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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 3
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demonstrationes Euclideas, ut a clavio exhibentur
talis
revocabimus quoad opus et ratio est, ad Calculum situs; quo melius calcalum
calculi Elementa constituamus.
seu recta per centramd
Diameter. Circulum bifariam secat. r
de monstrati
haec propositio ab Euclide assumitur in definitione 17. primi. Ejus definitionem e
tanquam a Thalete Milesio, ex hibet proclus.
Cirmferentia
(1) sit CA = CY et ABe ABd, E sit qu Y circulus A d BE
(a) A e idem quod Y A, B, A, M sit qu. Y.
(2) circum f. ADM, erit Y set A, B, C _ erit qu. Y
(3) AC: ACB recta
(5) punct in ADB oxtra A punctum Dquodc.  et
14
poterit ADB dici D. Eodem modo AC B dicetur E
D
od un. ad AB. Ergo (per def. Rectae nostram
(e D (5) quicquid omne punctum plani ad partes D AB d voce fud 
et omne ad partes. _ ABE vocetur. W seu omn P. e V sel W. et omne L  sit H
mne p mihi significat omne punctum plani. unde perit planum
et ert V1W X
e Acon (X) omne D est, et omne E est W
(6) Manente recta, ABB sit rigidus semicirculus Ad A t movento circa A∞ AB
ilo
Cmre 
Mancu
transferatur in alteram plani partem. Quod fieri potest quia ex nostra rectae definitione
quae ostenditunde constat quicquid in rectam non cadit, ips salvo ad ipsam quiescentem situ moveri
ex 4
fat (D. A.B ~ D. A. B
posse esque trans feratur ALB in A(D B   
dec quaedam  cM
1)Eadem erit, ) nam si C D = eA. et c intra (D AB, et sit N 2. CZ erit
d
lioce
eas dem partes ab pertio eG a C.
9 Iquam CL (per 1) G Ergo Ct) ergo punct  pi CG est partim intra partim AB() A
partim extragnobus eadem
(10) ergo
ips)
N.
n
Infreslus aut
occurrit
e 1t
alie
cum non occurrat ipsi AB, alioqui recta cg occurreret
asdem partes. Eritque aut altera
ta
e
ietiti
M dit ad
coinci per 1 hic.. Erqo  altera par
a C M
alterius non est
(12) si dua recta int in eadem recta et ad easdem partes ab extremo communi
et CM sontt
I (11)
et existant aequales, coincident. seu recta ex centro ducta ad unam partem secat
(12) Ergo L
circulum in uno tantum puncto. Nam si H recta ex C occurrat circulo  in
Schol.. in omni linea si ab eodem termino ad vasdem partes edrcantur
diversae lineae portiones linea in eodem seu in eodem ductu, ducaentur diversae
portiones, una minor prius deinde aliam partem addendo producitur major. Adeoque
aut una portio ab eodem termino lineae eodem tractu sumta alterius pars est, aut
aut ambae coincidunt si suit aequales. Hoc assumtum in num. 10
Dignum etiam notatu in ALB, significari A et B esse inter L. EF
hinc in ALB M A erit, A et B inter L, itemque A et B inter M.
caeterum propositio brevius poterat demonstrari, ex sola consideratione
med. in AB
Nam
et MC = AC. Et in ALB est ilidem eed ABCct AC. Ergo
ctur
determinationis, terminat AMA posito M
tor cnqeuent e AMBC et  iisdem posito
C med. in AB, et A LG = AC. _L existente ab uno latere rectae AB determinatAL. B
im posised M existente ab altera latere tectae AB determinatur A
AMBC
pot
C med. in AB et  MC = AC, M existente ab altero latere latera AB determinatur A
Ergo cum non nisi lateribus differant ipsius AB ACB, rectaque ab utroque latera
opni se habeat eodem modo, congruent ALB et AMB. Rectam abtem ab e
uetroque laters
sechabe
ex eo patrt, quia alioqui punctum ad eam unicum
extra ipsam contra definitionem