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# Title: [Geometriae Pars Universalis, Inserviens Quantitatum Curvarum transmutationi & mensurae] Geometriæ Pars Vniversalis, Inserviens Quantitatum Curvarum transmutationi & mensuræ (shelfmark Ms IV, 377a)
# Folio 140, page id 1047377675:0156
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T. 40
Per speculi rel leneis POKN exErEMILALCMS EX CCNErOA HaC
Sphera IONKII; icem per punccum D ex eodem centro AhaE
SphEFA FRDSC coius superficieiportio a Coni AIOKN sun
perticie comprehentas (icRFSD Ouoniam solex omni parce
aequolicerrediae, Facile cse deducere ex s detinitiones cle-
mentori omnes radios solares esse ad radios in speculu rel
lentem TOKN incidencess uc inceora superticies spherica ad
eius porrionem IOKVI. Se d ex archime de de Sphera ee cylin-
deo, inceera superticies sphaerica ese ad eius porcionem 10
KN requadracum diameeri ad quadracum chordae semissis
arcus IK; & proinde omnes radii lolares une ad radiosin
speculum vel lentem TOKNincidences, hoc escradios in ciru
culum MPL. Q congresatos, uc quadrarum diamerri ad qua
dracum chordae Cemissis arcus IR. Fodem modoprobatur
omnesradios solares esse ad radios in circulum DRES inci
dences, uc quadratum disceri ad quadrarum chordae sc.
missis arcuS D F. Ccd quonism orcuS IR, DE, unc similess
quadracum diamerri circuli IKHI eandem habene rarione ad
quadracum chordae semissis arcus RI, quam habet quadrarum
diamerri circuli EDC ad quadracum chordae semisis arCUS
FD; d ideo omnes radii solares candem habec racionem ad
radios congresaros in circulo L. PM Q, quam habene iidem
omnes radii solares ad radios congregatos in circulo RESD;
Eunc idicur radii congregaci in circulorPM Caqualesradiis
congresaris in circuloDSER. Deinde ex constructione Rl
est ad L. M UEK A ad D A; ee ob similicudinem criangulorum
XAI DAE; KA es ad D A vcKI adDE; d id COLM, DE, sunc
aequales; de igirur circuli LeM C, DSFR, CuneX qualeS: acque
aquales radiiin aequalibus spaciis cundem producune ette-
ctum: se proinde combuttio in circulo I R ES aqualis ett
combuttiomi in cirento LPMC
quod demandum eras.
Eeet.
1r1.1339t  a