# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1047377675:0112
# Permalink to this reading: https://leibnizlegible.com/page/1047377675:0112?run=74
# Title: [Geometriae Pars Universalis, Inserviens Quantitatum Curvarum transmutationi & mensurae] Geometriæ Pars Vniversalis, Inserviens Quantitatum Curvarum transmutationi & mensuræ (shelfmark Ms IV, 377a)
# Folio 96, page id 1047377675:0112
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=112
# Source image: https://digitale-sammlungen.gwlb.de/content/1047377675/jpgs/default/00000112.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 33 lines, status machine
# Lines: 33 recognised, mean confidence 0.87
# 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.

rAEIORE LALILCCLISLLL, CAM FK; eric eriam quadracum re a
IP aequale quadratis rectarum IN, IO; _ idem quadracum L
averinque addendo, erunt quadeaca rectarum lP; L a (hoc
est quadracum rectxe Y() aequalia quadraris recearum IO, l
H. Za hoc est quadraris receorum IO, IT Ccu TCrIT, hocelt
QuadraEOreCTA TC; (uNE ergO XqUalES RCCEX OI, FC; Cum
que hoc lemper cueniat in omnibus puncris curux hyperbo.
licxe a FC, manifectum est ex huius3 segmencum hyperbo.
licum F. d aZ. ae quale esse superticieierunci super curuahyper
bolica a TC seceae a plano per rectam PL cranleunce et in an-
oulo semirecto cum bale crunci inclinante; ec igitur, cum
quadracum rectae Z sc duplum superticiei erunci, cric X ra-
huius, dius circuliaequalis superticiei genice a rocacione curuehy
perbone naxem coniugacum L. L, quod demon
Arundum erat.
PROSSST. PROBLEMA.
inuenire rectam aequalem curuae Parabelicae.
em erota  lecurua parabolica CH, verricem habens C _ aXCm C
O, cuioporcec rectam invenire equalem. ProducaEVE
axis CO in A, veCA Aac equalis Pemissi lareris recti, (IEque
CK recta parabolam tangens in verrice e NR axi parallella
illi OcCurrenS in R: deinde sIC recta C. D angulum recrUM A
CKbitariam dividens, Astque hyperbola AC verricem ha
BenS A, CenErUMI G _ A(YMIBEOEON C D; PrOdUICAEUERCCFAN
R donechrperbolam sccec in puncro C lIcque A F rCCLE
X ParaLellai AaE Eandem VE recraBDUIUM AFKC ad leOMCN
cum hyperbolicum ACKC, ita recta C Kad rectam X; dico
rectam X Equalem else curue parabolice C: N. FX quolibet
curue parabolicE PunCEO M demitrantur in recFAS G O, CK,
perpendiculares ML, MHI, Ecque recra OTcuruam paraboli
sam normalirer (ECanS In PUNSTOM, _ reCFIS GO, C R306;
CUTTEM S
 a