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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 23, page id 175905688X:0045
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=45
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000045.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
# Lines: 56 recognised, mean confidence 0.80
# 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.

ctum
aleu
ille
no
aHO
CCaN
noc.
1
1
d
ca
O81
na
neta
M
L. P2.
B e
b. d
L I D E R S E C I N D U S.
NL Parallelam ipli CEA, quam vococ. Tum dico, utNI
est ad L R, velcad b, ita C B, vely, est ad BR, quae idco
exIE -: ac proinde BF  - b, _ AL X [ 7 - b.
Denique ut CB cst ad BL, vel y 2d 7 =b, ita est
GA, vel a, ad L A, vel x -f 23 = b. ad eo ut, (I
mulciplicem secundam lineam per certiam, produca-
CuI
b
= - a b, quod aequale exiEXy L 3 = by, ei scili-
cet, quodproducitur mulciplicando primam lincam per
ultimam. Acque ita xequatio, quae invenienda erat, est
hujulmodi, pt ∞ cy - 3 -= ay = ac. Ex qua CognO-
Scitur, lineam P C esse primi generis, quemadmodum a
illa re ipsâ nulla alia est quam LIyperbola.
Ouod si in instrumento, quod ipsi describenda in-
Terric, locorectae linea CNR siumatur inventa lxcFIy-
perbola, auc alia quaepiam primi generis curra linca,
quae planum terminet CNR L; incersectio hujus li-
nex _ regulx CEL, locoFperbolae F C, aliam cur-
vam delcribet, gua secundi erit generis. VE A C NR vide Pap-
fuerit Circulus, cujus cenerum L, describetur prima pum ad
prop. 22.
Conchoides Vecerum; & Si Parabola fuerie, cujus dia- lib. a; ex
meter R B, describetur curra linca, quam paulo ance Eurocium
dixiprimam cAc ac simplicissinam pro quaestione Pap. in commen-
tariis in se-
vi, cum quinque tantum lineae positione data lunc. Scd cund. li-
Siloco alicujus harum linearum primi generis limatur brum Ar-
quaedam secundi, quae cerminet planum C NR L, de- chimedis de
Sphara (5.
Scribetur ejus opc alia certii generis; aut s quaedam cylindro.
certii generis sumatur, describetur aliqua quarci, ex lic
in intinitum. Ve facile ex calculo est cornolcere. Et
sane quocunque tandem modo curra alicujus linca de
scriptionem quis imaginatus tuerie, modo ipla ex illa-
rum numeto, quas Geometricas voco, extiterit, pocc.
rit lem