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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 240, page id 1040780814:0258
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2.4.0
ALSLRONOMTA PAZSTOA
perimeter; invenienda est F. Iip Seos istius diaeter quaedam FP, est
que conjusata XY, magnitudine e positione. Ducta incelligantur
recta data puncta conjungentes, (ut in schemato,) quarum dua qua
dam aut parallela sunt, aur dua nulla. Hloc autem Facile perlpi
citur; cum enim dentur puncta N, MI, L, R, E, danEUE FCCLA BIMLIES
ea omnitariam conjunsentes, e anguli inter rectas iltas compre
henti. Si ergo deprehendatur angulos duos alternatim positos (ex.
EY. RMET, MMN) elso aequales, concludetur reCtaS dUAS MK, NII, IN
quibus praedicti ansuli alternatim tunt potiti, esse inter se parallelas.
Cas. I. Ponatur primo duas qua(dam MK, NE esse paraIlelaS. Bi-
secentur la in B et A, ex juncta B a producatur, donec FIipsi OC.
currat in P e P; erit haec (ex Flementis Conicis) Pllipleos diame
TEF, _ quidem (per 26. Dat.) positione data:
quippe per data puncta B ec a transiens. Du
Catur per L ipHI E F Parallela L X, F IipA in X,
recta MK in D, Q NE in C OCCUETONS. FF jun
Eta ZK, L MI OCCUFTANE FCCIX HN (RI OpUS CA
producta) in punctis Pe C. PeF PFOD. RVIT.
TIB. HIT. Flem. ConiC. Apollonii CR rECTanSU.
lum XDL ad rectansulum NDK ut ZF9 ad
ZYg. LLem ZCL. NCH:: ZFg, ZY9. FF isitur
XDL. NDR:: XOL. NCF. Scd (ut intra ostendetur) CA X DF.
NDR:: XCL. GCD. EE igItUT (PEF PrOP. IX. FleM. V.) CCL N CH rect
ansulum aequale rectansulo ccr. Atqui rectangulum N CE datur,
quoniam ejus latOTA NC, CH dantuT; tota enim N E initio datur tam
magnicudine quam positione, item recta L C positione, (per 28. Dat:)
quare (per 25. Dat.) dabitur e c punctum: item recta EC, quippe
cujus termini a ec c dantur; datur ergo (per 57. Dat.) ee magni-
tudine: Sed ee positione; ergo ipsum e punctum datum eAt. Datur
etiam _E K punctum; ergo e puncta illa COnjunGOnS rCCTA RP POF
tione datur, de proinde (per 25. Dat.) punctum x in FIlipsi (ubi
Politione data L.C, RP COnCUEruNE) etiam datum cA. Jungantur
reCta NX, L H dIaEEEO PF (R OpuS CA produetX) occurrentes in
R ec 5: Critque (per supra citatam PrOP. XVIT. LiB. TIT. Flem:
Conic.) TUm NCH ad XOL, CUM N A E ad E A F, SICUL Z Z9 ad ZFG:
unde NCF. XCL :: NAF. EAF. EF per inferius demonstratum est
NOF, ZCE: : N AFF. R AS; Quare (PeF IX. FI V.) e aS rectangulum
reCtanSMIIO E AF aequale clE. Sed E AS datur, (cum tria punCta A, R
_e S dentur, a quidem ut supra ostensum, R e S Per 25. Datorum;
nempe datae positione rectae FF cum potitione datis rectis XN, HL
COnCUEFUS:) rectangulum isituE E A F datum crit. Simili ratione
invenietur EBF rectansulum: _ dantur puncta A e B; ergo e ipla
F F magnitudine, ut deinceps ostendemuo: Sed prius inventa crat
ejus positio; quare diameter Pr positione d magnitudine data
CIC. POrTO, TFq CA ad E FGUE NCF ad XCL, UE supra ostentum est;
hoc CA, (Per T. Dat.) in ratione data, ob data NCF, X CF rectangula;
quare e prioris subduplicata ratio, nempe ratio FY ad PF (Per 24.
Dat.)
ID. IIL
dlic
DuIN
e