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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 101, page id 175905688X:0123
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=123
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000123.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
# Lines: 38 recognised, mean confidence 0.87
# 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.

L Z B E R. Y E R Y E I S.
1O+
per nocum Parabola vobis videatur incommoda, (a-
cile est plures alios modos in cundem finem exeori-
TarC. Ve, manentibus eildem quantiratibus pro AB ec
BL, nec non cadem pro BR, qua pro lacere recto prin-
cipali Parabolx supponebatur; describendus cMtancum
Pemicirculus RSF, centro ejus ad libitum in linca BR
allumpto, ita tamen ut lineam A B alicubi sccCE, UE iN
puncto S. Nlam poltquam a puncto T, ubiterminatuI,
versus R altumpea tuerit linea T V, aequalis BL, junga-
turque SV, acque a puncto A junctx S V parallcla duca-
tUE AC, quae rectae SC, ducta per punctum S, ip(i BK
parallela, occurrat in puncto C: Pric punccum C, ubilix
dua parallelae sibi mutuo occurrunt, unum ex punctis
per quod quaelica curra transire debet. Fodem modo
inreniri pollunt tot alia puncta, quot quis voluerit.
Ouorum omnium demonstratio latis facilis cAt.
Si enim regula A P una cum Paxabola FD adplice
tur ad punctum C, (eodem modo, quo constac cas ad
punctum C in curra AC H mucua interlectione delig-
nandum esle adplicandas) ex quidem C GVOCCTULV: CFIE
CDIS, cum latus rectum, quod est n, lic ad C. C+ sICuE
COad CFD. Auterendo auremm DB, qua est =
relinguetur Y - 2Y ~
B7
aCFD
onproCF. Deinde quia AB est ad
BE, uCC Gad GB: hinC CUM AB SIC Z P, BE erIF DY -V2
2n
ny
Eadem ratione li punctum curra C supponatur in-
ventum esse per intersectionem lincarum rectarum, SC,
parallela ipli BR, _ A C, parallela ip(I S V; SB, qux
aequatur iph C C, esty: ec cum BR aequetur laterirc-
cto Parabola, quod nominavi n, BP erit JV. est enim
UER Bad BS, ita BS ad BT. Cumque TV eadem (IE
QIIX