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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
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Lib. III
2.4. 2
ASTRONOMLA PAZSTCAF
RurfUS, Propter posteriorem aequalicatem est EB. BD:: AB. BF, e
componendo ED. BD:: F A. BF. Onde (per
Prop. XI. FL. V.) AC, CF:: F. D. BD: _ idcirco
rectanoulum contentum (UD AC E BD X.
quale cst rectangulo (BD CF, F D. AEgui rectansutum (UB A C E BD da
tur, (urraque enim recta data CM;) erso datum cA etiam rectangutum
(ub CF, P D. FF quia datum hocce rectansulum applicatur ad datam
rectam cD (nempe ex datis partibus C a _ AD Constantem) defi
ciens fgura quadrata, dabitur (per 58. Dat.) CF; e consequenter
AF (Per 4. Dat.) FF Proxter datum ab initio E A F rectanoutum
dabitur etiam AF recta; hoc eAt, ipla P e F puncta data crunt.
EROPOSTTIO XKKII LEMMA
Levenire umbilicos es vertices Fllipseos, quae per data quinque
punctatranseat, e Fillipsin proinde per data quinque puncta
transeuntem describere
Pappus in T ib. VIII. Collect. Math. hoc Probl. _ Prac. in uIuS
Architectonicos proponit e construit; ut nempe portione superticie
recti Cplindri daca, cujus nulla pars in circumterentiis batium in-
ceora servatur, inveniatur Cxtindri crassitudo. HTaec AAronomi
deinceps in utuS TLIOS CONVeRteTUNE. PeT PTRC. Lem. inveniantur
dua quaris diametri conjusata Fllipseos, qua per data quinque
puncta transeat, sintquehae AB, 0D sc mutuo bilecantes in CenLTOF.
ProduCatUE BA in E, Ut (E F. A H rectansulum aqualo quadrato Cx
DE; Unde (per 58. Dat.) datur FE. RK hujus medio punCtO K
erecta normalis XI. concurrat cum M AC recta per a ad Dc paral
lela, in L. puncto, quod proinde datur ob rectas ia, KP. positione da-
t45. Centro Y. Per F. Vel H ducatur circulus rectam ut AC in M _C
intersccans, cujus proinde diameter MC da
tur tam politione, (quia per a punctum da-
tum datae positione rectae cD parallela CAt,)
quam magnitudine, (cum st dupla rectae data
Duncta E. X L. conjunsentis.) Juncta recta AF,
MF etiam dantur, tam positione quam magni-
tudine. Ilarum autem positio eadem est cum
Dolitione axium quasitorum: ITam quoniam
rectansulum E AET (peT ZZXV. Flem. TIL.) ~.
quale est rectansulo nac, e per constructio.
nem E A E aquale quadrato a DR; CxIE F. D 9
aequale M A G, SIVO (peT PrOP. XVIT. F lem. VT.) F. D media provOrtio.
nalis inteF M A _E AC; ac proinde (PeF PrOP. LXXXVI. L ib. HII. GreB.
a S Vincentio) Fllipscos super coniugatas diametros AB, cD de
Ecripta axes sunE in EC, PM rectis. Arium autem magnitudo sIC
expedito determinatur. Per A ad FC, FM demittantur normales
ae AN, qua proinde dantur. Sumatur in EC recta FO media
proportionalis inter FC, FO; itCM in EM, F R media intCT LM, F N:
erunt rectae LD, P P (per 24. Dat. data) F. llipseoo semi axes per Prop.
RXXVTI.
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