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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)
# Folio 457, page id 851387705:0477
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Porerir, si luber, lector non magno nesoro vel hac ipla lemmata in Theoremata
formare, vel alia his similia seguencibus sertebus aptare, _ ad ca quae jam cradi
dimus actenderie.
Sed de alius adhuc est (A varierate lector delectetur) series has ordinanci mo-
dus, qui etiam aliquando non minus erir accommodus: Si nempe nec ab 0 (ut
in figuris inseriptis,) nec ab + (ue in tiguris circum seriptis,) sed ab intermedia
quancirate, pura Z, series inchoetur, (adeoque tiguram reprasentet quae inseripta
e circum exiptae est intermedia, Eire major quam inseripea ec minor quam cireum-
seripra:) Vr Cicus verhi gracia, leries primanorum Z = FZ f. 22 f 3 = ec. vel (quod
eodem recidic) x F 3 F 5 = Z ec. Quo casu lemma sic erit ordinandum, pro
Serie primanorum.
L15i
PTOB. CLXXXTI. TNEENLTORUM.
esreet Eos. isee
Et lumiter ad series sequentes, suous ecemetu abitineo ne lim prolixus.
i i
  +
4 +
5 + 6
+
+5 +
8 +. 8. +8 + 8
 Arque he qu Modus omnium optime convenit pFop. 25, 26, ubi Risuram
Spirali adjacencem cum Parabolica comparamus. Nam s in Heura spicali, ductis
quorlibet rectis MT angulos tacientibus continuos inricem aguales, li in lingulis
spatiis sectores inseribi supponantur, erunt corum arcus, ut 0, 1, 23 3, ec. Tin
circum seribi, UE 2, 2, 3, 4. _c. E vero ita adseribi
ut sectorum arcus d spirali BiseCentUx, CrUNE UC Z,
3, _c. vel ut +, 3,5,7, ecc. (nempe ue
aitterentia numerorum, quadraticorum:) adeoque si
arcus illi (sire numero intinici Cire finici, quamris
ibidem de intinicis cancummodo verba lacta Cinc
adeoque hanc curiolitarem illic omictendam duxe.
rim,) supponantur in rectum extendi es invicem
ContinUArI ut Fiant coridem segmenta diametri para.
bola (continue polita;) unde cracant diametri in-
TETCCPCA F, 4, 5, 16, etC. (nam 1 +
+
L5 = 9, _C.) quibus conreniant ordinatim appLI
catae (quipre in diametrorum ratione Tubdupicaca)
quae crunt ad invicem, uE L, 2, 3, 4, Scc. hoc est ut ipta recta MIF, MI F, ec.
in tigura spirali rera per limilium sectorum terminos cranscunces.
finitis (quod nos illic fecimus,) led eniam ex numero tinuis conclatam, spirali ad-
jacentem, cum fixuta ex cocidem parallelosrammis adjacente parabolae. Ouod
guidem (sine nova figura) Patis incellixi poterit. Si illi sectorum aleus ponan.
tus Ta, 3 a, 5 an ec. radii vero, (ipliS proportionales) 2r, 6r, LOr, ecc. erunt
sectores Far, gar, 25 ar, _c. (nempe semilles paralselo grammorum radiis et ar.
cubus respectiris contentorum.) Sumptis item in parabola diametro continuis
Tegmentis Fa 2 a 5a _c. adeoque diametris interCePFIS. + a 4. a (= X a L. 3 a
Da (= 4 a-F 5a) _c. e ordinatim applicatis quae illis diameeris conveniant (in
si
aeque alca, sed quorum alcitudines sint Arichmetice. proporrionales, ut 1, 3, 5, d
UE Patet;) Parallelorramma spaciis illis inseripta erunt La X 01, 3d X21, 5u2417
ec. vel Oar, 6ar, 20ar, _C. cireum (exipTa, CTUNE L a X2Y, 3d X41, 5dXOr, C
vel 2aY, T2aY, 30ar _c. nis aurem intermedia parrim IINTETIpTa parUIm CIF-
cum leripta, (qua nempe eam habent lacicudinem qua est Arichmerice media in-
M in m
2. + 32
F 4 1 +
Aique hoc pacto comparare licet, non modo figuram ex sectoribus numero in-