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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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ARTTHMETTCA TTOB. CAAXV.
dii Eit
Edsi La et so stobi
od et t. s 151
2t
tit eode  Coroatum.
Deoque Semi Circulus ad Duadratum Diametri, (vel etiam Semi- Fillipsis
ad Parallelocrammum Fllipsi circumscripium,) eam habet rationem quam
habent Radices quadraticae universales Residuorum seriei. Primanorum serie
Secundanorum mulitatae, ad seriem Primanorum illorum maximo aequalium:
Totus itaque Circulus (aut Fllipsis) ad illud Quadratum (vel Parallelo-
erammum) rationem habebit illius duplam.
=3E es
InIEx
ideoque V
vel
Ntam si diameter circuli (vel etiam
Cllixleos) ponacur D, (cujus pars intinite
  1
PacVA  = a,) eijque ordinacim. axpli.
centur infinitae rectae (requatitor ab in-
vicem distantes) Temicirculum (vel semi-
elliplem) complentes; crune illae (ut
nocum clt) midia proportionales (vel
Taliem in eliph mediis illis provortiona
libus proporcionales) incer camerri 1es.
menca; Puta
D 3 a 3
4. 
N. 2a0- 3a. Y. +a B - 16 a dc
V: CD-= C2
V. aD = d
cidem ipsi VB aegllau puta ad quadracum Diametri (Tallem ad diametrum
in alricudinem ductams)
uc V: a D = ~: = V: BD - B: = V: CD = 52: = 8c. usque ad V: DD = D
ad YD +  YD F  YDE + _c  = AYD = AD
Ideoque circulus intexer, ad idem quadrarum, ut
nid 2 y: aD   _C. ad AD.  sB gileg n teO
16
aigis sid 1.1
pt curcrs al se
P R OP. CZXXVI.
Corollarium. 
L proinde Si supponamus semparabolae cujusois insinitas rectas (or-
Mnatim applicatas) in ejuscumo inverso situ positae respectivas rectas
duci; quod provenit solidum ex ihsolatis illis Rectanculis constatum (vel ex
ducdlatis, aut aliis quidem fieute sinitibus, quae rectaneulis illis aequentur,
erit ad aeque alium Parallelep pedlum coneruum (nempe cujus basis aequetur
Duadrato basis. somiparabolae ut Semicirculus ad Duadratum Diametri-
Li quidem mediae proportionales erunt in subduplicaca ratione ordinatim.
applicalarum in Circulo vel L lips.) Sic eadem parabola A PO sicu directo,
et P A a Titu inverlo potita: crune ivicue
(ex natura Parabola) Gractrata relinatim-
applicatarum (nemve rectarum LD, DC ec
doscendendo; vel Ihco, D0, cc. aicendendo,)
intinita Cexies Prrmanorum; Puta a, 2a, 3a-
_c. vel corum loco a, b,C, _C. quorum ma-
ximum dicatur L(cumpe quadracum ba(IS
PO vel Ac:) Ec propterea, eadem inverlo
Tieu erune  = an L = 2 a, D - 3a, ec.
vel etiam D-
d
d
c, ec.
(A quale enim elt lingulorum incremen.
tum,
pidts P. R O R.  CXKZV.
V: aD a
Adeoque omniuu aogrexatum, hoc est semicireulus, (vel lemi elliosis) ad to-