# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0210
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0210?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 153, page id 1815201908:0210
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=210
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000210.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine
# Lines: 54 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.

n
d
ret
 L OHE TRIC X.
isitur plana sunt in concinua analogia, eriam bales AB, B C, xC. CTUNE~ COnFIHUIX 2 124. hu.
proportionales. Ouare exxquo ctiam AB, C D, P F, erun concinux: ergo p l2. ius
num AM est ad planum CO, vEb AB ad F P. Acqui sCrieS MK c est ad seriem b20 sexti
OK, veplanum AM ad planum CO. (sunc enim similium racionum leries) ergo
TerieS MIK est ad seriem OK, ve AB ad F P; incer quas impar numerus balium
incercedic, nempe, 3. Requi in coca serie basium, non postunc reperiri due aliae li-
nex, quae eandem rationem habeane, quam A B, P. P, nili illa incer quas idem cer-
narius numerus linearum incercedie, vei ex elemenris demonstrarur; isicur nuIIX li-
nex ex seriebalium, inter quas impar linearum numerus incer iicieur, candem hat
bene rarionem, quam series MIR ad liri parrem OK.
Compareneur modo dux serieS MIK, PK, intet quarum iniria paE planOEUM AE
numerus: Kurlum isicur octendemus rei prius seriem MK eMe ad leriem PK, ve
AB ad O TI. quare cum incer AB _ C TT, impar liNCATUM SIE NUMCRUS, nem-
pes; coca demonstracio prima pareis huic etiam quadrac: unde pacet propolitionis
VeriTaS.
PROPOSTTIO CLZ
Aca lic quadratorum series habens bales in directum ex cerminum
longicudinis IC. Deinde ex lingulis punctis B, C, D, _c. crectae sine
perpendiculares AI, BL, C MI, exc. proporcionales continux in ratione
dimidiaca proporcionis AB ad BC; e Cuper illis perpendicularibus in
alticudine linearum AB, BC, _c. hanc rectangula IB, L C, MD, _C.
Dicoleriem rectangulorum PI, ad seriem rectangulorum L K, cripli-
caram habere proporcionemrationis AL ad BL; cuius quadruplicaram
habet leries quadratorum P K, ad seriem quadratorum F H.
Demonstrario.
DRimumenim rectangula LB, L. C.
ecc. ese in concinua analovia siC
octendo. ratio rectanouli IB adL C,
coponieur ex racionibus AP ad BI.
hoc est exhypochesi B L ad CM, e
AB ad BC, hoc eAt BC ad CD;
Acqui cciam rectangulorum LC
MID racio componitur exracionibus
BE ad CM, e BC ad CD; CrgO
eadem est rectanguli TB ad L C, e
T C ad MD ratio: erooillarectan.
sula sune in continua analogia, ha-
DEFUEGUO PFODFCMO COnTIHUE PEO-
porrionalium rectanigulorum L. L, N.
84. huins
NVi K: quare series TK es d ad seriem L K, ve rectangulum LB, AA FCCIAMOMLAM L C: 82 haiu
Requirario rectanguli IB ad T C, componirur exratione AI ad BL, ec extacio-
nC AB ad BC, quae ponitur esse duplicara rationis AI ad BL; ereo ratio re-
Aanouli IB ad F Cs hoc est sicir modo ostendimus, ratio seriei IK ad Teriem L R,
est eriplicaca rarionis AIad B I. Series aurem quadracorum R R est ad feriem FR,
ve quadracum BP. ad quadrarum C F, hoc est in duplicata rarionis AB ad BC, c Nbid.
hoc est (Vcex hypoches collioitur) in quadruplicaca racionis A I ad B L, cuiuseri-
plicaca est racio seriei rectansulorum EK, ad leriem L. K. Quo derar demonstran-
eM.
1