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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 182, page id 1040780814:0200
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282
ASTRONOMLE PHESICA
pore Minimi Crepusculi. Datis vero paralleli Declinatione L
liquitate Peliptica, invenientur (per PrOp. XX.) Rcliptica puncta
bina, e (ex Theoria Solis) tempora Anni, quibus Sol est in datis lo-
cis; hoc est, quando Minimum At Crepusculum. Sic FondiniNTini-
mum Crepusculum cA Sole ab sEquatore declinante versis au-
Arum 65 7, ex F55 30  Vel X occupante, quod hoc aro circa diem
22 Februarii e 27 Septembris anni Fuliani contingit. ITOc à
Blancano in Sphaera annotatum cst, qui ait Crepuscula brevissima
circa dimidiam Libram ac dimidios Pisces contingere. Problema
hoc proposiit ac solrit (per binas tamen analogias) Petrus NoniuS
in Libro de Crepusculis Anno 254. F edito, quem sequuntur Am-
brosuus Phodius e Clavius.
PROPOSTTIOXLII
Ndato positione plano, cui FToroloeium Sciotericum est ebe
dum, Lineam Meridianam, Anculum Styli, es Lineam Substy-
larem determinare.
Planum omne, cui Sciotoricum FTorolorium inscribitur, per cen.
trum Sphaerae trantire supponitur, (quia respectu distantix Solis ejus
distantia a centro insensibilis eAt,) adeoque hujus intersectio cum
Sphara superticie es circulus maximus. Sit tale planUM FRSMCT
per Mundi centrum r transiens, quod ad superticiem productum
circulum efficit IRSMC. Sit ATO habi-
tationis HTorizon, HZ0 Meridianus (in quo
Polus P, e Zenith Z) priorem circulum ad
u interlecans. lix data plani TRSC poll
tione datur ejus Declinatio, per angulum
TTH Cire arcum rH menturata, qua nem
Deplani TRSC recta Llorizontalis ic decli
nat ab e0 linea Meridiana in plano FI0.
rizontali per PrOP. XVI. ducta. Datur eti
am ZR; nempe arcus circuli verticalis ad rr se normalis inter Le.
nith e dictum circulum interceptus, Inclinationis vel Reclinationis
plani dati mentura. In triansulo Sphaerico mz R rectansulo ad R
datur ZR, e angulus R ZM aequalis complemento anguli FPH ad
rectum: (Nam verticalis 2. R in circulum ER se normalistantum de
clinat a verticali primario (per ortum e occasum Aiguinoetialem
traducto) quantum Fr ab Hr; adeoque illius complementum nempe
RZM, aequale est hujus Lr e complemento.) Inrenietur ergo latus
RM, sire (quem hoc menturat) angulus in Scioterici plano R TM.
Sed datur re positione; (eA enim in plano dato perpendiculi succe
dancum, sire recta Florixontali recta FrC normalis;) quare dabitur
guasita Meridiana recta TMr in plano Scioterici, sire communis
sectio plani Neridiani cum plano Scioterici. In eodem triangulo
MZ R inveniuntur etiam latus Z M ec angulus RNZ, usiri modo fu
Tura. Rursus, per Polum Mundi e ducatur arcus circuli maximi es
ad exse normalis: Fr in criansulo esm rectangulo ad s datur an
SuluS
ib. TI.