# Leibniz Legible — https://leibnizlegible.com
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# Permalink to this reading: https://leibnizlegible.com/page/175906937X:0391?run=74
# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 367, page id 175906937X:0391
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=391
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000391.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 72 lines, status machine
# Lines: 72 recognised, mean confidence 0.86
# 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.

iiliber
mque
minuS
21-
erit
Ore.
olIuS
Per 4
Primi.
IHI
De
DE AI ONS FR A FFOH FBUS.
367
Demonltrationis series eodem modo Pe habet quo AnalycOS,
cum ueriu (que rectisia consentiane, quibus ab hypotheli ad qua-
iti conclionem perducimur. ETci hic ridere est.
Fxenim cum C SIE
UE F C ad BF, ita AC ad A B:
Y. ∞ X 
erit quoque d
2
UCEIFC ad EIBF, ItaB AC SeuA AB. F BBGadD AB Sexri.
Yy - 2V7. (-∞ X - - X x = ZZ, Id CA, a A -+ yy 1 a 4.
ee diridendo
UEDFG - BBF vel FII,
id est, ∞BOHIS adHBF, ita HBO ad BAB
yy = 2 X y = - X X - 7) 1 aa.
permutandoque s
utD BOFTadEBC, rel h’ucHTC ad B, ItaHBF adD AB
y -- 2X - - y - X X I a a.
Fd est, invertendo st per conversionem rationis
ut D AB ad A AB - BBF, ita GB ad BFI
aa -  aa = X X - - Y 1 2 X.
ee duplatis antecedentibus k convertendoque
utEIAB = (IBFad 2EI A B, ita B H ad 2G B sCu B P ad BC
a a = X X - - 2 a d
Ouod erat octendendum.
X 1 y.
Ouod liaurem Algebrae ignaris sire in inreniendi arre impe-
ritis ipla demonstratio sic exhibenda, pocerit ea praetermistis jam
hisce restigiis sic adhiberi.
Sumatur FHI aequalis F B. Cum igitur in eriangulo ABC an-
ruus ad A recta A F bitariam seCtuS LIE, CrIE m UE FO ad BF, ita m per 3
AG ad AB. Sed cum linearum proportionalium etiam propor- sexri.
tionalia sint quadrata, eric de n ut quadratum FC ad quadratum n per 22
BF, ita quadratum AC, id est, per 47 primi, Cumma quadrato- sexri.
rum AB, BC, ad quadrarum A B. FF diridendo ur quadratu 0 per 17
FC minus quadrato BF vel F HI, id est P rectangulum BOFI, quinti
ad quadratum BF, ita quadratum BO ad quadratum A B; Per - P per 6 se-
cundi.
mucandoque q ut rectangulum BC FI ad quadratum BC Peu r UE 4 per 16
FIO ad GB, ita quadratum B F ad quadratum AB. IlOc est, guinri.
11)
1per 1 sexti.
Cper 3 sexti.
d per 16
C per 17
quinti.
F per 6 se-
cundi.
5 Per 10
quinti.
Aper I sexti.
i per Cor. 4
quinti, e
Per Cor. 10
quinti.
vide Cla-
Dium ad 22
quinti.
1per 15
quinti.