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# Title: [Differentiae in seriebus numeralibus constituendae ad instar regulae Slusii in figuris] Differentiæ in seriebus numeralibus constituendæ ad instar regulæ Slusii in figuris (shelfmark LH XXXV, V, 12, Bl. 1 - 4)
# Folio [2]r, page id 00066619:0003
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s
isferentiae, in series mimeralibus constituendae ad
instur regulae sta
14
iguris
it aequatio a = 3a + +a p
men non difficite. Kilicet:
N.
Ergo 3 a E
a8 a +1, a +2 seu Sa + sa p
112, 3
Hoc method.
sit da pB
api a a+ β. Ergo 2 sap a + a.
Ergo: 2a p dae + β. Ergo da  2a - β.
a +a 
3a
a
2
a
2 2a
a3 3a L
a+ 3a +2a
Ergo a 7 65a - 94- 7a
2
(2a-(3
it ergo da p β. erit
6
tori
ergo a =a integeu
a + 3a + 2a. Ergo sa, a +9a +7 a
ta 3a + 3a
e
La 43a - 9 da
u
=7 da. Ergo da3 1, 3a -9a + 9 B 3a -ga Fβ
2c
-
ZC
da 2a - β. et das 3a= 9a + (.
Hinc facite demonstratur pi si primae differentia ab a sint 1.
func
eundus ab a fore 2. tertias ab a3 fore 6. quartas ab at. fore
in fallor 124.
nempe. 1. 1,2. 112, 3.
Nam dd a  2β -0
6
2
12, B, 4
24
1V (3
dda3 6β 96a6a - 3( - 9β +0
Ergo ddd a2 116β-0-0+0 Unde facile patet
7
biud
latro cur non nisi
isti numeri, 1. 2. 6. 24. de. prodeant facti scilicet naturalium in
senevicem caeteris evanescentibus. i quia semper dβ 0. ex hypothesi
Hinc proposita eformula: a F +Ba + ea B N erit LN
3a - ga + β
ta
1
daN  6a = 12β
+ 2b6
intervallum B
ddd NB
6(
e
huius progressionis
Arithuraticae valde parvum non tntam duo ingentia commoda
+c
habebimus, unum quod omnis numerus intelligi protest cadere in hanc pro–
pressionem, alterum quod evavescent multa, ut dec fiet 3a. dafierba
E
mo si C tum parva est, nogligentur et differemtne disferentiarum
gusti
16777