gau-deaf motu , quamlibet in ifto _cor¬

pore lineam _{perpetuo murare} pa-ralleliimum, excepto axe , qui

ii-bi _parallelus

permanet

_(§.

LEMMA.

§.9. Si corpus v. _{gr. Spbjericum,}

dum _{per orbitam c^rciliarem}

move-tur y idem femper

bemifphärkim

c en· tro obvertat _{(hoc efb Γι}

fphsrici

meridiani _{alicufus? feu circuli}

per po¬ los _{jpermeantis, planum}

produåum

per centrum orbitae _{tranfeat), illiid}

eodem _{tempore circaaxem}

rotatur, quo

orbitam _percurrit.

Sphasra in A fui

hemifphserium

DBE centro orbita? C obvertens ,

( meridian! piano ,

quod

referats

AB, _{per C tranfeunte)}

_absque

motu _{vertiginis, arcum quemcun«}

que circularem , v. gr»

cΛΕ,

de-fcribat.

o $&·

δ

_ -m ο

fcribat: atque linea AB, corpore in F _{conftituto, coincidet} cum _linea

TG , Tibi parallele (§.7.) Si _aurem,

quod heic fupponitur , linea AB

in fitu quoque _{Fprodu&a per cen¬}

trum C _{tranfeat; ideoque}

cum li¬

nea FH ad _{priorem anguloGT7#}

in-clinata coincidat: certe in _fpha?ra

per arcum ^AF translata _pun&um

B vel G arcum _{GHdefcribit;iicque}

ipfa motu fertur _{vertiginis ( §. 7.).}

Immo, qvum ob parallelifmum

re-&arum FH & _^ABangulus

GFHx-^qualis fit _{angulo FCA ( Prop. 27.}

Llem.1. _{); quantum fpha?ra}

per or-bitam _promovetur

, tantundem in

circulo _{revolutionis circa axeriu}

interea _{pun&um ßvel G emetitur;} & _{confequenter illa, dum}

quatuor re&os in _{orbita complet,}

unåper

quatuor quoque re&os circa axem

gyratur, feu _{integrum vertiginis}

motum abfoivit. _{Q. E. D.}

9

hypothes1s.

§. ίο.

Lund

in

bit

ckaäd-ri, centrum_occupat

_Terra,

motum

_{penodicum coiificit.}

SCHO LfQN.

§. 11, Vera quidem crbita efl ETti~

ptica,/?/ quaLima Tellurem in

EÉipfe-os _foco alterutro (kam _{ca ratiorn}

cir-cumit, ut radius veclor ex centra

jl-lius in centrum _{hujus protenfus femper}

verrat areas temponbus

, qmbus de-fcribuntur ,

proportionales^:

le¬

gem omnibus planetis cummimem ex

objervafionibus lllußris Danorum

A-flronomi tychonis brahe, in in¬

gens

Philojophiis

coelefljs

bigenwfisfimus

plerus, & deinde ab omni

άγεωαε-τξησίαςlabe

_{liheravitGeometrarumprhu}

autem diflantia media Lun<e d TeEure

fit femdiametrorum

_hujus

Éfttmtw

cen-*o _{-m ο}

a centvo _{circuli excentrlci}

, eorun·

«te _{norniiß 31, aäeoqueåecim<ε oΒα¬}

ν£ _{parti rada excentrici vi}

χ _£qpalts\

orbita Lmu ä ctrculari hand adim

-dum _{dijfert. ,}

OBSER VATI O.

§

Lun&

_pertochcus

efi dierum

2jjior.

min,

/<??.

OBSERV ATIO*

§. 13.

iun&

idem

factes teUuri

_jemper

obxertltur,

meridi-ani Lunaris _{planum per centrum} tel-Iuris traniit.

SCH0L10N.

§. 14.

Easdemfere

jugiter

ohfervamus

Bipparchus

<fr finus

gfluum

(Jecun-dam mmenclaturam Ricciolinam ) i»

•$$3 ο i#* t?

meåio di_{fco, wäre Crifiiim prope lim*} bum occidentalem , Grimaldns in

o-rientah , 'lychonk valiis Ludda ad

au-ftralem, ψlato demqiie_prope

_borealem

mmquam nah appareant. Dtco autem

fere: warn _{telefcopii [altem ope , per}

vices macuL· nonnulU in_{partem a tel·}

Iure _{averjam je recipere, aliis tl·}

< lin_{c m}

conjpe&um prodeuntibns ,

de-prehmduntur:

Li-brationem Luna? _^Aßronomi

vo-cam.

SCHOLIO N.

§. 15. Mirari convenit, ex eodem

hoc _{principio motum vertigtms Lünes}

& _{afßrmari & negari. Namque a~}

Iii illum _{refwientes dicunt \ β Lima} circa axem _{fuum volveretur, ean¬}

dern _{jemper fäciem nobis non}

0-flenderet. _{Cujus fententiee patroni}

fu-erunt _{ftimmt Aßronomt, Keplerus}

in

_Lpit.

