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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 18C
# Folio 52v, page id 00068193:0106
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Sect. 1. Cap. 3. De Ductitus
Causa, mudternativis aestimandis; ut si tres aestimatores à u
dice deputan rem aertiment, unus 8t, alter 90, tertius 96 num
morum aureoeum, medium pretium eligendum erit 267 seu 69
aureorum: Idem m’alea et aestimatiome spei obtinet. Eodem
autem modo et meduum. Geometricum inter plures quantitates
intelligi
potestcujus scilicet logarithmus est medium arith
meticum interi logarithmos quantitatum.
Serop. 18.
Applicatum totius resultans ex applicatus constitu
entium, est medium arithmeticum inter omnia appolicata
aequalium totius elementorum.
mt (
rg. 19.) ipsius AB elementa aequalia 01, 12,
23, etc. m quae ordinatim ducantur quantitates 0. 10; et
1. 11; et 2. 12; etc. Ut si elementa o1, 12, etc. sint partes
virgae, et quantitates 0. W0; et 1. 11; etc. sint ut partium gra
vitates speufiea, erunt partium moles seu pondera ut ipta
rectangula 10. 0. 1, et 11. 1. 2, etc. quarum summa est pondus
c
ga, dat BG gravitatem ejus speuficam (mediam) per def. 5.
Sed eum eadem sit rectangulorum ubique latitudo, idem prodit,
si dividas summam longitudinum per numerum elementorum
aequalium, quorum unum quodque consideratum. initar unitatis
nihil matit. Itaque BG est medium arithmeticum inter
omnes ordinatim applicatas 0. 10, et 1. II, et 2. 12, etc. Idemgs
est, et si partes iptius AB sumantur data quavis minores,
atque adeo st figura sealaris abeat m. curvilineam.
Prop. 19. Probl.
Medium Arithmeticum invenire inter quantitates nume
ro infinitas homogeneas, inter quarum duas quas vis alia et
Ips.