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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)
# Folio 3, page id 85138403X:0019
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DE
CxCLOLVC.
Screpatum dggregato aequale, et duplum duplo, guadru
eriL. 880
plum quadruplo, ec. Hoc elt, Cuperticies rSF ZC Y li, Se-
micrcloidi A C F; ee Semisuperticies Cplinari (quippe illius
supla) Creloidi AC D F; e coca superticies hujus dupla
Qod erat propolicum.
6. FRigitur C Yclois AC D F, circuli genitoris cripla. Duod Cyolois Cir-
Eic colligitur. Cylindri inceori modo expolui superticies cur- culi triplas
va, aequatur facto ex alcirudine (quae aequalis elt diamerro BaliS)
in balis circumterenciam; adeoque elt quadrupla circuli balis:
Cui si basis urraque adjiciatur, aggregacum eric, baleos (hoc est
circuli genicoris) sexcuplum. Est aurem, uc supra octensum est,
duplum Crcloidis: Ergo Crcloisipla est circuli Genicoris Pri-
Pla. Nempe Trilineum C AFZ Semicirculi C Z F du
Dlum.
y. Porro, l expolita quae prius superticies (nempe semisuper. Sermentum
ficei cxlindrica Temissis) FEF ZCYF, secetuE ad huc plano CY Z.
2y T, Quod sic plano elliprico FSr uparallelum: Superticies
abscista  Z C T2, aequabic seomencum Cycloidis C Y Z. IIaM,
propcer Cylindricae superficiei sectiones parallelas, congruet
22C IPAFE C, hoc est erilineo C 2 J. Crcloidis; sed e C. Y2
urrobique equalis; Ergoaggregacum agoregato aequale.
8. Si super Crcloide A C D erisatur (uc in A9. 3.) Semicy- Sotan nals
lindrus rectus, sive Prisma, (ueroris enim nomine dicatur per-  D.
inde est.) alcicudinem habens C 8 duplam rectae AD; quod pec
axem secet LC a sectionem in lacere faciens C o rectam; cui
plano incelligacur planum aliud recte insistens, per rectam F a
transiens, Solidum abscindere D A e C D: Fuic SOlidO RGUAEUE
Polidum factum ex convertione Cycloidis A C D circarectam
AD. Cum enim sIE A D aequalis peripheriae diamerri F C; c-
ric ipsius dupla C’a, aequalis peripheria semidiamerri FC:
adeoque (proprer angulum F C _ rectum) criangulum F C ∞ X
quatur circulo ex convectione radii F C FaEO. EF similiter ollen
decur criangulum ZZ E aquale circuloradii ZZ: FF sc ubique.
sireo omnia criangula omnibus circulis, adeoque Tolidum solido
aequatur, ex segmenca seomentis respective sumptis: Puta, Toli-
dum Z ZE A, solido ex convertione plani Z Z. A Facto; e sc
ubique: Irem prisma XZ Ev Y F solido ex convertione paralle
logrammi Z Z X F; adeoque ex solidum Z. Y C _v E Solidocy-
lindrice
Fig. 3.