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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 320, page id 826603459:0366
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320
Elemenii guinti Fuclidis declaratio.
L. a1199
ipsarum aeque mulriplae; (REMDEDET N ) Propter aequalia aequali
BuS ablaca,  Palll.
ed
+=  uy
C =- M 3
U3
7 SEquales ad eandem, eandem habent rationem, e eadem ad aequa
les. PuTa ( A == B, erie (aequalicer dividendo)
e
edeoque A. a:: B. a. Icem A = B, adeoquea. A : : a. B,
Vel AC (A OpuS) per lenma nottrum; Guia R A =- B eric 8
A a = aB.
8. Inaequalium major ad eandem, majorem haberrationem quam mi-
ner. Et eadem ad minorem, majorem habet rationem quam ad majoreme
Nam
A Z F
A
F
a C= a a a Item A FF A Ouipre
crescente Diridendo creleie quocus, Sed crelcente Dirilore, min
nuICUE.
9. Duae ad eandem eandem habent rationem, sunt inter se aequales:
e ad quas eadem eandem habet rationem, ipsae item aequales sunt. NV am, (1
a à crum (mulciplicando per a) B =A. Icem, (I
at
A = D adeoque (per COrOIL. PF.4.) a a D erUnE_ A =B,
uE Prius. Vel perlemma nostrum, AA. a:d B. _. vel a. A: :
a. B. Crit A a = a B, adeoq; A = B.
20. Duantitarum rationem ad eandem habentium, quae majorem ha
verrarionem est major; ad quam veroeadem majorem habet rarionem, illa
a t
minor est. NTam H B major quam B, Duta aequalis B
erie, aequalicer mulciplicando, A(= a F E) ~ a. Tcem. L
A minox sic quam a pura a qualis a FE (Per Pr. 8. d exie Pex
COF. PP. 4.
e tc
Badeoque A = a
a2 Ma+
et