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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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PFOD. XVII. DeChlculo Centri C arlatis
Oux quidem A ra Fesura dindum versorum, sumpiis arcubus arictintet
proporcionalibus; est eciam, alia consideratione, Fieura Arenum, Lumpris nemve
Sinubus Verlis arichumerice proportionalibus. Sumpeis ueigue A V, AC, A =, ec
Sinubus versis arichnerice proporcionalibus; (divila scilicee recta A a in parte
quocliber aeguales) qua ipsis occurruE recta Z V, dC, CZ, ecc. aqualibus inter
vallis diltitae lisuram Ara complences; hoc ellu eC, ed, ac eC. XQUanC areu
bus correlpondentibus, AZ, AD, AF, ecc. e sic ubigue.
Ductis jam in Semicirculo rectis Xa, Z o, Da, _c. dirimi intellisatur Semieir
culus in iocidem Sectores Aa X, XL aZ, Z. a D, _C. QuOTUM arCUS A X, XZ, ZD
Ecc. sine aequales; adeoque Sectorum Xa A, Z. ∞ A, D a A, eC. aFeUS A A, Z A,
DA, _c. arichmerice proporrionales.
Ouibus quidem arcuum aqualium Sectoribus A a X, = a Z, Z. a D, _c. respOn-
deaur, in tisura Sinuum verlorum, quadrilatera A aGX, XE(2, ZGd d, _c. ba-
sium aE, E6. 68, ecc. aequalium, cum inter se, cum ipsis AX ZZ, ZD, _C. a1-
cabus; (Droxter rectam a 2, Semiperipherix ADa, aequalem, ee similiter divilam.)
Adeoque arcuum arichmerice proporcionalium Sectoribus, Xa A, Z a A, Da A, _C
Tinilicer relpondebun quadrilinea XEo. A, ZG a A, d d’a A, balium acichmetice
provortionalium aE, a6, a8, ec
Suncque haec Ouadrilinea, Sectorum illorum, (Singula singulorum respectire
TUMPEOTUM,) dupla. Ouod sic oltendicur.
Incellisatur vel tora A Da Semiperipheria, vel ipsius areus AB, in partes aequa-
les numero infinitas dirimi; adeoque (duetis a diritionum punctis ad a rectis
Za, Z. a, EC.) vel cocus A Da Semicirculus, vel ipsius Sector Ba A, in toridem
Sectores dirimi. Ductisque, 2 diritionum punctis, rectis ZO, Z P, _c. tangenti
ra parallelis, incelligatur Sectori Inseribi figura ex cocideni Priangulis, OX a
PZ a, _c. Ductisque Porro eidem rangenei parallelis, AG, ZI, ecc. (productil.
que a X, a L, ec.) limilicer incellixacur sectori circumseribi tisura ex Peransulio
AQa, XTa, _C.
Dc similicer Figura Sinuum vertorum A+ a, vel toca, rel ip(us vortio BBa A,
(Sectori B a A correspondens) in toridem Ouadrilinca, ballum aequalium, (Secto.
ribus correlpondencia) distribui; (recta Scilicer a z, vel a B imiliter dirila, prout
diriditur AD a vel AB, arcus; ductisque rectis correspondencibus, 5X, 62, dc.
Ductilgue XO, Z P, _c. ipI Z a parallelis; inseribi incellisatur Ligura ex Paralle.
LoBraminis OXEa, DZC5, _cc. CFriansulis O X a, PZ a, _c. correspondencibus.)
Ductilque eidem =a paralelis A 9, XL, _c. (productilque 52 62, ecc.) C ir-
cum seribi incelligacur Fisura ex Paraltelosrammis A4Ea Xiha, _C. (Friangu-
NIS A Qa, X Ia, _c. correspondencibus.)
Suneque haec Parallelogramma Priangulis illis, (propter rectas Ae, X6, Z. C, dec.
iplis Aa, Oa V an _c. ex constructione aequales,) lngula singulis relpective
sumpris, aequealca: Tum quae Circum scripias, cum qua Inleriptas tiguras complent
Sunc aucem Inscriptorum Parallelosrammorum Bales, balibus Priansulorum
inscripiorum correspondencium, ubique majores; e propierea P’arallelogramma
Triangulorum, (singula lingulorum respectire, adeoque de omnia omnium.
plusquam dupla. Fs utique Parallelogrammi OXEa, balis XO, Peu Za recta,
hoc elt, (urpore ipsi aequalis ex constructione) arcus X A, major linu syo XC
(base Frianguli correspondencis;) uc patet. In reliquis aurem; WC PZCE: Pa
rallelosrammi balis ZP, leu SE, recta; (aequalis arcui Z X, ex constructione) est
major quam Z. X chorda: Sed et haec major est quam Z. P, balis crianousi cor.
relpondenis PZa; proxier angulum Z. PX (Frianguli PZ X) illi oppoticum
majorem angulo huie oppositO Z XP. PA enim angulus Z PX, vel huic aequalis
PXO, HoC clt, a XO, angulus in letspula areum subcendens (in opposico Se-
micireto) aequalem arcui Za; _ ansl L. XP, hoc elt, Z Z a, ansuluS icem
in Peripheria, Subrendens arcum Z. 8, (dreu X a minorem;) elt igicue anguluS
PZO, hoc ct angulus Z PZ, major ansulO Z XP; adcoque Z X recta, major
recta Z. P; _ mulco masis Z X Curra, seu huic aequalis (E leu ZD balis Paralle
loerammi, major erit quam eadem Z. P balis Friansuli: adeoque Pacallelosram.
mum Fetans Plusquam Duplu. L lbique. ER icaque PiBUTA Cx Pa.
inserlpra plulquam dupia lelila ex Priansulis inseripia sire con Semicireulo, sive
(69
70
rallelosraminis, live eori Figura Sucuu vectorum, sive iptius portioni AZC
declori Ba A.
LCCCC2
S