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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 129, page id 1815201908:0186
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Ot
Ceale
M, qu
inct
Det 1
BFOMETRIC A.
Demonstratio.
DLanum AN
est ad planiim
BN, in duplicaca
BC.
ratione AB ad
planum
BN est ad planu
duplicaca
racione BC ad
C. D, id est ex da-
tis AB ad BC: 11-
milicee planum
COestad planu
DC in duplicala
racione CD a0
CAFUESII
ABadBC: Cmi.
licet octendam
COi
ert
L3
ommla celiqua
incer se esse in duplicata ratione A B ad B C: manifectum est ipicur omnia este iit
conrnuz analogia: Duod eracprimum. secundu pars simili plane discurlu ostende:
cur; pacecisitur vericas propolirionisi
RO FD
Eseile CCM 2G IE
D
F X V
ea be
Ademposica fisura daca line duo plana similia, batibus tomolo st
indirectum politis, A M maius, B N, minus. Pecicur inveniri cermi
nuslonsirudinis, ad quem proporcio dictorum planorum sine HaTuCOn-
ciruata CHCUEreES 
2C5OMI
Mrre
Constructio es demonstratio.
DEroctua gesim Lluiusinueniatur proeressionis balium AB, D C terminus, Cicq. K.
Dico etiam R cerminum esse lonsicudinis ad quem series planorum excurrec: pla-
na enim similia quae hene super terminis progressionis basium, per praxecedentem
erunt concinue proportionalia, ac proinde linearum planorumq; in infinicum pro:
pressio, pari palsu procedene: quare veriusque cerminus exie R. Ouod erat detmon.
strandum
Corollarium.
Demigitur punctum, terminus est progressionis balium, ec cerminus longicudinis,
quemhabet seties tigurarum similium: sive, quod idem est, linca quae aequalis eAt
exiei balium, est lotigicudo seriei figuracum Emilium, super balibus deseripearum:
PROPOSITTO CZZVI
Ata sic planorum similium continue proportionalium leries, homo-
losisbalibus AB, B C, CD, ecc. in directum policis, habenstermi-
num longicudinis punctum H;
Dico, cotam planorum sexiem MI H eNte ad primum cerminum AM,
ut cltrora leries balium imparium AB, C D, L. F, dec. ad primam AB.