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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 94, page id 1047377675:0110
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=110
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 32 lines, status machine
# Lines: 32 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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lia acCo quadracum recte CP aequale es quadraris re
ctarum C L C,O. hoc est, quadracis rectarum C A, C. Chis
aucem quodraris equale est quadracum recce AO aequales
ereo sune recte C. B, AG; cumque hoc semperereniac in om
nibus punctis curre hyperbolice F. QP, manif: um est exhu-
ius 3 segmencum hyperbblicum FHRS equale eNe suPCrA.
cicirrunei super curua hrperbolica FOT seccae a planoperre
cram FScranseunre, e in angulo semirecro cum balc crunci
inclinance; ee isitur cum quadearum receae X sic duplum su-
perticicierunci, erie X radius circuli equalis superticiei co-
noidishrperbolicae geniex exrocarione curux hyperbolica
FDTcirca axem FS, quod demonstrandum erat.
PROP, SO. PROBLEMA.
Si curva Byperbolicaroretur circaaxem coniucatum; invenire
circulum aequale Cuperficiei ab illa curva hyper-
bolica rotata genitae.
 Ie curra hyperbolica a C, que rocata circa axem suum
d coniugacum FZ. signie superticiem; oporcet huie luper-
ticiei aequalem circulum invenire. Sic curux hyperbolice a
cenerum Z, vercex an asymprocon Z. D: hyperbolam cangac in
verrice arecta ak equalis lemilsi laceris recti ciuldem hyper:
Bolx: lF rectA TTK rectx Za ParaIleII3 _ aequalis, quae produ.
catur indehinice hyperbolam secans in R ee eius alympco.
EOnZ. D in M; _ in illa SUMAEUF reCEA H V, cuius quadracum
aquale lic quadraris reCtArUM HIR, HK: deinde cenerOZ ver
eice a lichyperbola aV A, qua prOdUCAEUE dONCCRECFAM FC
A Parallelam rectae Za incerlecer in A; ec PCBM eNEO By PeF
bolico F A V aZ EAC ae quale quadratum, cuius diamecer X:
dicoZ cNC radium circuli quaelici. Sic hyperbolae invenca
alyM PEOEON ZB rectan HV CccanS in L, e ex quolibechy.
perbolae propolicae puncto Pin verumque axem (li opus Clt)
PTO.