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# Title: Qua Continentur, Oratio Inauguralis. Mathesis Universalis; sive, Arithmeticum opus Integrum, tum Numerosam Arithmeticam tum Speciosam complectens. Adversus Meibomii, de Proportionibus Dialogum, Tractatus Elencticus (shelfmarks Leibn. Marg. 84:1, Stück 1; Leibn. Marg. 84:1)
# Folio 332, page id 826603459:0378
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Elementi quinti Euclidis declaratio.
CAP: 3S
34 Si sint quorcunque quantitates, A, B, C, XC. aliaeque ipsis nume-
r0 aequales, a, B, y, _C; (orq. majorrario primae priorum ad primam pon
steriorum, quam secundae ad secundam, e haec major quam terriae ad ter-
B
iam, es sic deinceps: _ = B =  _C. Flabebunt omnes priores
simul, ad omnes posteriores simul, majorem rationem quam omnes priores
relicta prima, ad omnes posteriores relicta prima: Minorem autem quam
prima priorum ad primam posteriorum; Najorem denique etiam, quam
ultima priorum ad ultimam posteriorum.
et
Suncoprimum ucrinque dux, A, B, _ a, B. Ononiam igitur
A +B
e
A + B
adeoque permutando  pd e componendo
a +6
E Pric, permutando, _ Per DrOP. 33,
a +C C= B)
a Dux erane probanda. Et similiter
BLC
probandum erie B L 7
C+ D
2 F st
P
st
C
3 = Y
L
C.
y
2 2
B
L
La
Icem
Fchcabiriss
R
Secundo, Ponantur utrinque tres, a
permembrum primum à lr B
B
B
C
 Ouoniam
BFC
B+ 33 exit permu-
AFB +C, a+et7
tando BFC CF7 e componendo B +C
t
+y
icerum que permucando, e per membrum primum, et Per PF. 33.
Erit
A. FB + CC
B F C
a + B+ 3  6 + 3
C
).
A
a quae eranc de-
B+C + D C.
monaranda. E.c similiter probabicur 6 + n + s
C+D
 +s
3
a
Fodem