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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. LL. De Calculo Centri Ceravitatis.
Scomentis remotis AVO, seu ABO; aut ungulis Soliditre ce
spectantibus. Sed neque de Ongulis Solidisque quae Conclioeidem
totam spectant (utringue ab AC Porrectam) uae Contrum ora-
ritatis habent in ipla AC rectas
N exposica quavis recta AP, dicatur P volus, A vertex, punctumque quodris
intermedium C. Cenrrum, rectaque intinita C FIII (ad exvolicam AP perpen-
dicularis) Regula: Acque incellisatur A P recta (ad partes Pquantum opus cst
continuata) circa Polum P manenrem lic converti, ue C punctum in recta CFI
perpecuo mancat; punctoque sui extremo A, curram designet AOO: Hanc cur-
vam veteres Conchoeidem dixerunt.
pranitestum autem est, (Propter rectam PO, regulam CH Secantem in H,)
punctum O ad CHI regulam nunquam perventurum: Sed e (proprex HO per
pecuo aequalem ipsi C A, et sectionis angulum continue aCuTiOTEM;) eo tandem
verventum iri uc puncti O ab ipta CHI distantia Fucura Cic data quaris minox:
adeoque rectam CFIHI ad curram AOO Alimpiocam esse; spatiumque, inter-
minabile. Quae demonstranda erant.
Cenro C, radio C A, deseribatur circuli quaclrans C A R (quem Cenitorem ap.
vello) resula CHIHI occurrens in R; licque ordinatim applicata qualiber in Oua-
drance VB, in Conchoeide YO, (quadranci occurrens in B;) junxancur CB.
Manitestum est, (prOPter aequales C A, C B, HIO,) parallelas elte OB, HO,
hoc ele, CB, PO: adeoque ansulos ACB, A PO, aequales este.
Fst aurem VB, Sinus Rectus Anguli ACB ad radium AC; E CFI, hoc est
BO, ejusdem ansuli APO sCu A C. B, Pangens ad Ractitim PC; (quani F V-
centricitatem appello:) Hoc clt, ad cundem radium, uibi PC, CA, aequantur:
ad dirertos, ubi non aequantur. IIas cgo Conchocides Primarias appello; has
Seccundarias; et quidem vel Contractas vel Protractas; prout Rxcentricitas PC
minor est vel major quam Crenitoris radius CA, quam Micudinem apDello. Puta
in Ai8. 207. AOO est Primaria; Sccundaria vero, A00 Contracta, d A cco
Protracta.
Adeoque; ut in Creloide, Ag. 166. Ordinatim applicata qualibet b BV, com
Donitur ex Sinu recto BV in circulo genitore; et ex BB, quae respectiro arcui
aequatuT; nempe ipH B A in Cvcloide Primaria (cujus Balis f a r aequatur ve
rimetro Circuli genicoris,) vel in Sccundariis, (sire protracta line, lire contractae,
Tunili arcui alterius circuli; cujus nempe perimeter xequalis elt expolitae Oreloi
dis bati; (uc ad prov. 20. hujus ostentum elt: ). Sic in Conchocide Hg. 206. Ordi
nacim applicata VBO, componitur ex sinu recto VB (ad radium C R inseripii
Ouadraneis C AR) et ex BO, hoc cs C II, tangente correspondenris anouli; e
quidem ad cundem radtium, in Conchocide primaria (ubi PC, C A, aequancur;
sed in Secundariis, live protractis sive concractis, (in quibus PC, C A, non aeguan-
tur,) ad divertum; nempe, ad radium PC. Ouod icidem erac demonstrandum.
(Ec quidem num illud ante me quispiam animaarerterit, neleio.
Componitur itaque Semiconchocidale Spatium interminatum C AOOHY, ex
CA R Ouadrante Genitore, _ RB AOO, Figura Fansencium (diltorra) unius
quadrantis, Racio PC conreniencium, linibus vertis arichmerice proportionali
bus respondencium: Sed, quae alticudinem habeat AC Parirer aique componi
cur Semicycloidale spacium Ara fix. 166. ex Semicirculo Grenitore AD et
ADar figura Arcuuni distorca (linibus versis arichmetice proxorrionalibus re
spondentium,) ad eundem cum cireulo genitore Radium, in Primaria; ad aliur,
in Sccundaris; sed quae Alticuainem habeat eandem cum Crenitore circulo.
Hinc sequitur; In Conchocidibus divertis, ejusdem alticudinis, (incellige, qua
rum eadem sic ractii C A longitudo, seu magnieudo eadem quadtrautis Genitoris
CA R,) Sed quae inxquales habeant LXCCHErICitateS PC; Conchocidale spatium
(quod excra Circuli quadrantem est) RBAOO, (quam Tansencium tiguram
ele, jam ostendimus) vel eriam ejuldem altionatum quodris seomencum lordi-
natim applicata ableiltum) ABO, vel duabus ordinarim applicaris incerjectum
OBBO; in ea ratione majora elle rel minora, qua majores sunc vel minores sux
respectirae Excemricirates PC. Pam qua racione creleit vel desereseic racius P C
eadet
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