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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 60, page id 797435492:0280
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E E C F. VTI.
bini, eodem ordine sibi respondentes, termini (puta D, P in prima, e
P, R in secunda) erit A : D. A - : F :: M =: P. M -3 R.
A. B. C. D. F. F.
Mt. IY. O. P. O. R.
Nam harum rationum utraque par est illi, quam habent ad se nnme-
ri N, M, quales in praecedenre delignari Tunt.
Eli vero Numeri N, M vulso rerminorum, quibus aptantue, expo-
nences, aur Indices vocantur, in sexie quaris proportionalium; quales
nos semper in sequenribus intellisimus, ubi liceras has achibemus.
XIII. Sint quaelibet quanta A, B, C; D, F, P continué prOPOE-
cionalia Arithmerice; nec non alia roridem, ab eodem termino A in-
cipientia, Geometrice proportionalia; siE au-
rem illorum secundum B non majus horum sc. A. B. C.. D. F. F.
cundoM; erit quodlibet in serie Geometrica
majus eo, quod ipsi coordinatur in serie Arich.
metica.
A. HI: BI. O. P: D.
EA enim A -)  NC 2M (vel C) 2B =A. 7. C. ergoNC C
undeM- 1 NL B -]C = A J D. F.Ct anteM A -]- OC, M - )
N. ergo A. I. OC. A + D. EtidedOL D. CrgO M. . OC
B. .D = A. ). F. FCE autem A. ). PC M f O. CrGOA 1 P
L A J F; adcoque P C P. Cimilique porro discursu quoad
velisa.
XIV. Bine, (I rursuS FuerinE A, B, C, D, R, F  Rrichmetice,
ec R, M, N, O, P, Q Cinc: Ccomerrice; sirque ulrimum Fnon
mirus ulcimo Q; erit B majus quam M.
Ntam li dicatur B non majus quam M; erit inde P minus, quam
conera hyporhesin.
Aceta; iildem positis; erit penultimum E majus penulrimo .
2V. Nam sI F = 9; constat ex praecedente Fore PL P (scilicetu
tranique seriem invertendo) sin FC Q. Poriori jure liquet Fore
E P
metica majus elt coordinato quolibet in lerie Geometriea; puta, C
majus est quam LI.
Es
-L. umenum, iildem poliris, quolliber in Perie LALMI
8
i