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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 59, page id 898203430:0087
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=87
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
# Lines: 44 recognised, mean confidence 0.83
# 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.

VEL LINIT.:ORDINATIONM CONIC. LIB. L.
BF esse ve rectangulum BF L. ad rectangulum BK L.
Producantur BL, GF, quibus OCCUF.
rat producto F. I in M, N, de ex F lic
concinsens, sive ipsi RM parallela RH.
Tam, cim sic BP. aqualis L I ( ob semi-
rectos angulos ad B, L in criangulo BL L)
eric, e BF aequalis E II, e B KC aequa-
liS KM.
Fc quoniam quadeacum semiordinata
KF aequale est 2 rectangulo sub BK, RN..
e est BK aequalIS KM, ergo quadratum.
RF aquale est rectansulo MI N, quibuS Mt oBC
Si verinque aequalia quadrara addaneur H B, H M, crune quadraca F HE,
IEB, sive rnicum BF aequale rectanguIO NI M cum QuadtFAtO K M, (1
ve vnico rectangulo N MK.
Insupet quadrarum E FI ad rectangulum N M K habet rationem com
pOsitam ex ratione E FY ad NM, sive ex PF ad IN, CIIC Cx P. F ad L. K.
X Cx FatiOnC C PI ad RMI, Sive ex ratione BF ad B IE, ex quibus com
Donitur ratio rectanguli BF L. ad rectangulum B RL, ergo quadratum
EET ad rectangulum NM IE est ve rectangulum B L. L. ad MKL, sed
quadratum P. HI aequale est quadrato BF, de rectangulum NM HE equale
est quadrato BF, ve superius demonstrauimus, ergo quadritum B F ad
quadrarum BF, CA vE rectanguum B F. L. ad BK L.. Ouod CraL,
_C.
R
Eparet hinc quadratum rami cuuscunque BF aquale este rectare.
CL 10 (ub NM, MH, vet suB NK cum K B in KB, 1 equodeit
ee
PROPOSITIOLLMI
N Sectionibus oppositis. Ouadrata ramorum ad vnaia
Ayperbolarum ab orisine abi sobat dtamibe
ligue ex oppositis ductorum, sunt inter se et rectanou
la sermentorum axis inter ordinatas ex ramorum ter
minis, Co terminos Moduli ex vercicali, eiusdem oppo-
sica interceptorum.
1l
i eu
N Inc Sectiones oppolica ABC, OVK, quarum axis transuerus VB,
a focus vero alterius iplarum, nempe ABC, (I F. inter quem, ee vereiu
cem B sic sumpea ramorum origo D, de per D ordinata ad axem AC5
luper eam se criangulum ciccumseriptum A B C op _ iunta explicacusin.
d, P1OpDV
pr. tuius.