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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 13, page id 175905688X:0035
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=35
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000035.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
# Lines: 38 recognised, mean confidence 0.88
# 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.
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# After the first blank line: the recognised lines in reading order, one per line.

1
L E B E R P R E M Y S.
equale illi, quod producitur ex mulciplicatione reli-
quarumi; vel etiam ut unum ad alcerum dacam habcat
rationem. id enim quaectionem difficiliorem nonreddit.
Primo itaquerem ut jam Factam (upPOnO, aEque UE Duomodo
ex harum omnium lincarum contutione me expediamm, ponendi sine
considero unam ex datis, aEque Unam Cx GuXlILIS, CXCM- hac Gua-
pli gratia, AB _ C B, velue praecipuas, e 2d quas siane, ut ad
relionaS OImneS FCFCEKE COnOT. Ponendo nimirum les
mencum linex AB, quod intra puncta Ae B continC= niatur
tui, rocarix. B C autem rocariy. aliasque lineas datas
omnes productas esse, donec secent halce duas, etiam
productas, si opus tuerie, de iplis non sint parallela.
quemadmodum hric apparet illas secare, lincam qui-
dem AB in punctis A, L, _ C; BC vero in punctisR,
S,. XCT. Deinde quia omnes anguli erianguli A R B dati
lune, data quoque cricratio, qua est inter ejus latera
AB _ BR, quam Pono ut Z ad b, ita UE, Cum AB (U X
RBFucura SIC =, CR autemy 1 : siquidem punctum
B Cadit inEeF puncta C _E R; nam SIR CadeTCE InFeK C
sB, CR ellery - -; (I VerO C caderet inter B_R,
CR FOFCF =y. 1 . Similicer, dantuE GuOGLICErES AH
ouli erianouli DRC, unde d ratio, gux est incer latera
CR _ C D, quam PonO uE Z ad C: IEA UE, CHM CR (IE
= CD FIIEUIEa SIC =Y - BCH
Poltea, quia lincae
AB, AD, _ P P positione datae LUNE, data quoque exit
distantia puncti A. a puncto E: quae si nominetur k,
habebitur E B aequalis k  x; Foret autem ip(a k - X,
si punctum B caderet inter P ex A;. at verO = k. + X, I
E caderet inter A e B. Rursus, quoniam anguli erian-
ouli ESB omnes dantur, dabitur quoque ratio lateris
B B. 2d BS: quam si ponam eNC ut Z ad d, BS
rCE
Termin Et
sEquario
nem deve-