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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 75, page id 898203430:0103
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=103
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.90
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ORDINALIOEIVM COMC. JIMITIBVS LIB. L.
F P potest 2 quadrata semiaxium COniuBAIOTI P. A, A M) ab his igitur
dempto communi rectangulo P AO remanei rectangulum N P O, live  5. buius
RBL aequale rectangulo AF C, SIIC reCTAHOHIO F RFL, hoc Cs quadra-
10 RFT: Sed recta linea C7F FL est D Limes Ordinationis aleicu AIMUI NOT-
malium incer Sectiones AB, CD, de axem conigatum F R ( quoniam b 35. huius
AC est semirectum ipsarum, _e F est CEHIrum) quare si normaliIS a pUn
eto B super Sectionem A B ducta feriE B V, ipsiuS altitudO R V TUX Or-
dinaca RHI aequalis exit; e quadratUI erGO FTR, live rectangulum KBL. c ibidem:
ipli nuper aequale octentum, aequale erit quadraco R V, quibuS COIMU-
ni addico quadrato BR, CtUNE reCtanGUIUIM K BL, ee quadrarum B R.
Tiuc rnicum quadratum R R aequale quadracis Cunul BR, R V, siuc vni
co BV: quare normalis BV lux semiordinatae R K aequalis cst.
Sit tandem quaecunque alia normalis Y X, de per Y Sc ordinara Z6
Fyperbolam AH, C L seCanS in Z G aXEM BR in 3, _ Limitem G F I d 2. huius.
alticudinum normalium in 4 erit ergo rectangulum R BL, ad2. Y6vd
quadracum RE ad F 3, vel ve quadratum RHL, ad 34, led permucan-
do rectangulum K BL aequale est quadrato RFI ve supra demonsteacum
tuic, ergo de rectangulum Z. X6 quadeato 3 4 aequale eric, Peu quadra-
to e 3 X alticudinis normalis X Y, Si his itaque addatur commune qua-
dratum X3, hec rectangulum Z. Y 6 cum quadrato Y 3, sive rnicum
quadracum 2 3 aequale quadraris simul Y 3, 3 X, sive vnico quadeato
YZ. ideoque normalis YX aequalis sux Semiordinata 32, e SiC de sin-
culis: ac similicer idem de alia Fyperbola CsL alteri AZ. IE oppOTU2 _C.
Ouare convexa harum oppoliarun lune Limites Ordinationis propoti.
18, OUod e.
c35. huius 
rum superius octensum M quadratum F. P aequale quadrato F. M,
de rectangulum NPD quale quadraio AF; eric quadratuIm F P,
cum rectansie NIPO. sie rnicum quadra um E N, vel R R
aequale quadruris simuL FM, MA, Peu quadrato M A, cum duplo qua-
draei F A.
Finc obuia Ae alia constructio ad quaesitorum Limitum delerixtionem.
Nam si per B C in quo lemiordinara per focun P convenic cum HTyper-
Bola AB) OrdineTr R BR ad aXem COnIUGATII F R, SUIATUEGUC RR
Porens quadratum semiaxis coniugari A M cum duplo quadrari lemiaxis
EPaNSHerEI E A, _E CIM CONErO F per verticem A, dC peT BUNCTUM R
describatur Hyperbola A K, ipla erie Limes quaelituS, de démonstratio
paulo diversa à luperiori. R R vero Facile venabitur lumendo nempe.
RV aequali ipsi RFI, vel ips AF, iungendoque B V. Nam B V Gua
est norinalis ex B super Fyper bolamm AB, ipsI R K aequalis est. RK igi-
cur porect quadracum distariciae incer cenerum, et focum una cum qua
deaco semioxis cranluersi datae Hyperbolae.