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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 233, page id 1815201908:0290
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D SEC YIONES C
N
vet aqualis semidiameero P F, vel maiot. O uare cum A T ipE A F, _E TR ipE FB,
SinEEquales, erit quoque FI Iaut aqualis IK, aucmaior. Ergo verrex Tcrianguli AIR,
vel bilecabicarcum FIK, vel eric alcori punctum bilectionis verlus R. Dcinde quia
AD, hoc est AL. maior CA quA AF hOC eAFILCTICAECUS HI L maior arcu FTL, AC PEO-
inde vErEEK L crianonli FT L Rnon Coluim Eadec viera punctum quo BilecaEuF ar-
cus TTEK. Sedetiam propius adhue incideeversus K, quam alceriuscrianouli ver-
cex I. Minorigicur est alcicudorrianguli ITL R, quam crianguli HTK, adcoque
minus est ALK hoc eA ADF, criangulum, criangulo IIIK hoc CA AFP. AF.
qui criangulum A F P aequarur criangulo AFB, cum omnia veriusque laceca vi-
eissim sncaequalia. Prsocriangulum A DF minus cciam est criarigulo AFB: ac
proindecriangulum F A G duplum ipsius AD F (est enim P C ex constructione
Bilecta in D) minus est crianoulo B RC duplo ipsuS AF B. Similicer demonstrabi-
musquoduis aliud criangulum quod per axemnon sic Factum, minus esse crianguto
per axem. In consisitur recto, _c. Guod crac demonstrandur. ul
Duod aurem in demonstrarione tuic alsumprui, (in recto) nempe conoacuranoulo
axem semidiametro basis eAc maiorem, in conorerorecto rectasulo x qualem, Pau-
cissic demonstrabo.
SiE COnUS FCCEIS acuranontus sectus crianoulo per axem B A C. quoniam in
criangulis BF A, C F A, lacerD B A, C A, BF, F C aequalia sunE, ee F A commu-
nes anguliquoque F AB, F AC aequalia lunc, sed eocus B A C eA minor recto ve-
Poceacucus, ansulus isieur PA B ipsus dimidius minor est semirecto. Ouare cum
angulus BF A rectus sic, eric reliquus AB F. minor semirecto, hoc est maior angu- 219. primi.
10 F AB, ergO axis AF 2 minor eA semidiamCErO F B.
Ouod h conustuerit rectus rectanoulus, tunc anvulus B A C crir rectus, ac proin-
de BAF, dimidius eorius B A C, semirectus est. Ouare cum angulus B F A rectus
lic, necesse est, vereliquus FB R eriam sic Cemirectus, adeoque aequalis angulo
BAF. vnde axis A F. ex Lemidiam eter balis conixequales erunE.
PR OPOSITI
XII.
Lter expedillus pracedens cheorema hunc in modum demon-
Alat.
Demon