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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 192, page id 1040780814:0210
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19.
AS FRONOMLA PHFSICL
Fclipticae occurrit, ex arcus Z F, portio nimirum verticalis circuliinter
Zenith e Fclipticam interceptus; e angulus Z. L F. inter dictum ver.
ticalem e Felipticam comprehentus. Similiterque in obserratione
Sccunda Phanomeni in D innotelcent punctum Reliprica C, arcus
XC, ec angulus X CL. In triansulo isitur BoL, ex datis ansulIs BCL,
BLC _ latere interjecto cr. (distantid nempe notorum in P.Cliptica
Dunctorum) innorolcent latera BE, BC, qua ab arcubus prius inven.
tis ZL, XC ablata relinquunt ZB, XB. Atque hi rurtus ablati a ZB,
Xb, Coenitis distantiis apparentibus à vertico, relinguunt BB BB
Phaenomeni Parallaxes momentis obserrationum congruentes.
PROPOSITIO LVTTT LEMMA.
Int duo triangula rectilinea ABC, DEE Babentia angulos ABC,
DFF datos; sint que datae rationes AB adt DF, AC ad DF, (G BC
ad EF: oportet ex dato latere aB utrumque triangulum invenire.
Fiat ansulus aB C aequalis D P F, Cumaturque BC talis, ut ratio BA
ad BC aqualis sE rationi composx ex rationibus datis Ba ad FD
_ FF ad BC, quod Aet capiendo Bc aequalem quartae provortio.
nali ipsIS FF, BC _ FD. Deinde, in BC positione data eligatur
punctum c tale, ut junctarum ac, cc ratio a qualis sIE compotita ex
daris rationibus Ac ad DF Cc FF ad BC, quod Hiet ut prius. Deinde,
TIt BC ad B H in ratione BC ad F F, Atque AI Parallela ac: Dicotri
angula ABC, BHF esse quaesita.
Manifestum cM ex constructio.
ne, rationem BC ad BI esse aqua-
lem rationi Bc ad FF; item anou.
IOS ABC, HBT ORe aequales datis.
Porro, ratio aB ad BC (per constru
ctionem) componitur ex rationibus
AB ad F. D e F. F ad BC: Sed ratio
AB ad BC componitur ex ratione
AB ad BH _ ratione BH ad BC, ICu
F. F ad BC; _ ideo aB eandem habet rationem ad B er quam ad FD.
RursUS, ratio Ac ad cc (per constructionem) componitur ex ratione
AC ad DF _ ratione R F ad BO, SCu AT ad cC: Sed ratio Ac ad cG
componitur etiam ex ratione ac ad HT _ AT ad CC; e proinde AC
eandem habet rationem ad HF quam ad D F. Triansula isitur ABC,
BHT requisitas habent conditiones.
PROPOSTTTO LIZ. LFMMA.
Datis ratione sinuum arcuum interrorum ad datum circulum
. pertinentium AB, CD, ratione sinuum arcuum ablatorum AF,
eF  ipsis arcubus relictis E.B, FD; arcus interros e ablatos AB,
CD, AF, CF invenire.
Sumpei concipiantur, ex circulis dato aequalibus, arCUS CL, L. H, LMI,
ux respectire duxli ipIOTUM A E, F. B, CF, FD: unde _E GLH, TMK
iptorum aB, eD erunt respectire dupli. Compleantur criansula
recti.
Lib. II.
d