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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 43, page id 898203430:0235
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=235
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 recognised, mean confidence 0.91
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ARDINATARVM POTENTINM LNT. LB. IL
i Il data AB, GHE PFIO COnCIPTaC ACCCa S C, SC C CACCMaA
ae meci Lacioneim, ita ve B A ad AL. Ic ve AL ad CB. Coiiltat
rectangulum AB C quadraro C A aequale esse: quare s legmentum maius
AC vecunque secetur in I, rectangulum sub tota A B in legmentum B. L
maius minore B C, maius exit reccangulo A B C, ideoque maius qua-
drato A C, _ eo maius quadrato reliqui Logmemi A L. Dico itaque (8
producta BA ad P ita ve sic AE aequalis dimicio BA, _ centro P cum in-
ceruallo radii F C delcribatur Lemicirculus, C F FI, - CuIUS peripherix Oc
CUTrAE In F RECtA AF ex A super diamerrum CH perpendicularicer du-
cta, alque ex P ordinetur II. vsque ad peripheriam; hanc posse disserenciam
inter rectangulum ABL lub daca, de parte maiore minoris sesmenri BC,
_ quidratum AI reliquae ex tOca.
Suver AB tac alcer semicirculus BM A Ordinatam IL. secanS in M, ee
iunsantur BM, AL, L. F, acque ad I. sC Circulum continsens L. N pec
ducrae diametro occurens in Il.
TaIr guoMam A B secta est in C secundiim extremain, de media ea
rionem, F:C vero, ex constructione, constat ex maiori segmento AC, _
ex AF dimidio torius datx AB, ipsa F C porerir quincuplum quadrari a PrOP. L
ex dimidio eiuldem AB, nempe quincuxlum quadeati AF., sed F F ip(I lib. 13. F. 1.
EC aequalis est, viraque enim est eiusdem Circuli radius, ergo quadra
Ium FF, Circ duo simul quadrata F A, AF: aequaneur quincuplo quadrati
AE: quare quadeatum F. A quadruplum est quadrati A F, hoc est linea
F A dupla linex AF, cuius posita est quoque dupla BA, erGO AF, AB
sunc aequales. Ouoniam vero F. N Circulum contingit, erit angulus L F 1I
rectus, aeque est F A perpendiculario super F N balim trianguli rectaneu.
li EFN, ergo criansula F AF, F A N inter se sune similia, adeogue ve
B A ad AF, ita F A ad AN, sed es E A dimidiu AF, ve supra osten
dimus, ergo et FFY dimidium est AN, sed AB ip(I AF est aequalis, ve
nuper demonstravimus, erso AN axis semicrianguli Circulo CFH circum
Teripri sectus est bitariam in B.
OuLIGUE AF, AP. sine eami in Circulo ex origine interna inEeF Cen-
trum, ee verticem, Se AN axis praedicti crianguli sectus sic bitariam in B,
CTIE QUadEaLUM AF ad AL ve b linea BA ad BI, vel ob semicirculum B e1. lib. I.
BM A, de normalem LM super diamCErUM BA, ve quadratum B A ad qua- huius.
dracum BM, sed permutando est quacracum A F aequale quadrato BA
cum