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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 11
# Folio 10r, page id 00067970:0019
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si A.B.  _ e. D serit A B a sed
patet ex uo quod congrum sunt similia.
si sit A. B 8 B. C c A. C erit
(45)
A. B. C ∞ B. A. C. vel ulteri ordint, alio ordine
quocunque. Numquia B. C. GAB. seu g B A ergo
simul congruent B. C et B. A. Nam transferatur
 (A)
A. B. C. t A. B incidat in locum ipsius (B) (A) quod fici potest quin A. BC B seu AB∞
et quin B. C∞ A. C et B∞ (A) Nam si
congruentibus A. B et (B) (A) ascribas congruentia C. et (C.)
congruenti modo quia A. C g (B). (C) et B. C g (A) (C)
fient congruentia A. B. C ∞ (B) (A) (C) sive
A. B. C e B. A. C. Parentheses enim tantum
confusionis ex repetitione fa vitandae causa
ascripsi. Hinc patet quid sit congruenti modo
ascribi, cum scilicet omnia simul sumta ab una
omnes combinationes ab una parte enuntiationis
sunt congrnentes omnibus ab altera parte.
Unde patet si A. B e BC. e A C. fore
A. B. Cy A. C. B. 8 B. C. A. 8 B. A. C.  C. A. By C. BA.
(46) Si A. B. C. _ A. C. B. sequitur (tantum A. B. g. A. C
sive triangulum esse isosceles) nam sequitur:
l
ex quibus B. C. 8 C. B per se pates, reliqua duo A. BgAC. et A. C g AB.
eodem recidunt, hoc unum ergo inde duximus A.B. y A. C.
Si A. B C e A C. B gB. C A fiet A. B. g A. C Y A. C
nam ob A.B. Cg AC. B. fit A. B. 8 A. C.
ob A B. C, B. C. A
47) Si A. B. C eB. C. A.. sequitur A.BgB C A C. F sin triangulum esse aeqpilaterumi)
Nam fit A. B. GB. C. B. CgC. A.
(18) si A. B. C∞ A. C. B. et B. C. Ay B. A. C.
fiet: A. B. gB. C. 8A C. Nam ob A. B. CgA C. B
fit A. B 8 A. C. eodemque modo ob B. C. Ag B. A. C.
fit B. C. 8 B. A. sive A. B. 8 B. C.
Fitaque quandocunque in transposito ttu punctorum
ordine duo qua unum extribus eundem in utroque
ordine locum servat  inde tantum, probari
potest Triangulum esse isosceles sed si nullum
ex punctis servat lorum, et nihilominus situs
posterior priori congruit, Triangulum est
aequilaterum.
(49) Si sit A. B yB. C. ∞ C. D ∞ D. A. et A. C∞ B. D
erit A. B. C. d∞ B. C. D. A~ C. D. A. B. e D. A. B. C.
1GD. C. B. A G A. D. C. B es B. A. D. C. YC. B. A. D
Hoc ex praecedentibus facite demonstratur, multaqu
alia hujusmodi, quae sufficiet demonstrari cum
ipsis indigebimut id. Nunc satis habebimus principium
dedisse qu ista demonstrari possunt solo
bc
calutosie inspectine sivera
1)
+per praecedentem
fig. 18
Ftitusque posterior priori congruus est,