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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 296, page id 826603459:0342
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296
De Proxressione Geometrica.
C AP. 33
MR -V; ergO R)V =M. IdeOque R) V XAR =MXN
= M9.
33 Trium ergo continue propor.
tionalium, dacis duobus quibulvis,
dacur ec reliquus. Cum enim, Per
praeced. AV i M g. FrIEA) M9 CV,
_V D Ba (A, _Y AV  YM9
 M.
Dacis Baculo
A) M9C
V) Nq (1
VAV =-M
34 Acque idem ralec de tribus quacuorre cerminis progret
lionis concinux, ucur non immedince proximis, modo equali-
bus incerrallis distancibus. Pata ( a. b, c. d. e. f. B. i eriu
ae n C; nam _ a. C. e  per 14. Item af  cd; e d e = b β3
_ Sic alibi. NTam a0c:: d. f. vel a. d: : c. f. _ B. d: :c. 8.
vel b. C:: d. 8. EEC. DeF 12.
35 Scd e praecedentium aliquoe converlae pariter demon
Arancur. Puca converla prop. 28. In concinue provortionalia
bus, (excepea cancum aequalium progressione, uF. I. I. L. L.
_c.  qua Be deinceos aliquocies excepta intellisatur;) le
duorum cerminorum incermediorum rectansulum rectansulo
extremoram aequecur; lunc illi ab excremis aequalicer ucrinque
remoti. (hoc ett, quot gradibus eorum alcerurer ab alteruero
extremorum distat, eoc ee reliquus a reliquo.) Pura. si lino
a. b, 6. d. c. f05. i Acquec e  a5; cocidem gradibus distant
anC, aCquC e, 8; item a. e, 219; c, 5. Cum enim duorum c, c, alcer
sC a Rd, alcex Rd) 8; adeOque Rd ) EXa Rd 
(Ce ) aB; aequalis erit uerobique Rd (uc dirisio _ mulciplis
cario le mutuo destruant) adeoque et distancin D verobique
aequalIS. Per PP. 13.
36. Ec converla Prov. 29. Si concinue proporcionalium.
incermedii alicujus quadratum aequetur rectansulo extremon
rum; aequalicer ille ab ucroque excremo dittac. Probacur,
uc praecedens.
37. Icem converla Prop. 33. Siunius cermini quadratum
equecur duorum rectangulo, erie ille medius inter hos Geome-
ericus. Si enim AV =M9 =-MM, Fric Caequalicer ucrinque di
videndo) A - MM
M
V _ A
M= V. ErBOAt. M. V i
38. Similicer _ Converla PrOp. 30. Si ex cerminis quacuors
duorum rectangulum rectangulo reliquorum aquen
TaTS