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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 453, page id 1040780814:0471
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Lib. 1.
accden
ata l
ninatae)
jectoria
excellu
excellum
R +
eceden
im Mu
utatan
primo
crelto
1
sum, I
TYA.
eniets
ite de
auct
sedt
oBens
ect
litGue
laOc
Lib. V.
eE GTEOME PRICE L LEMENTA.
6d
volae, est praecedentis subsesquialterum) erit , nempe: iptius
POrTO, cum vD sit =  , e Y5 = f, exit SD =   f. E8 sit inter v et
D, ut in fig. +m; vel si D st inter V _ S, ut in 2, erit SD = f -
hoc ett, in o cali SD = s e in 2o 5 - : Unde rect.
f2x
oneulum sub AD _ DS cxit =  9 vel q; de proinde hu-
+
∞  = Yc +F X - ~ 2
Ft isitur spatium reaS (nempe in F casu aquale rR a D dempto
triangulo aSD, in 2 aequale YEAD auctO ABD) erit 
24
x3 = 4F2 ~
in +mo cau, et 07 F 8 in 2d; e ideo in omni casu YR AS
aquale v: + 1 25.
245 . AIquE OPOrtet hoc aequari ip(B; ideoque 24 5B
= a + F2 f. a. FF disposita aequatione, ut moris est, erit
x = - T2 f. X + 24fb. Per rulsatam isitur Regulam Car-
dani ralor iptius x sive aD quantitatibus cosnitis expressus exit
VC: 12fB + Y 1415 20 . + 645 - rC: 12 fb = Y 144f 2 b. + 6450. NOtd
rero aD non latebit rD; eAt nempe aequalis quadrato iptius AD
ad quadruplum coenita rs applicato. Data isitur eA (per 3. Dat.)
composita ex DY _ VS, cui recta Sa aqualis est per C Orol. 2. Prop.
XIV; e proinde dabitur e haec magnitudine: Sed e data est DA
datur erso (per T. Dat.) ratio inter S a e AD, hoc est, inter radium
e sinum rectum anguli asD, quem sa cum axe comprehendit. In-
noteseit isitu ansulus iste a5D vel YSA: e prius innocuit sa
lonsitudinc. C. F. F.
Fi converso etiam in data Parabola invenietur area V R AS, qua Fa-
ciat sa rectam aequalem data rectae; hoc est, inrenietur ArCK YR AS
ratio ad quadratum rectae v8, quae laciat da in ratiore data ad Y8
rectam.
SCHOLLOM I.
Suverius exhibuimus methodum Calculi in Astronomicis usita
tam ad determinandam, magnitudinem _ politionem recta 1S. Si
constructio seometrica arrideat masis, illa Facillime obtinebitur, a
quationem Cubicam superius inventam x3 F F2f X L24 fB =0
methodo Crcomctrarum universali construendo
per Parabolam propolitam R re d circulum.
Vocetur propolita Parabola latus rectum
(quod aquale CA 4. f) L; I2f2 =9, ∞ 24fB
=r, ut aequatio proxosita sit in forma Scripto.
ribus ulitata x 3 F q v = r = 0. Capiatur (secun-
dum rulso nota praecepta hujusce constructi
onis) vC = :L in Parabola axe, e GH =
de quidem retio rersus vercicem, quia ett + 9) hoc eAt, in noltra
a qua