# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/898203430:0066
# Permalink to this reading: https://leibnizlegible.com/page/898203430:0066?run=74
# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 38, page id 898203430:0066
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=66
# Source image: https://digitale-sammlungen.gwlb.de/content/898203430/jpgs/default/00000066.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 58 lines, status machine
# Lines: 58 recognised, mean confidence 0.89
# 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.

VINCENTH VIVLAMT PRO LOCIS,
SCHEC R R) Si lateralis contingens C F produICatI doneC Cum KR Con-
veniae in R, etiam diagonalis DC producta convenic in R, _ TF, C R
secanE lC UTuO in P, erSO OcCUTTUS M 2 reCrarUM D GFL, PF cadic in.
Tex BC, HR verticales tangentes Sectionum OpDOTICEUM.
In FllipC autem prolaca quintae fiourae; laceralis LAnGCNS C: A minor est
b verricali C B, quare F C ad C A maiorem habet rationem quam ea
dem F C ad GB, vel quam E A ad AD, vel quam S D ad D A, vel
quim TD ad D A, ideoque FT, FIC D conveniune simul ad partes cen
eri O: sed TTOD produCta ErANSIE per R, c in quo contingens verticalis
RR convenic cum lacerali FANOCHEC F C; ergo occursuS rectarum HICDR,
E TV cadic intra verricalem HV, ve in M. Ouod primo loco supererat
demostrandem.
PraterCa. Dico in Parabola a secunda Eigura extribica, diagonalem.
DC laterali cangenei F C parallelam esse, in Fyperbola vero a certia A.
Sura expOsica, ipsam C D productam nunquam convenire cum lacerali
L C ad partes verrici B oppolicas.
In Parabola enim, cum iplam concingat recta AF, erit D B aequaliS d
BE, ideoque, ee AC aequalis C F, eltque AD aequalis DC, erSO GD
aequidistat ipsi F. C.
ACin Fyperbola, oBFANGENEeM, AF, est D B maior O B F, ergo e
un nolix AC maiOE GF, sed AD aequalis est D C, ergo diagonalis D C COn
VIaE. de venit cum lacerali C P ad parres verricis, ad contrarias vero, intra A C,
MaL. XMIB. hx semper magis inter se removentur. Ouod secundo ostendere propon
nebamus.
Insuper, si in Cngulis figuris, prima excepta, ex occursibus FI, M dia
conalis DC cum iunctis SF, FF agantuI Ordinatae HL, MN. Dico,
S BiseCeEUT aXIS LCGIeNCUM NIL in P, punccum P in Parabola, aut IIy
perbola, aur Ellipsi oblonsa cadere inter P verticem trianguli circum
dcriori, _ Ordinatam FCIOTIORCM MNI.
PEOduCatE ETL ad T. Eric iam, in crianguIO NMD, ve ND ad DL,
ita M N ad HIL, vel ad aequalem L I, vel vE NF ad FL, sed ND ma
sOr eA DL, ergO _ N F. maior L. L, ac ideo punctum P bisecans NL.
est INTeF NI, e L.
Amplius, dico in Typerbola certiae figurae, punctum P bisecans NL
cadere necesario inter cemrum O datae Hyperbolae, ee ordinatam HL
vercici B propiorem.
Nam si dicatur ordinatam reliquam MIW cadere in centrum O, vel in.
Fra, inter 9, de P; manifeste pateE prOPOsITUM. AC SI: M N cecideric in
TeF K, X O, ordinata HL lecer lacerales tangentes AB, C F in O, Z, e
ordinata MIN laceralem productam CP R in Y.
lam, cum tam criangula ad verticem MNF, IL F, quam triangula
YNM, Z LP Sinc interse Similia, CFIE EOTA M N ad COTaM L I, vel ad
TIL, hoc eA MD ad DFI, in triangulO MDNT, ve ablaca YN ad abla-
tam LZ, vel ad LO, ergo ec ve reliqua MX ad reliquam ITO: R igitur
CAMD ad DHT VE MX ad EO. iuncta DO secanS C B in V, Si produn
camr, incidet in Y, de vicerius producta secabit R K in X.
2 26. Huiu.
b. 87. lib. 2
de max. d
MI.
C Corolt.
PrOP. 16
luiuso
d 25. primi
COMC.
e CoroII.
DrOP. 83. PFI