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# Title: [Johannis Wallisii SS. Th. D. Geometriae Professoris Saviliani Oxoniae, Tractatus Duo] Johannis Wallisii SS. Th. D. Geometriæ Professoris Saviliani Oxoniæ, Tractatus Duo (shelfmark Leibn. Marg. 103)
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19. 18.
E
CxCLOTDE
Defimtio.
Polygo sesacum CKclordi circumseribi dicieur quando
unusquisque angulus internus Creloidem concingir, acque idem
anseri dicitur quando unusquisque externus accingit.
TBeorema.
urra linea Creloidis primariae est quadrupla diamerri C eni-
TOTIS.
Sic Curra senicycloidis 00R, cujus Ba(IS sIE OD, Diame
TeF A D eaM CyCloidiS qUAI GCMIEOTIS A SD D. DicOCur-
vaI 00 A esse duplam ipSIUS AD. SInCGCEUE SIE CurVa vel
major vel minor duxlo AD. Ec SE sive excettus, Cire dete-
Etus X.
Genicori polroonum serratum inseratur, atque aliud circun-
decur, ica uc disterencia Cummae larerum urriusque sic aequalis ipti
Z. FE producantur Parallela Polrgonorum lacera ND B uc se-
cent curram in 00. Ee ductis cangentibus ou, ou circum seri-
bacur Cycloidi polrgonum serracum infinitum. Fc ab iisdem
punctis o ductis oc, oc, ica uc quaeque parallela Cic ei subten(a
AD gux in eandem e D parallelam incidic, inseratur Cyeloi-
di polrgonum serracum infinicum. Ononiam igitur ipla Ou can
sune Crcloidem, ergo Parallelae sune X aequales ipsIS D B FIN
oulx lingulis; e quoniam iplae oc parallele sunt, _ aquales
ip(S ND, ergo latera Polrsoni Crcloidi circumseripei aqualia
sunc lateribus polygoni quod Circulo circundatu:, et lacera poly-
soni creloidi inserri, ejus quod circulo interitur. Juare latera
Dolrsoni circumeripri simul omnia excedune duplum diameeri
excesu DC, Scilicer minore quam Z, ee curva quidem adtuc
minor est: ex lacera polreoni Cycloidi inserri deficiune a duplo
diamerri defectu D M, Scilicer minore qua Z, X curra qui-
dem adhuc major est. Acque idem demonstratur daro quovis de-
Fectu vel excessu Z. Frgo Curra semicpeloidis non est major
neque minor duplo diamerri. Froo curva Crcloidis primaeia
est quadrupla Diamerri Genitoris. Duod erat demonstrandum.
Corollarium.
Fodem prortus modo demonstratur, portionem quamcunque
curre, a verrice abscissam, ut oo A, duptam esse lubten(a AV
Ecilicet quae a sectione Basis portionis, _c genicoris ducitur.