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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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De Proportionibus Dialoeum.
2 A oetipondium; lubduplum = A, bipondium: Pric quident
distancia dirisionalis, ucrobique aequalis; nam cum A) 2A (2,
eum = A) A (2: ac in subductione lecus ett, quipDe 2A  A
 A
3at A = ZA = = A. Nonisicur, hoc sentu, eadem cset
urrobique rerminorum dictancia. Neque incerim dicerepoccst,
reductionem Faciendam esse ad communem vel ancecedencem
vel conlequentem, priulquam tiac haec comparatio: nam neqi
allehoc facie, cum dicic rationes Z _ =, (aut etiam Z _ =,
inricem xquales, quod cermini aequalirer utrobique ab inricem
distene. Nam raciones Z_4, ad communem conlequencem
reduea, CrunE, 2 _Z; ad communem vero ancecedentem
redueta, crunt 23 _ =3; ac neuero modo erune aequales tex-
minorum differentia, sed in alcera 12 = 9 = 3, in alcera
16 = 12 = 4. Incelligendum igicur erie, vel ad mencem luam,
de distancia divitionalis ex diritionis quocience altimandas
quam e nosagnolcimus racionis Gcomeeriex Fundamentum
CAC.
50 Nesamus camen, hanc dirisionalem distantiam, esse iplam
racionem, sire (ut loquitur) naturam e essentiam rationis Geometri-
cae: Sicut _ ance negarimus rehduale differentiâ cHe rationem
Arichmecica. P. A quippe ratio, ea quae ex hac distantia oricur Re.
lacio, que incerim, prouc hunc illumre cerminum relpicie, eR alia
acq; alia; puca tanuplo maius, D rantuplo minus. Atque hoc didicisse
Dotuerat ab co quem cicac p. 167. I. 2. Theone Smyrnaos
cujustaec verba Protere; iro ess so ves nd er, n ano r erds
ves ra so, casr er ni rd avrd, ndz) Erp. s uin sio
es 2d er, SiNaOO. 5) Erdsres ra so vous. Abinario
adunitatem, e ab unitale ad binarium unum idemque est intervallum.
(de incerrallo divitionali. loguitur; qualia Cunc intervalla
eFiCa;) Ratio autem diversa: binarii ad unitarem dupla: unitatis
ad binarium, dimidia, Fodem plane modo, quo Patris a Filio, ee
tilu a latre, idem eAincerrallum; ac diverta racio; nempe
Baecillius inversa; veraque ab eodem Fundaenco Orta.
6 Pettime icaque infertur, ob idem urrobique incervallum,
sive aequalem distantiam (dirisionalem,) aequales esse rationes
duplam e lubduplam. Ouipperario dupla 2, relatum dicie
correllaro suo esse duplo majus; ac subdupla Z; duplo minus esses
Eodem plane modo quo, binarii excestus t 2, indicae binario
majus esse; e binarii delectus  2, binario minus esse. AC nemo
Tobri