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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 81, page id 898203430:0109
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=109
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.91
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OADTNATIONVM COHIC. LIMITIBVS LIB. I.
O simul adscriptae, _ cum eodem recto latere BF, casque secene ordi
natim duecae IIF, TM, erir rectansuum LIBR ad rectangulum IA MI VE
2 quadeacum BD, ad DC, rel ve quacrarum BF ad C F: Sed permu a 6. huius:
carido rectangulum IIB F aequatur quodrato BF, ergo de rectanculum
IA M aequale est quadrato C F; sed latus CF xquale est b ipsi C K a l- b 43. luius.
cicudini normalis AK sUPCF PaIUM B A, CrOO _E rECTANGUIUI TAM qua
deato CK est aequale, et communi addito C A, rectangulum TAM cum
quadrato C A, vel rnicum quadracum C I duobus simul quadratis RC,
CA, vel vnico AK xquale erit: ac ideo semiordinata C I in delcripta
FEyperbola aequalis ipsi normali AK, _ Sic de Singulis RC. GuarC COHCA
num Eyperbolx LIDF: est Limes propoliae Didinacionis. Duod etac _c.
PROPOSIT1O X4AXVIII.
N TEyperbola. Limes Ordinationis normalium supet
ramos ex vertice in ipsa ductos erectarum, est ad Lo
cum concauum alterius Frperbola sibi simul adscripta.
cuius idem sit supremus terminus transuersi lateris; rer
ctumque datae recto sit aequale, transuersum verd sit ter-
tia proportionalis post summam laterum datae Fyper-
bola,  ejusdem transuersum latus.
Sco Fyperbola AB, cuius axis BC, verrex B, tranluersum latus BD,
L rectum BF ipsi BD perpendiculaticer applicatum; BD vero sic se-
cetur in C ve rectum E B cum crantuerso B D ad ipsum BD AE VE BD
ad D C, ee per verricem C cum crantuerlo D Ci, rectoque locere ip(
B F aequali, delcxibatur
Eyperbola G HIcirca.
cundem axem C, B. Di-
Cohanc esse Zimitem PFO.
Doluum. FIOc CA si ex B
lic ramus quicunque BA,
cui Tinormalis AIL, hanc
semiordinatae C L per A
aequalem esse.
AOuUE ex C ipA B F.
equidittans CL, quae IWI.
ete regulatrici D F OC.
currac in L iplaque F H
producatur ad H vique
ad Hyperbolam CFI.
Tam, quonium EB cum BD ad B D est ve B D ad DC, erie divi-
dendo E B ad BD, vel LC ad C. D ve BC ad eandem CD: quare L. C
BC. sune xequales.