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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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LCL. OIVe.
cur adhuc plato etsipeico f d quod plano fCP rectum lir; Semisuperliciei illius
semistis TS FZ C X P aquabit Semicycloidem C AF; (nempe Semicirculus balis
CZ P tig. 2. aequabir Semicirenlum C Z F tig. L. es Superticies Curra PSF ZCF X
quabie cxiluIcum C A P Z.)
5. Nam, Sumpro ubiris in Creloidis axe puncto Y, unde paralleta BaSI ducatuF
Y2Z: rectae C X in aXC CyClONiS LumaCuT C Z aequalis in diametro balis Cylin-
drica, unde dueatur Z. lateri CF parallela, diasonali FP Occurrens in v; d per
punctum, plano bati F ZC Parallelo, puta vec, secetur superticies Ciylindrica
sectionem exhribens sc arcum circuli, quae (propter parallelaS) CongrueE arcII
2 C in basc Csinc hde et alem LC cirenli renitoris, adeoque 2Z. rectae aequa-
lis, (Sicurve congruit rectae X2. Sive inbale Cy lindri sire in circulo generante.)
Duod cum ubiquetiac, erunt omnes currae in luperticie Cylindrica rE F Z CP, ipl
Cparallelae, aequales rectis omnibus ipli ZC. Parallelis in Prilineo Cycloidis C A F 2,
ee lingulae lingulis, ee limiliter polux (in cildem pura Cire 2 bale sire a vertice
diltantiis:) Adeoque, propter aequalem etiam ucriulque tioura alcicudinem, tioura
tigurae aequasto. Iperteles CMaa plano Frilineo; (led e seomenta illius re-
spectiris legmentis hujus, ut paret:)  li addaneur urrobique aquales Semicir-
culi C. 2. F, erit agpresacum aggregaco aquale, et duplum duplo, quadruplum qua
deuxto, ac. Hoc elt Superticies FSFLC YF, Semiereloidi AC. L; et Semisuver-
tieles exlindri (quixpe ictius alpu) Cycloidli ACDf; e cora superticies, hujus
6. EIL iisitIE Cfcloi A C. DF, ehculi genitoris cripla. Ouod sic colligitmr.
Cstindri incexri modo cspolut Lufscurra, aequatur facto ex alcirudine (qua
aqualis elt diameero Batis) in Batrs Circumterentiam; adeoque elt quadrupla Cir-
culi balis: Cui Si basis vrraque adperatur, agoresacum erie, baleos (hoc est cireuli
genitoris) sexcuplum. Fst aurem, ue supra oltensum est, duplum Cycloidis: F. P∞O
Crclois ipsa est circuli Genitoris Lripla. Nempe Prilineum C A F 2 Semicirculi
DFEFZCYF, Secetur actum plano 27 X, quod sic plano elliprico FSF u
Parallelum: Superticies abscista VC YZ, aequabit legmencum Cycloidis CXZ.
Nam, propter Cylindrica superticiei sectiones parallelas, congruet 72. C ips F3C,
hoc est Trilineo CZ L Cycloidis; sed e C. I2 urrobique aqualis; F1GO aBBrC8 2.
8. Si supex Cycloide CD erisatur Semieylindrus rectus, sire Prilina, (utro-
ris enim nomine dicatur perinde cst) altieu-
dinem habens C a duplam rectae AD; quod
peraxem secet FC a planum, sectionem in
lacere taciens C. a rectam; cui plano incelli-
Batur planum aliud recte inlistens, per rectam
Fae cranliens. Polidum abscindere D A e CD:
Tluic Polido aequatur Poridum factum ex con-
vertione Cycloidis AC. D circa rectam A D
Cum enim lic A D aequalis peripherixe diame.
tri F C; erit iplius dupla C e, aequalis peri-
Pherix Semidiametri F C; adéstue (Propter
angulum F C∞ rectum) criansulum P C ∞
aequatur circulo ex convertione racii FC
Facto. Ec limiliter ostendetur criangulum
XZ E aequale circulo racii ZZ: e bc ubi-
quo. Frgo omnia Priansula omnibus cir-
culis, adeoque solidum lolido RguatuX, S
sexmenta scomentis respectire sumprio: Pura,
tur solido ex convertione plani Z Y C cirea rectam Z Y Facto. Nam _ Hic c0.
dem modo oltendetur, teiangulum un d aequale circulo radii or; de de reliquis simi-
liter.
. Simili-
perticies curra, dupla crilinei C. A F L: d Ex denique si ea Semituperficies bilece.
Crclois
Circula
pripla.
dupla. Duod crat propolicum.
C2. F duplum.
cu axpresato aequale
7. POTTO, S expolica quae prius superticies (nempe, Semisupersicei Cstindricx
Sogmen-
cum CxZ. Semiss
solidum Z Z EA, Solido ex convertione plani ZZ A tacto; &e sic ubique: Frem
Prilma LLEvPF Tolido ex converlione Lalallelosrammi XZ. PF; adeoque et
Tolidum Z X C ev E Tolido Cylindrice excarato conversione plani Z. Y C circa rectam
A F facto. Sin achue secetur plano EdL Val Parallelo, Peementum e Fun Xe quabi-
Solaum