_Afiron.

"

"ίφ4ϊ·· ο _{ϊ ι}

55 55^·j-ß·ricciolus

_hf%Almag.

9 _pAg- 208

Hevelios /0

_Selenogr.

294»

ut

_{reliquostaceam,}

, motmn

rertigims hmc adßruentes, fic ar-guwentaritur :

wfi

juiim volveretur,eaudem _femper

faci-em mbis qop _{c/Ienderet. Horum}

pri-mus _juit

jagacijjtmtis

Newtgnijs, in

Ρbil, Nat. _{Princip. Math.. Lé III.}

prop. 17. quem jecuti Piri

_Clarißimi

D. Gregorius m _{Aflron. ^}

Geom. hlem. Lib /. _{prop. 30. G.}

whiston PrHed.

_{Aftronom.pag.}

109,G. J. s' Graves ande in _{Phyj Ε«}

lem* Mathem, _{Experim confirm. Tom.}

iL _{Lib IV. cap. iTI, pag}

m. 131.

«/i-ique ; _{quoque jequi ventas}

ipja ]am demonßranda jubet.

THEOREM

§.

16.

Lana

_fitum

revolvttur eodem exa&e _tempo¬

ϊ_{3 ·*$■§ °}

re, _{quo mtegram}

orbitam

ercur-Tit: hoc eil, motus _verriginis

ieudiur-nus Lunae motu» _{ejus penodico feu}

menilruo _squatur.

Demonßratio.

Omne mobile_{,quod orbicam}

cir-cularem _{peragrando idem fernper}

hemifphasriurn illius centro

oilen-dit, eodem _tempore praeeife circa axem _rotatur,qoo periodum _ipfam

peragit (

§.

Afqui Luna in. orbita circulari

movetur ₍ §. _{10.) &} eadem

ejus

facies _{perpetuo terram in centro} locatam _{refpicit( §. 13. ).}

Ergo &c. E. D,

COROLLARIUM.

17. Hinc manifeftum eil

a-xem Lunarem continuum

paralie-liimum fervare _(§.s)·

COROL-*4 o

CORO_LLARlüM.

ΐ8·. Motus _{quoque Lunae}

ver-tjginis

abfolvitür

diebus

noftra-tibus 17 hor. _{7. min. 43. fec. 5.}

( 5· 12' _)'

S_CHOLION.

§. 19.

Ipfum

_{νυχ&ήμέμ»}

Jeudies naturalis htLima medins

_menji

ejusdem Jynödicoy dier. 29. bor, 12.

min. 44* fec. 5. tequatur.

SCiiOLlON.

§, 20. Ter motum hunc Lmitt diurnum _{facili negotio explicari}

_poteß

hbratio Lunte in

_{Longitucffiiém}

ris Lunafk inclinatwne ad _orbitam

,

illa vero ab orbitte _{excentriciiate, jeu}

nuquabili motu periodico cum motu

vert_iginis

_tequabih

junclo ■> anginem

ducit. Sed hac de re

_fufius

Philo-o " _tf Phihfophi£ Ncwtoman* Interpretes,

in _{primts Laudatus Gregorius in} Elem. _{Aßron. Pbyf & Geom. Lik IV.}

prop. 58 , Joannes Kf. ill

Introd, ad Veram Aftronomiam _Jen

Leä. _{Aftronom. /wg. 292.}

SCHOLION.

§.'21.

pro-prmm axem_figura ejus quoque

deter-mwari _{poteß. Si enim Luna omni}

motu circa axem_{privaretur, érejus}

pariicuL· verjus centrum,proutin

Ter-ra,_{gråvitarenl ,ac präterea nunc aut}

olim _fiaidä

_{fupponerentur}

fpbäricam , ob äqualem

undique

par-i///;/; _gravitatem,

_affeäare

mdue-re deberet. _Quum

autem Lima circa

axem _{vohatur, vi}

centrifuga

gravitatem

immi-nuentes _{juxta aquatorem,}

wo-tjgs celerrimus , ajcendere conan-fr#*i &_{fic afcenfu materiä}

_fimdä

« wtfri ώ _{äquatorem augentur,}

_&

_axis

dejcen-ckfcenju

Lima _{figuram jpbeeroidis ut}

_aäquirat,

neceße efi ; qua tamenob motas ver»

tigmis tarditåtem minus eft

_fenjibilts.

_caaffam

_fluidum

ÉP _remottflimis

_elevandum

Lmt£ _fpbttrotdem

_oblongem

, ίγ//«χ

0-λγ/j maximas _{produÜas per centrum}

Terree

_iranßt

Nrvto-nus;_qui& _{itide rationem reddit,<7//#}

-Luna eandem_{faciem teiluri}

obver-tat. Vtd. Princ. Phil _Nat.Math,

hb.HL_{prop. 38· Coroll.} ; F ί Ν I s.