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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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TFLN
lFOD. XI.
Cum enim (proptet aquates angulos) iplae
reCta MT, M V, SC. GInC UL L, 2, 3, 4, ec
(per constructionem Spiralis:) ec propterea Spi
rales MIF, MT, _c. (iltis rectis contermi-
nX) sinc in rectarum ratione duplicata (per
DEOP. TT.) NEMPC UE X, 4, 9, T6, CC. erunE ipIa
legmenta continua, ML, TY, _C. ut 2, 4
9= 4, 26 - 9, Ouod erat demonstrandum.
SCHOL. ZVM
Foca hac de longicudine linea Spiralis doctrina; continuis quatuordecim pro.
policionibus jam cradica, est, apud Archimedem in libro de lineis Spiralibus, pe-
nicus omitta: Neleio an ab alio quoxiam ex recentioribus tradica tuerit.
e ROP. XIX.
Lemma.
tul
T PrOBON selles Suantitatum in duplicata ratione Arithmetice.
 proportionalium, (sire juxta seriem numerorum quadraticorum.)
continue crescentium, à puncto vel o inchoatarum, (Duta UE O, L,
An 9, etC.) propolitum sic inguirere, quam habeat illa rationem ad se.
riem totidem maxima aequalium:
Fiac inrestisacio per modum inductionis, (ut in PTOP. L.) eritque
0 + X= Y
+ F = 21
0+ F + 4 +0=24
O+ x + 4 =
+ + 4 + 4 = 1 2 = 3 f 15.
9+ 0+ 9+9- 36 18 5 1 15.
0 ++ + + +9 +26= 30
26+16 +16. + 56 +26 -808 2 5t 2.
0 +F + 4 +9 + 16 + 25 = 55
25 +25 + 25 + 25 =25 + 25 =450 3
0 f F f 4 + 9 = 16 F25 +36 = Or
5 + 2
36 + 36. + 36 + 36 + 36 + 36 + 36 = 352 30 = 3 + i.
Et lic delnceps.
Pacio proveniens est ubique major quam subcripla, seu J. Fxcestus aurem
DErpCTLO dCCTELCIL DTOUL NIMETUS EETINOTUM AUIS CIIE, DUT 53 133. 183 213 263 35, _C
aucto nimirum tractionis denominatore, sire consequente rationis, in lingulis Jo-
eis numero senario, (uE Patet,) ut sic rationis provenientis excettus supra sub.
rriptum, ea quam habet umicas ad sexcuptum numeri cerminorum pote 0. Ad.
coque-
PROP. XZ.
Theorema.
LPoponatur series quamicatum un duplicala satione Arithme
rum) continue crescentium, a puncto vel o inchoatarum; ratio quam
habet illa ad seriem totidem maximae aequalium, subtriplam supera-
bic; exitque excessus, ea ratio quam habet unitas ad sextuplum nu-
meri terminorum post o; sire, quam habet radix quadratica termini
primi pott o, ad sexcuplum radicis quadraticae termini maximi.
A42 3
cice proportionalium (sire juxta seriem numerorum quadratico-
Puta