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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 33, page id 1047377675:0049
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=49
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
# Lines: 50 recognised, mean confidence 0.78
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

qu
dit
2iOL
tiIi
BM
21d
UA
di
A.
UI
CC
IO
nO
Is
ute
UB
AA,
N
ouloADFTE, Sed ex pexcedente ongulus involutionis re
Ctanouli AC C F maior est angulo inrolurionis ADTIF, de
proinde angulus involurionis rectilinei ACCTIMI inuoluri
maior est angulo involurionis rectanguli ADMI: eodem
prortus modo (A ducantur rectae RB. VZ, Parallele rectis
AB, TMI, _ recta R a, V X, parallella axi AI, ut compleatur
rectilineum AaR BCTXVZ MI) demonstrabitur eius anou-
lus involutionis esse maior angulo inroluriouis rectilinei
ACCFIMI, e proinde muleo maiorerie angulo involutionis
rectanguli ADMInempe SNX, supponimus enim lectorem
SHIX ese rectangulum ADMI inuolurum: deniq; eodem lem.
permodo demonstratur, quod, quominus differe rectilincu
circum Peripeum a figura ABMB, co semper maior AC exceltus
anguliinrolurionis rectilinei supra angulum SNX, ee ideo
muleo excedit angulus inrolutionis ipsius Agura PNX angu-
lum sNX, _ proinde Agurae evolurae axis AI seu arcuS d_
mulcominor est arcu OZ, quod demonstrare oporruit.
PROP. 14. PROBLEMA.
Fic data Reura involura, ejus dem evoluta auem invenire.
Ie figura inrolura I. BK, cuius erolueae oporrec invenire
D AXCM. C CHETOL HE CirCULI AECUS ME; lEque AcurAOP78
concenta: ceris parallelis OP, 87, receaque OB illas norma
licer seconce _ linea Py calis nacurae, vc (in involura sumpra
qualiber recea L. C produera in H, icem in AguraOP 78 du
CrareccaSV recex O8 perpendiculari ex cam secance in ra-
EIOnCMH ad NE) 87 scadSV uE LK ad L. C. dico receansulI
circum scripeum OR 78 eNC ad AGUTaM OPZB UE AECUSMK ad
AXCI AIDUTA L BIE cuolVEX: A nOn SC iEA, SIEVE OR 78 ad O P
78 IcaMK ada, quae disferat ab axe tigura L BR cuoluex qud
citace s: deinde c cenero L. circum lcribancur sigura involu.
ex L. BC Similes arcuS circulareS AC, FC, HIK, e eidem in-
Tcri-