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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)
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C A P. 35.
Elementi quinii Euclidis declaratio.
32-
22 Duae eidem eedem sunt ratiores, inter se sunt eauem. Nars (I
a B
y erit a y
22. Si sint quorcunque quansitates propertionales; ul est una antece-
dentium ad suam consequentem, ila es emres antecedentes ad emnes con-
seguentes. EAtO a B vy _C. = R. PrICIBITE A = R0
B =R B, C = R y _c. ad c09; A F B + C _c. =R a + R B f
Ry _C. = R in a + B + y _C. Ideoque (a qualicer dividendo)
A F B +. C _C.
a F B+7 _C. = R = a Vel AC A. RA:: A F B F C, BC,
(R in A FB + C_C =) RA F RB F RORC. BE PALCE. AUE
per lemma nostrum, quia A in RA + R B + RC _C = (ARA Z.
ARB F ARC _C =) RA in A FB F C _c. EA aucem haec univer-
Talis proposicio ad prop. 1. Ouod enim illic ostenditur speciacim
de Racione mulcipla; hic oltendicur unirerlalicer de qualibet
racione.
13. Siprima A, ad secunuama, eandem habeat rationem quam terria
B, ad quartam B; terria autem ad guariam majorem habeat rationem
quam quinta C ad sexiam y: habebit es prima ad secundam majorem
rationem quam quinta ad scaram. Namm a (.
+E
e
q Vetic.
24. Si prima ad secundam eandem habeat rationem, quam terria ad
quartam, sitq prima major quam tertia; es secunda quam quarra major
erit: P aequalis, aequalis; A minor, Monor. E AO a B Siau
LeM A = B, eric e
a 3 er8Oe B C=
adeoque a = BPer PF. 10. Vel SiC, quia A. B:: a, 6. Ut dein-
ceps oAenditUF DEOP. 16.
25. Partes (aliquoiX) inter se comparalae, eandem habentrationem
quam habent earum aeque muliplices inter se. HOC