# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/898203430:0305
# Permalink to this reading: https://leibnizlegible.com/page/898203430:0305?run=74
# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 113, page id 898203430:0305
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=305
# Source image: https://digitale-sammlungen.gwlb.de/content/898203430/jpgs/default/00000305.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 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.

ADDENDA LIBHO TCKSI.
In cribus enim luperius demonstraris PF, FIL, F CE. in continua
rarione harmonica, tres IF, ICF, ITI lune veique in concinua ra-
eione geomerrica; sed media lCr octensa est aequalis ip(i IF, quarum
veraque est dimidium corius H. CF differentia interprimam, ec certii
erium harmoniearum, _ IF aequatur summae IC+ cum CEF, live lum-
inx ejusdem dimidii cum cerria; ac demum III, est differentia in-
Eer LE (quae est summa dicti dimidii cum certis) _ TIF, qua est me-
dis harmoniea data intex exeremas dictas F. P, PCF. Ouore, _C.
SC I OI YV M AL
gEnigue. Si PTOdUCANFUE deXErONLUM ReCIX ABN ad C, B M
ad 1, BC ad 5, AD C ad F, acq; curra ParabOlA BFIC ad H;
et exErA NC ogatur quaecumque recta ch, ipsi NVC Parallela, quie
necessario singulas lineas productas secabie in punctis c, i, 5, F, ec h.
Dico, hujus rectae eh eria segmenea he, hF, hs sempee esse in
quadam continua ratione harmonica.
In similibus enim criangulis C BN, gBC sectis a recta BMi, Osten-
Ta est C H aequalis MNI; quare sc gi aequatue ipsi ic, sed (ob Para-
Bolam BTTCh, _ aequidistantiam rectae in ad diametrUM BD) EreS
iR, 15, iF, sune in quadam continua ratione geometrica; illarumq
erium hc, hF, hg, recta hF est summa differenciarum maxima cum
media, de media cum minima; summa vero ex ih maxima erium, de
ex i8 media, est ipsa hc (quum ic, sic aequalis iph i8) e maxima
demum difterenciarum est tig: quare, per primum Scholium hojus
tres he, hF, ho Cunt in quadam continua racione harmonica: adeo-
que prima hc adcertiam hg, est ur c F prima differentia ad F8 sc-
cundam. Ouod erat demonstrandum.
Ad pac. 86. super fieura, quae ibi, immediate inter
versus 15.  16. addendum est sequens
ILLLM.
D mibasibus DA, DB, sive aequatur luo recto laceri, guxvis sC
ips diameero F D parallela, est media hormonica inter parces ince-
BFaNECS AC, C B datae rectae AB, omnesque ordinata F. D, F C, per
Parabole propriccatem, incer se lunt, ut rectangula ADB, AC B luD
parcibus basis AB; sequitur hinc, quod omnes medix harmonica
E D, F C InCOT DATEOS INEEGTANEeS CaIdeM RECTAM A B LUINE DEO-
porcionales ipsis rectangulis ADB, AC B sub partibus integean-
ribus iplam AB, e incer quas illae lune medix harmonica.
SCa
Fd in hac Parabola, cuius digmeter F. D aquatur vtrigue ex (0.