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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 222, page id 1040780814:0240
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222
ASTRONOMTA PHZSIOA S
bus punctis H, P, C inveniendum est Tempus iptius Solstitii. Pa
Tet rectaS HF, CF ese intervalla B(
dictantiarum Solis in eodem verti.
cali ab ITorizonte, vel a Vertice;
(hoc est, per supra octenta, mutatio
nes Declinationis.) Nam ecu mi
nime dittert ab arcu circuli centro
B distantia Bc descripei, quia FBC,
ABC ansuli sunt admodum parri.
Et si loco plani cD, cui BC CA nOr-
malis, umibra excipiatur in aliud  + et
quodris planum ex ad cD inclinatum angulum DCF non admo-
dum magno, ex. er. in punctis h, F, 8; rectae hf, ef candem fere na-
bebunt inter se rationem quam EF, C F, quia recta fF, ec, Br sunt
Fere parallela; quippe qua concurrunt non nisi ad B punctum Patis
dilsitum respectu distantiarum fF, eG, BH. Problema isitur de in-
reniendo Solstirio ex datis punctis F, G, H, e Temporis momen.
tis quando sel in eodem verticali positus puncti B umbram ad ista
Projecit, ad sequens Problema pure Geometricum reducitur.
Trium rectarum par allelarum AB, TY, F. 5 in eodem plano jacen-
tium datis mutuis distantiis AY, TF; describere Parabolan
REM, cujus axis CYD est ipsis AB, TY, FS parallelus, illas se-
eantem in punctis K, L∞ M, ita ut ductis ad axem ordinatis
WIIILHES LDS ME interceptae axis portiones FC e em sint rectis
didatis aequales.  LoC 11.
Ita enim AIOE, BIEC ((I DG _F FH aequales FuerInE iPSIS FC, FH Per
supra descriptam obserrationem signatis, e ratio ar ad FF Cadem
cum ratione Temporis inter obserrata puncta H et F, ad Tempus in-
ter obsexrata puncta P _ E) KH, L. F, Ma respectire repraesentent
Tempora inter obserrationes puncto-
rUm H, E _ C, e ipsum SolMicii mo.
mentum; id eAt, ut punctis a, Y _ F
reprasentantibus Temporismomenta
quibus obserrata est Cinomonis umbra
in punctis H, F e c, punctum c re.
praesentet ipsum Solctitii momen
tum. Vocetur linca AT, a FF, B.
FH, C; F C, cu TC, . IInde AC FIVCKH
=a + d, e F. C sre OM =b = a. Parabola latus rectum principale
vocetur r. Frit per Parabola naturam x =V FAr, adcoque VF =
 Similiter est VH = a +2a x + x ec Y C - b = 2b x +
= (FH = VH = VF =) a + 22Xi _ a = (FC = YC -VF-
Rejecdque, opc duarum harum aequationum, ipsar: invenietur
a2 + 2a ∞ B2 = 2 b x
a. Ordlinataque aequatione ut vulso, fiet quae sita X
rad t Ebc; hoc est, spatium temporis interjectum inter notum
momentum
aa d
E
Ouate