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# Title: LBr. 57, 2 · Bernoulli, Joh.
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Demonstratio Mullisaitionis Angularis in ratione data
sive surda sive numerica, inserta act. erud. Lips.
an. 1701. m- April.
Lemma. L.
Lectangulum sub deagonalibus trape i cujuscunque circulo
inscripti eit aequate suna rectangalorum sut lateribus
oppositis.
Demondiatio Lupo satii nota est et passim habetur
in fuigonoa etricit.
Leama II.
Sica semicuculo ADB, duo habeantur
arcus aequales AC, DE, quorum ille dia,
metio sit contiguus, alter ubicunque sum
Luc, ducanturque subteata CB, DE, EB
ut et CA, DA, EA; duo reitang. sub DB
et CB minus reitang. AC et Ad, fore aequale reitang. sub
AB et EB.
Denoncr. Ob simil. trnaag. AC F, BDA eiit AC. CF:;
BD. AD et AC ia AD = Bd in CF, iteunque ob simil. triang.
p0 
BdA, BEF erit AB. BD:: BF. BE et AB it BE = B in BF
= BD ia BC - Bd in C F = BD in BC - AC in AD. Q. E.
Lemma. III.
lositis iidea duo fore reitang. suib BD et AC plus rertanque
sub BC et Ad aequale redanque. sub AB et AE.
demonitr. Conjungantur punita C, D per rectam
CD qua parallela erit ipsi AE, et ducatur DG parallela
ipsi AC, qua etian pii AC vel DE erit aequalis adeoque
duuto radio oD, erit trang. OBD sinile Lrcaas. Gd2, ob
aagulos 00d et BGC eidem arcur visistentes aequates. Htcus.