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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
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TIMD
C A l2CL L.
S I V F
NOrA AELHODOS IHOBTREHOI
in Currilineorum Ouadraturam, aliaque
Difficiliora Matheseos P roblemata.
PRO P. I.
Lemma.
Y proponatur series Ouantitatum Prithmetice proporcionalium (sire
juxta naturalem numerorum consecutionem) continue crescen-
tium, a puncto vel o (ciptra, seu nihilo) inchoatarum, (puta
UE O, 2, 2, 3, 4, _C.) Proposicum sic inguirere, quam habeat ra-
tionem earum omnium axxresatum, ad axeregatum tocidem maxima
aequalium.
Simpliciltimus investisandi modus, in hoc et seguentibus aliquot Problematis,
est, rem iplam aliquousque praestare, de rationes prodeunces oblerrare atque invi-
cem comparare; ut inductione tandem univertalis proposicio innotescat.
Es isitur, exempli gracia,
0 = 2+ 2 + 3=6
3 + 3 
= +2
0+ c + 2 +3 +4 +5 = 75
+ 5 +5 +
+
+
10
0 = T
0 + r + 2 =
1 2 + 2 =
O = F + 2. + 3 + 4 = 20
4 + 4. + 4 + 4 + 4. = 20
0 = 5 + 2 +3 + 4+5 +.6 = 27
6+6+6 +6+6. + 6 +6 = 42
Et pari modo, quancumlibet progrediamur, prodibit semper ratio subdupla. A-
deoque-
PROP. II.
Theorema.
U7 sumatur series quantitatum Arichmetice proportionalium (sive
juxta naturalem numerorum consecurionem) contimue crescenti-
um, a puncto relo inclioatarum, et numero quidem rel tinitarum rel
intinitarum (nulla enim discriminis causa erit,) erit illa ad seriem cori-
dem maximae aequalium, ut 2dd 2.
Nempe, Si primus terminus (LO, secundus 2, (nam si secus, moderatio achi.
vencta erit) e ultimus l, exie summa-, = Y (erit enim, eo Casu, RUETIS LT.
minorum I. + L.) Vel, (polico numero cerminorum m, quancuscunque sic terminus
Sccundus) Zm 
PROF.