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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 98, page id 1815201908:0155
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(e puti. p II uII u A B
L 2CIC655LHLS
Constructio prima.
B.I: 1217 1 did Moserianun
IE AM ditterencia primorum duru celminorum: siacque de ANL Aet BB CIC
ueidua
cundum cerminum de BC ad cerrium quempiam C k. Dicde  ast
cum primo AB. d lecundo cermino BC, aequalem ee serier vhillelsitu A L A L
CD, _CC.
Constructio secunda.
FlaE VE A ME duorum primorum terminorum disferencia, ad A B primum cerii
num, ica lecundus cerminus BC; ad cerciam aliquam magnicudinem BK. Dico
maxnicudinem B H, cum primo cermino, exhibere quancicarem, equas epp c9si lerici.
Constructio cercia.
TFerencia duorum primorum cerminorum A ML. de primo termino AB, cerria
proportionalis tac A R. Dico AKcoram leriem exhibere.
Demonstratio
Daimae constructionis; AM es ad BC, ve BC ad CK; isieur componendo AM
cum B C, hoc est AB, exir ad BC, VE BK ad C R: e permurando, AB ad
a79. blius B. K, ve BC 2d CHAk magnicudo, tioc est CK, cum AB et B C pri
Secundae constructionis; A M est ad A B, ve B C 2d BK ex constructione: igieUE
dividendo; ve AMI est ad NT B, id eA ve AM ad BC, SC B C ad CR. icaque per de-
monstracionem primae constructionis, AR(hoC eAt B K una cum primo rermino AB)
aequacur chetfelici.
1
Terriae constructionis, Cum sic ex constructione A M ad AB, vi A B id AK; erie
inverrendo, dividendo, rurlumque inverrendo AM ad MB, vE AB ad BR: 8
componendo AB ad M B, hoc est BC, vE AK ad BR. OUAEC AK b cori seriei
679. huins. _e qualis cst. Factum isitur es quod perebatur.
erimâ ieieur constructione exhibetur coraseries prater primum ex secundum terminum.
2. constructione habetur series tota praeter primum. terminum. 3. constructione simul tota pre-
ducitur series. Duius aurem problemalis, ac constractionis ejusdem vniversalitatem amplius
deductam habes in proposisione 123. huius, ex corollario quarso ibideM.. WP P. C1- + 1C
t2 = ldettdtek
enu
15B A
Vla velo vicuo
lacio guatum
miscerminis, tori leriei xequalis est.
Culitele llaci
catun ac eas Lccu
Porest, hinc, eriam se-
quenri mechodo, li
Deam cori Terici pro-
cortionalium linea-
ru, reperierius aquale.
Constructio ex demonstratio.
X punctis A ee B, erige ad quemuis angulum, patallelas ANL BN5 quae ipsis
A B, B C sinc proportionales; _ per puncta M _ N ducatur recta M N, con-
CurrenS Cum. A BC in R. Dico AR, cori serici AB, BC, CD, ec: xqualem esse.
uvane   BC. PBa PatetCXCO, quod BC ex
tiypo.
uoi u ii.  i  siuu u  piu u ite  te e . s   iu  e s   u pe t s i  t 1        t  m puen