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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 51, page id 898203430:0079
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=79
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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 0.90
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# After the first blank line: the recognised lines in reading order, one per line.

VEL LLMIL. ORDNATIONVM CONC. LIB. I.
est FO, in dimidium recti, quod est a OT) ergo A O ad FI Y erIE VE 2 ex 20, sec
noctri de
ouadratum eiusdem AO ad rectangulum NOI, vel ad sibi aequale qua Mak. ACMIN.
dratum OC (ob triangulorum MOC, CFOT Similicudinem) Ouum ita-
que quadratum primae AO ad quadratum secundae OC sIc ve priima AO
id tertiam FII, eric rectangulum sub extremis AO, FII aequale quadr2-
eo medixe, seu minimi rami, vel normalis OC. Ouod erat in Parabola
demonstrandum.
In reliquis vero Aguris duCatI ex A CUPer FanGentem A F normalis
AN, axi, in quo est Origo O, OCCUEreNS in N.
Fc cum ob LanSenteS A L, C M, d ordinatas ex contactibus AO.
37. 38. PrI
GT, SIE VErUNqUE rECtaNGUIOTM ML. L, F L. O aequale B quadrato semiaxis mi Conic.
transuer (I L. B, vel in quinca figura quadrato semiaxis coniusati L P, ipla
reCtanGUlA MLL, FL. O incerle aqualia CFUHE, quarE ML ad LO est vI
FY ad L. I, X in secunda Aigura obloneae FllipsIS dividendo, de pCrmuI-
tando; in terria vero Eyperbolae convertendo, per convertionem rationis,
de iterum convertendo, de permutando; de in quarra Flliplis prolatae, ee
in quinta Crperbola, componendo, de permutando erit MO ad L L VE
OE ad LI; sed in omnibus OI. ad I. I est ve NO ad OI C veraque enim
racio, in singulis figuris, nempe LO ad OH, de L. I ad IO est ea quam
hrabet e transuersum latus ad rectum suae Sectionis, ac ideo permutan.
C ex 22. e
23. de MaX.
do OI. ad L. L est ve NO ad OY) ergO, de MO ad FY eric in omnibus ee Min.
ve NO ad OI. Ouod memento.
Cumsic ergo NO ad F I ve NO ad OI, eric rectanoulum sub extremis
MO, OI aequale rectangulo sub mediis NO, FI, led rectangulum
MOIaequale est quadrato OC (cum OC, Cu media proportionalis inter
NO, OI in trianculo rectangulo M C O, _C.) croo, et quadratum
OC aequatur rectangulo lub N O, FT, at quadeatum perpendicularis
OA super basim FN crianguli rectanguli F A N aequatur rectanoulo sub
NO, OF, ergo quadratum OC ad quadratum O A cst ve illi aequale rC..
ctangulum sub NO in PI ad huic aequale rectangulum sub cadem NO in
OF, hoc est ( ob communem rectangulorum altitudinem NO) ve linea
FI ad F O, vel ve linca TH ad O A parallelas in crianoulo FO A. Cum
isitur quadratum secundae OC ad quadratum tertia O A (E ve prima
TEI ad certiam OA, eric rectangulum lub extremis IH, O A aequale
quadrato mediae. seuminimi dati rami, vel normalis OC super datam.
Sectionem ABC. Ouod L. D.
Vod superius speciatim monuimus, nempe MO ad F LCin singulis
figuris) esse VE NO ad OI, set uu Casseuam Corollarium pro se
quencibus in Cutem Hoattu. sel hummoru ramotuims de
al t
cate Mtte cilone Male ette Mcte didtte
Scholium