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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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PFOPXXXI. DeCalculo Cenri Cravitatis.
Duae aurem Fyperbola, TTOO, H00, sie compotiixe; veur similes Fint, et gul
dem quamris (ut in Primaria, tis 326.) communem habennt Aris Verricem II:
non camen eandem concinuane Curram hyperbolicam; sed Angulum in EI Faciune
producteque, se mucuo secabune,) Rectum quidem in Primaria: Acutum, in
Protracta: Obculum, in Contracta; magisque vel Acutum vel Obculum, quo ma-
Sis vel Prorracta rel Contracta Fuerit: adeo ue in ralde concractis, fere videaneur
Una FaCOTE COnFIHCIAM CUEVAM.
Pomuntur enim (si8. 326.) HOO, Hao, semihyperbolae, sieu distorco; prop.
ter dirempra puncta C, u; (qua, ut OHlo Foret una hyperbola, idem elsent pun-
Ctum nempe commune centrum semihy perbolarum F10O, H00;) converoenei
bus punctis M, 1; 2deoque e O, o. Neque est AH urriusris vel Axis vel Diq.
metrorum ulla: UEDOTE Gua Per C crantire debeu omnes quae spectant LIOO; e
Der n quae L100 Spectant.
Si vero, in figura Primaria, (Proptex EI verticem Avis, manente communi
Duncto F, diraricari incelligantur currae Oo; simulque Asmptoca in MV do-
nec in unum cocant K, n pnncta; cranescet angulus ad II, tierque oF]O una H-
verbola. Sed non item in Secundariis, (in quibus FInon cA rertex Axis:) POF-
nelcente ansulo ad HI, coeant in unam curram, at non in unant syperbolam (Led
duarum porriones.) Manifestum enim est (ex constructione) II) PerDOtaS L100
e HI00 omnino similes esse et congruentes: tieri aurem non vocelt in usso pe-
bolx puncto, praecer iptum AXis Verticem, ut curra utrinque adjacentes con-
gruant.
9. Verum hic carendum estne existimetur OTIO Fg. 326. eadem curra cum
ocootis. 186. Duanquam enim AaO gc sic oriam figura Secantium, (sed COn- F18. 186.
Eracta, PrOpEeE AO minorem quam AC,) uE SB. prOV. F7. insinvatum elt: SINL
tamen illa (non ut hic; Secantes finibus vertis, leu complementorum rectis, Sed)
Sinibus Rcctis, arichmerice proporrionalibus respondentes Sunc chin AsiC Fecta
Vo=
(sinibus rectis s = V B, areuum AB, FCCIPTOCX; ) HC reco, ==
iptis a = VC sinibus complementorum B D reciprOcK.. HoC est; Sumpiis A V
arithimetice proportionalibus; spatium complentes recta VO f18. 326. Tunc arcuum
A B Secantibus C T Ag. 327 proportionales; sed
V ctis. 186. Proporeionales complementorum BD
Secantibus C. 7.
20. Cumque Fints =V: R= = v2. Si Tuman-
tUT N =C. V, (ad Coque _ V = AV) arichmetice
provortionales; crune omnes s, ut rectarum in
varabola, axi parallelarum radices quadratiex, seu
in iplarum racione subduplicata; puta quae sine
in rectarum VBfis. 264. lemiparabolam complen.
tium ratione subduplicata; (cum enim rectae RS
complentes semiparabolae complementum Cint ut
x2 quadrata primanorum; crune harum concinuationes V B, axi parallela, 
R= = x 2; sUPIO AXC ut RE: ) quaeque, ex iltiusmodi radicum reciprocis consta-
cur Figura, est ipsa C. A Octis. 186. Omnelque s2, lune ut iplae recta axi Para
bolae parallela. Pura, ut ipsae YB fB. 164. (vt p. 212. Arichm. Insir. de BV.
PrOP. 25. hujus Cap. 5. Ostenditur: ) acque harum reciproca,, E 3. funE ut rectarum
Va ((8. 186.) = vel = quadrata, seu ve carum mementa respectu Aa; aUe
circuli earundem conrertione circa A. Facti. Rectarum veto V9 = = fe. 325
CrO e
Cspatium hyperbolicum complentuum) qadala Leu momenta, U=, TuM UE Ip.
Tarum BS (Fig. 264.) rectarum reciprOCX. OuX aurem SyHE iplS Pb fi8, 264. vel
VP F8. 178. orclinatim applicacis in parabola reciproca, Fync ut Va figuram A aO co
tix. 178.) complentes, curvae Cseloidalis pextienlio (concinue Lumpiis) pro-
porrionales: