# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/175906937X:0200
# Permalink to this reading: https://leibnizlegible.com/page/175906937X:0200?run=74
# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 176, page id 175906937X:0200
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=200
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000200.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.91
# 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.

E L. E ME. C U R Y A R U H
Corollarium 4.
Constat praeterea, assumpeae cujussibet diametri parametruI
esle rertiam proportionalem duabus rectis, quarum una est vel
axis vel data diametri porrio, intercepta inter ejuldem verticem
e cam, quae P’arabolam in assumpex diametri termino contingit,
altera vero ea praedicta contingentis pars, quae inter dataim d
in Lu. 2umpeam diametrum inceriacet. Demonstratum enim est
rectam MI, ex eo quod ipsis AI, IM certia sit proportionalis,
alumpex uccunque diametri MO paramerrum eAe.
Corollarium 5.
Fx demonstratis quoque non difficulter collisitur, quo pacto;
datà politione qualibet Parabola diametro, ejusque verrice, et
latere recto, nec non angulo, quem taciune ordinatim ad dictam
diametrum applicatae, alia ejuldem P’arabola diamerer, quacum
applicata alium quemlibet angulum constituane, ac iplius ver-
tex, e latus rectum inveniantur. Si enim data politione diame-
ETOMIO, VerTICO MI, _E laEerC RCCEOMTK, anouloque SMIK vel
V MK, quem applicatae faciune ad dictam diametrum MO,
aliam ejusdem Parabola diametrum invenire oporteat, quacum
applicata angulum constituant aqualem dato cuilibet angulo
ABM: ducatur a terminoR adS V recta I P in angulOR V V
ipsi dato A BM aequali, dirisaque PM bitariam in L duCatUF per
Trecta IB ipli MO aequidistans. Deinde ab M ad candem IB
applicetur recta M B in angulo M B Idaco angulo aequali, divisi-
que BIbitariam in A, erit quae lica diameter AB, vertex punctum
A, ejusque parameter AC, recta nempe, quae ipsIS AB, BM ter-
tia proportionalis existit. FA enim = punctum M in P’arabola,
qua efficiente ip(i B MI Parallela ac intervallo A C describieur, quan-
doquidem quadratum applicatae B M ex constructione rectan-
sulo C AB est aequale. Deinde quoniam limilia Cune criangula
BIM_ PMK, ob aquales angulos ad B _ P (ex constructione)
4 per 29 pri- acque ad L_M + (ob parallelas AD, M O), erit  ut BIad LM,
mi.
per asexs; Ita PM ad MK. _, Cumpris antecedentium dimidiis, ur A I ad
in 2 bujus. LMI, Ita TMI ad MK. Ouare secundum ca gua superiis s demon-
sraca lune, Parabolae diametris AB, MO, ac parametris AC,
MB
Jus.
Per TBu
3Per 17
sexti.