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# Title: Où il répond à plusieurs difficultez qui luy ont esté proposées sur la Dioptrique, la Geometrie, & sur plusieurs autres sujets (shelfmark Leibn. Marg. 43:3)
# Folio 259, page id 82327652X:0287
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=82327652X&page=287
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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 0.88
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

DF NIx DESCARTFS.
25C
Sicratio mediorum, sive rario resstentix medii densioris,
adrelstentiam medii rarioris, re recta data D F. ad dacam
exerinsecus M, qua quidem minor cric recta DF, cum resi-
Rencia medii rarioris sic minor relistentia medii densioris,
exaxiomare plus quam nacurali; Mensurandi isieur veniune
mocus qui Rune per rectas C D _D I, beneficio rectarum
M_D F; Iloc estmocus qui fic per duasrectas reprasenta-
cur comparacive per Cummam duorum rectangulorum,
quorum rnum sic lub CD _ rectaM, _ alrerum Lub D I e
recta D F.
Eo icaque deducitur quaestio, ve ica lecerur Diamerer A
B in puncto FI, ve ducta ab eo perpendiculari III, e junctâ
D T. summa duorum rectanoulorum (ub C D _EML, _ CUD
D I_ D F concincac minimum sparium,
Duodre secundum nostram Merhodum, quae jam apud
Creometras invaluit, e ab Ilerigono in curtu luo Mache-
macico anre annos plus minus rigincirelaca est, inveltise-
Mus; Radius C D dacus vocetur N; radius D Lcriricem N,
recta D F rocetur B, ex ponatur recta D II eNe A; OPOrTCE
DE.
a
igicur NM F NB escminimam quantitarem. ver it acintrtsuu
 et
pedegeae os 
Incelligatur quaeuis recta D O, ad libirum Cumpra, esse
aqualis ignOcX E, _ jungantur recta CO, OI; quadrarum
rectae CO, in cerminis Analpricis erie AF + F - 2 BE, (a
quadracum rero recta OL, crir H3 F P + 2 A F, ergO
rectangulum sub C O in M, erie in iisdem cerminis radix
quadrata(M N F MI F  = 2M BE; Rectangulum vero
TubOT in B, erie radix quadraca B NT= + B L = + 2B A
E; Ilac duo rectangula debene ex praecepris Arris 2d-
xquari duobusrectangulis M N ex BN. .
Ducantur omnia quadrarice, ve collatur alrmmerria,
deinde ablacis communibus, _ termino alymmetro ex vni
parre collocaro, her novus ductus quadracieus; Qud per-
acto, dempris communibus, ec reliquis per E dinisis, ac can-
dem elisishomogeneis, ab F. affectis, iuxta pracepta me-
chodi, gua dudum omnibusinnocuie, et facto paraboliimo,
tis condem simplicistima aquario incer A, _ MI. HIOC est d
 k is