# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0965
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0965?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 908, page id 1815201908:0965
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=965
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000965.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.85
# 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.

908
ROPORILDMLMLLMTI
GF OMLLKICAEVM
ARS TE RFIA.
Verationum mupaom jeu compositione.
DMionum multiplicationem à compositione non differre satis arbitror, is in-
llicet, qui non noret definitiones 5. libri sexti elementorum, eaque lece-
 quae in secunao principio huius libri exposurmus. Tunat tamen, quandae
epius deinceps i a me assumi debet, L. ectori verbo 2no memoriam refrica-
re. Datae sint tres quantitates A, B, C, aut plures: Di-
cimus ereo, rationem AC ex componi ex rationibus
AB, BC, ex produci ex ijsdemrationibus inter se mul
ciplicatis, ac proinde rationem omnem produci ex mul-
tiplicatione earum rationum, quae ipsam componunt.
EROTOSTTID LXXV.
Aex Cincraciones AB, dC D. Fiatve C adD, ita B ad F
Dicorationem AB ductam in rationem C D producere ratio
Mt
Demonsttabio.
Actoes AB, B F componunera
tionem AH. Cedracio BL. Clt ra
tio CD ex constructione. Frgoracio
AB Cum ratiONC C D componic Fa-
cionem AF. ergo racio AB duceta in
nem AL.
cationem CD producir rationem AF. Ouod erac demonstrandum.
A 2d P
Corollarium primum.
Inc facilè deducemus candem
racionem proaues ex cacione
 i caciorrem C B, qux AcCxFd.
cione CD i cact AB. haC
enim ve C ad D, HCB ad F; ede
ad F. igieur per 75. racio A B in rarionem CD, Facicracionem AF
ex racio CD in racionem AB Facieracionem C F. Aequiraciones A F, C F cxdem
E
(UnE. ErgD, eCC. quod aucem rariones AF, C F snc exdem, siC ostendieur. per constr.
D cAt adB, ve A ad B; e C est ad D, ve B ad F. er5023. quinei, C cA ad F, ve
orollarium secundum.
 Cato Lactor    C Labimus cationem qua producitur ex ra-
eionc AP ducta inracionem C.D.
FiaB