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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 4, page id 1047377675:0020
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=20
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
# Lines: 35 recognised, mean confidence 0.90
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

CUrVARSTV ATCuISK2, Y S. sescomprehentum. Deinde
Aac uc 93 ad5] ita Z alcicudo cylindrici ad 3 N; idem RerI
supponimus in omnibus aliis rectis spatiiRV S2 recte 28 per
pendicularibus, uc compleatur spnrium PHI SE comprehen
Cum a curra PII _ rectis HS, P 23 28: hoc est inrelligo duo
mixcilinea esse delcripea quorum primihaec es proprietos,
ue ex eius currae puncto quocunque Sin rectam 26 demilla
perpendicularis 53 sic aequalis perpendiculari ad curvam 79
CD in puncto cransitus g nempe 96. secundi vero haec HE
Propriecas, ve ex eius curree puncto quocunque Nin rectam
26 demissa perpedicularis NZ sc ad alcicudinem cxlindrici
X. re eius pars incercepca in primo mixtilineos; ad eius
partem incercepeam a curra daca 93. dico mixcilincum se-
cundum PFISE esse aequale superficiei cylindricirecti, cuius
Basis CA curra daca7oCD, e alticudo recta X. Si mixcili-
neum PH SE non est aequale superhiciei cylindrici praedictis
inter illas erie aliqua differentias quae sic a planum: applice-
cur a planum ad rectam X, sicque lacicudo inde oriens B. du.
CaCuE ex punCtO7 recta7 A curram 7 D eangens in puato7:
e Cx puncto D ducatur recta D_ curram cansens in pun-
eto D. Acque recteD parallella7 v, e ex punctis 7. D, in
rectam 26 demitrantur perpendiculare5 7 23 SD; dividatur-
que recta 2 din EOT ParTES ae QualeSS UEAb CXETCMIEATE CA-
rum primae crecta perpendiculari 3 A, excessus tangentis
abicissae A supra parallellam ablcisam 7 r sic minor recta
Bhoc enim lemper heri posse manifectum CA, s FanSenS
Anon scperpendicularis recte 2s, nec curra daca sinuota.
a dinitionum punctis 2, 3, 4, 8 exciceneur perpendiculares
2P, 3N, 4L3 SII, curram datam secantes in punctis 7, 97
C. D; Curram prima invencam secontes in punctis R, S, T, V.
e secundam in punctis P, H. LHI; deinde curram daEam CAN=
Sences in punctis 7. 9, C, D ducantur rectae 7A, 9B, C F, D3
aproximis perpendicularibuscerminoca, (ncque recta 783
90, CF, D5, YV, HIK, L. C, HII, LM, NO ipsis parcibus aequali.
b