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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 13
# Folio 4v, page id 00068010:0008
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(30). Theorem. Majus majore est majus
minore. eu si a pi b et bpc,
erit a pc.
Nam quia a p b (hyp. 1) erit
(per 26) a = b + l. Et qui a (hys. 2)
bp c, erit (per 26) b = c + m. Qui
valor ijrius b substituatur (per 2)
loco ipsius b in aquatione inven.
la a = b + l et fiet inde a = c + m+ L
Ergo (per 26) a p C g. E. D.
(31) Froblema. Onvenire b medium
arithmeticum inter a et c id est,
ita, ut b tanto sit majore a
minus quanto est minore c majus.
Constinetio. Addantur in unum
a et c et summae ditridium enit
b, quaritum.
Nam quia (ex hype constructionis)
b et dimidium ipsius a+ c, erit
duplum b aequale duabus dinci-
dub, hoc est toti a +C, seu atc erit aequale duplo b, sive fiet
at C =b + b Ergo (per 20) a- b -b- c
id eet, erunt differentia extie
honum a medio b aequales,
sive excessus a super b aequa-
tur excessui b super c. 4. E. F.