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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 43, page id 898203430:0071
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=71
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 47 lines, status machine
# Lines: 47 recognised, mean confidence 0.89
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# After the first blank line: the recognised lines in reading order, one per line.

VEL. LLMLLL. DHWMLMAL LABTAVM COMTO. LID.L.
BE ad DO, vel ve praedictum quadratum BC ad quadeatum O Y C in
similibus criangulis ad verticem C, D B, IDO) eric rectangulum X B Y
aequale quadrato OI, quibus addito, vel dempro communi rectangulo
FIB erie recrangulum XIY aequale quadrato O B, vel quadrato O F.
Trilgi denuo aequalibus addiris, nempe rectangulo V Y Z d quadrato F O,
qua superius aequalia demonstrauimus) erune duo simul XIY, de V XE.
nempe rnicum rectangulum V IZ aequale duobus simul quadratis OF.
E. O. Sive rnico quadrato rami P. P. Simili modo incer singUla FAIIOTI
guadraca, de hiuiulmodi rectangula aequalicas oltendetur; Sed ratio re
CranguIOrm V IZ, SD T componitur ex ratione rectae V I ad S D, vel IH
ad HID, vel OL. ad L D, _e ex ratione IZ, ad DT, vel TM, ad MD.
vel OH, ad ND, acque ex his rationibus OL ad LD, a ON ad NYD
componitur quoque ratio rectangulorum NO L. ad NDL, ergo rectan
Gulum VIZ, vel sibi aequale quadratum rami P F ad rectansulum SD T.
vel ad sibi aequale quacratum SD, vel ad quadracum rami tangentis
F A es ve rectangulum NOL, ad NDL.
Iiem eadem ratione demonstrabitur rectangulum SDY ad 9CTP esse
ve rectangulum NDL ad NBL, sed SDT aequatur quadrato SD, sivc
quadrato rami P A, ee rectangulum  C P aequatur quadrato rami L. B,
erso quadrocum rami F. A ad quadratum rami E B est vEND L. ad NBL.
In Elliph eandem oblonsa, vel prolara pari modo octenditur rectan-
Gulum 2R 4 2dSDT CNC VE NRL ad ND L, Led 2 34 XGUatE qua-
deato rami F.K (ve primo loco superius monuimus) de S D T quadrato
SD, vel E A, ergo quadratum rami F K ad quadratum rami F A eA ve
rectansulum NVH L. adNDL. Ouod tandem exac in lingulis demostrandum.
 seuu quadrata legmentorum axis Coni-lectionis a verrice
trianguli circumleripei sumprorum aequalia esse rectangulis, singul 
lingulis Tub ordinatarum partibus inaequalissinis a lateribus crianguli,
cum circumseripci, cum circumaucti, comprehensis. Octensum est enim
primo in luperiori rectangulum V Y Z aequale esse quadrato segmenti
axis F O, ee rectangulum S AF quadrato P.D, ec.
MI
V
dd
NY I X
L mis consequentium Fheorematum; vtilia admodum in Geometricis.
tanquam Corollaria, elici poterant; ex praesenti videlicet, rectangulum
XRY aequale quadrato OT. Rectanculum XIX aequale quadrato O _, ac re-
Etanzulum VIZ aequale quadrato F. F; hisque similia, es qualia in primo,
ex secundo libro edirae Diminat: in quintum apolloni, pluribus in locis, de
potestatibus linearum obiter explicanimus in ipsis problematum, et Theoren
matum demonstrationibus; verumtamem cum non omnes ex huiusmodi pro-
prietatibus ea respiciant, quae huc pertractanda suscepimus, illas tantiom
indicandas elesimus, qua ad institurum faciant.
Fia quoque ex hoc, veluri ex aliquibus praecedenium, atque ex pluri-
PRO.