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# Title: Concordia Scientiae Cum Fide, E difficillimis Philosophiae Et Theologiae Scholasticae Quaestionibus Concinnata ... (shelfmarks Leibn. Marg. 183, Stück 1; Leibn. Marg. 183)
# Folio 307, page id 1665034815:0315
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D E A TY + L1 5 I.
parit, id omne naturae leges adoprant. Arcana lubinde vicia rebus prin
aspectu probaris alre insidene, quae vix lonsa d  Krucacione
produneur. Agenunc, tingamus circulum
Ad GEOMCTTIA NORMIAM eXACTUI, aeque ad
sonum B cerminum radii A B, rectam BC
ad perpendiculum radio insistentem, haec
peripheriam canper cantummodo, non seca
bic. FHoenim, E Fieri porest sectio in D.
Ouoniam aucem erianguli A B D lacera
AB, AD, urporeradii, suneaequalia, an
guli quoque oppolici aequales erune: est au-
cem ex constructione angulus AB D rectuS
igicur e AD B rectus esset, id quam ab.
Eurdum Be Geometriae cirones non ipno-
rane, seu quod binos in criansilo reperiane angulos duobus rectis aequales
Eire quod rectas A B, A D parallelaserincone, camersi in eodem Signo con-
GurranE. Rectaisirur perpendicularis ad exrremum radii tangit non secat
circuli ambirum. Vicissim autem ( B C. ponatur circulum rangere, etiam
radio ad perpendiculum insistere concedendum. Nam si A B non FueriE
perpendicularis ad BC, esto A C quae ulera conractum incidac, e peri-
pheriam secet in F. Ouoniam A C est majOFPArEO A F, erie eriam major
AB (HaT A F. A B Cune radii aequales; qua tamen aliunde proBAEUE
minor, quod minoriansulo Cubcendacur, nam cum angulus AC B CN COn-
structione (crectus, alter AB C recto minorefficieur. CInde apparer rectam
in uno solo puncto circulum tangere, nam si Angerecur rangere in duobus
dissieis B, D (conciona Geomerrarum nemo poluie, neque Philolophorum
quilquam ne lupea vidimus ponere porest) Forene ambo radii AB, AD,
ad eandem rectam BD perdendiculares, ideoque binianguli BD, ADB
duobus rectis aequales. Fademque opera planum à sphaera in unico puncto
cansi constabie. Nam ( B, D, binae sphaericae Tuperticiei punCta ponaneur,
in quibus contractus fingaeur exiltere, per ca heri porest sectio quae in exri-
malphaera circulum maximum, in plano subjecto rectam exprimac, quae cir-
culoBD, e Tangenti B C respondenne, ue in Elementis sphaericis Theo-
doli de Cieomerria nostra cernitur, arque idem absurdum, eodemque omni-
nomodo deducieur.
5. 30. Ouamris eriam absque Geomerrix nociria in prompeu sicincelli-
vere extensum in currum quacunq; curricate, extenso in rectum exrensione
nulla congruere; utrumque enim, qua sibi murua commentione respondent,
vel simul currum, vel amul rectum existeret; icaque vel in puncto, hoc est
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