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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 376, page id 175906937X:0400
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=400
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DE CON CLNHANDES
Flinc existente bb x a X X = ayy = CCX = a a X
X
Si in locum ay
Substicuatur ex de rice rersa: habebitur bb  =X- ex) F ca) - aav
DADC FGDB DABC
id est, bb∞ax =cy; Seu, quod eodem recidit, cy + bb ∞ A X
Ommino uc in antecedenti Theoremate. Unde Facile elt, cooni-
EIS AB, BC, AD, e D C, invenire BD.
Ouod si autem, existente bb D A X = Cy, PrO x Scribaeur
 tiet bb ∞ -- = cy vel b bc ∞ a ay - c07. id est, diridendo
C
Utrinque Per A4 = 66, erit a a = c0  y. Vel, resolvendo X qua-
GAB--LAD EBD AD DC
litatem in proportionem, erie uE a 4- c6 2d bb, itac ad y. Simi-
CCX
liter, ( Proy Scribatur erit bb ∞ a x - - vel bb a D AAX- CCH.
bba
id est, diridendo utrinque per a a - 66, etie a a - c ∞ v. Vel,
AAB= HAD
resolrendo aequalitacem in proportionem, eric uEaa -5c ad
VIBD AB BC
bb, ita a ad x. Ouae quidem insuper ostendune, quo pacto ex
eribus laceribus al ABD inreniri possint BC e DC.
Atque ita constat, si ad praecedentis Theorematis in vestica-
tionem duntaxat adhibeantur 26 es 47 Propositiones primi
libri Fuclidis, qua ratione ex calculo non modo idem Theorema
emanet, verum etiam Propositio 22 15 23 secundi libri, 3tia
sextr, aliaque proposiiones, in Fuclide non extantes, quae trian-
culum concernunt, cujus angulus bifariam est divisus.
Caterum calculum hunc mulio prolixiorem esse calculo an-
recedentis Theorematis nemini (ut opinor) mirum videri de-
bet, cum ad illud indacandum supposuerimus Theorema, quod
ei immediate praecedit, tum etiam Prop. 22 aut 23 secundi:
signidem rationes, quae in iis comprobandis cunctae ac singula
sunt perpendenda, illis sic jam prae suppositis omnino praetermit-
Euntur; qua alioquin, si rem ipsam penitius inspicere atque a
prim