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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 223, page id 1040780814:0241
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I
TUI
s
DTaM
FUII.
Jan
Lib. TII.
eE CTEOMETRLOR L LFMENYA.
223
momentum per rreprasentatum, (quando nempe Cinomonis umbra
in F obserrata eA,) ee momentum Soltitii qualicum: Unde dabitur
iplum Solctitii Tempus. O. P. F.
Ouod si quaratur Tempus interjectum inter obserrationem um
brae in n ec ipsum Solttitium, ipsi xe modo inventa addatur AX,
tierque quae sita aC = (a + a =) 6c+2 abc + a
v-
2a d + 3bC. Pari modo crit P C
b2c + 2 ab d = a2 d
2ad +2bc. Si vero is sic obserrationum ordo,
ut obserratio umbrae Onomonis in P sit exacte media inter ejus.
dem obserrationes in _ ec C; hoc cA, RI A T = TF, Cive a =B, aequatio
Paulo simplicior tiet; erit nempe distantia Temporum Solcicii e
2d
obserrata umbrae in P aequalis : d F 25, Solstitii dictantia a Tempore
obserrationis umbrae in H aequalis 3 ac. + ad
25 +243  a momento obserra
C + 3a d
2C + 2a; hoc ell, in schemate, sieut
2FH + 2F C ad GH, (IVC L HF - 2 GH ad GH, (IVC QH F = GH ad ZGH,
ita Cemistis Temporis inter primam obserrationem umbra in H _
ultimam ejusdem in a verlantis ad tempus interjectum inter oblerra-
tionem mediam umbrae in I. ex iplum Solkitii momentum quasitum.
Primus modum hunc Solstitiorum Tempora determinandi exco-
sitarit e publico impertirit ACutiM. Pd. FTalleins in Transact.
Philos. incunte Anno 1695. ec exemplis Solcitiorum Binorum, Der
obserrationes W’altheri de Gassendi, ex hoc detinitorum illustravit;
ubi etiam in praxi adrertenda quadam notat de Cinomonis (Itu et
figura commoda, de Ombrx accurata obserratione aliisque.
PROEOSETIO XTI
LUni Vertentis quantitatem definire.
Cum Annus vertens sive Fropicus sit Temporis spatium quo Anni
tempeltates caedem denuo redeunt; hoc est, quo Sol ab aliguo H
eliprica puncto (puta illo in quo Tropicum continsit) digrettus ad
idem revertitur; patet ejus quantitatem definiri, si Sol bis in eodem
Ecliptica puncto oblerretur, (V. 8. bis in eodem Aquinoctio per
PFOP. X, aut in eodem SolsitiO peF XE,) ee tempus interjectum
diridatur per numerum revolutionum Telluris circa Solem interea
factarum. Si quis sc error in Aequinoctii vel Solcticii momento
detiniendo, ne hic Anni Tropici menturam turbet, conrenit Sol-
litia vel  quinoetia adhibere quam tieri potest maxime inter se
distantia, uc error in plures partes discerpeus (dirisione tacta per
magnum serolucionum interiectarum numerum) imtenlibilior
eradat.
Sed quoniam Solsticiorum Tempora disficulter discerni Veteribus
videbantur, ut ipse Ptolemaeus ait, qui propterea Metonis d Pucte-
monis ipliusque Tristarchi Solsicia pratermisit; quod et Recen
cioribus ulque adeo rerum eAt visum, ut Ricciolus asserverit Piole
maeum