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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)
# Folio 557, page id 851387705:0577
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1
L.L Llnarouos.
Nescirisse liquidem videtur, curram ABC H5. 7.
non aliam esse guam F. IipLI LGF Fg. 2. in planum
expantam. Si aurem centro C, diltancia Cili, in su-
perticie cylindet fi8. 2. Cemi ductu deleribatur
FRque hXC, ni Fallor, ea curra quam Gycloidis Comitem vel Dociam (la Com. Cyet
Paene de la Rouleste) appellat Auchor Fistoriola, utur aliter apud ipsum acque socia
me generata. Onam enim ille dimtolam aulta alnt in superficie Cplindri rect
descriptam dicit; nos simplicius sectione Cylinari pland sudm locami defexibimus.
linca, non eti illa LE Lpo (communi plani
et Cylindri sectione tacla, sed alia curra, com-
muni Sphaera le s te facta, quae in
planum expanla omnino LS erit curra BC
tig. 7. prioris LeH. Si enum MceMgatur, (in Fig. 2.
FCF circini auctu deseripta, deleoque C8 recta
ubique ips C. L’aequalis, unde aenicta G2 in super
Ficie cylindri occurrat basi in 2: Ouia cum C. Z E
2F Subrentae, tum C Z _ Z6, aeque possine ips C
rectae, hoc CIE CF; exit Z F subtenta aequaliS ip(I
ZC; Adeogue omnes Z6 (dirila FZC in partes
aequales in punctis quotlibet Z) erunt ut chorda arcuum in lemicireulo arithuse-
rice proportionattum, hoc elt, uc linus recti in quadrante, hoc cst, ut rectae rili
neum BBC Hg. 7. complences, ipl Bb ordinatim applicatae.
Adeoque l incellisatur semieslindro FZ C F fg. 2. Timilis alius cujus balis dia-
urrague expalidatur, congruent.
meter sic semissi hujus F C. aequalis; Curra ut FC P circini ductu delcripea in lu-
perticie minoris; et semistis PCF semiellipleos in superticie majoris, si in planum
Porro A incelligatur, non jam F A uE in L3. 7. hoc Cst FZC fig. 2. sed FC. Curr.
ut in fig. 30. sire CiF, ret CiF recta, vel otiam F F, AC. 29. dividi aequaliter; Ellixscos
deoque F A F8. 30. hoc est FZC fg. 29. dividi pro ratione arcuum ordinatim
applicaris sire linubus rectis aequaliter distantibus respondentium: Frunt (in Dar
cibus intinice exiguis) quadrata particularum ABC curra, huie dirisioni respon-
dentium; ut quadrata ditterentiarum horum arcuum, quadraris aequalibus aucta
(Duorum omnium radices, ad omnes illas vel ditterentias, vel diametri particulas
aequales, sune, ut ABC curra ad rectam AF, vel ad P C: quibus quidem axere
satis proporcionales supersicies planas, tacile est concipere; sed non ita tacile ra
tione noca explicare, magis quam rationem currae Fllipseos, ad Circuli vel peri
pheriam, vel diametrum.) Sunc aurem illae arcuum ditterentiae (DrOPIEE areuUM
intinice exiguorum e chorcarum quali coincidentiam, adeoque s cenirorum era-
vicacis, mpore quxe arcui de chordae incerjecta este debent,) ut , hoc est Fa.
dum ex se radio et diametri aliquora parce exieua  per sinum rectum s diri-
sum: (Ouod ex Archimedis de aliorum demonstratis, qui luperticierum, Sphae
rica se circum (eripix Cylindeica, sesmentam parallelis planis abseilta, aequalia este
oltenderunt, tacile collisitur: nempe  2 =5c, tactum ex Radtio in A, aequale
este facto ex sejusdem distancia a diametro, in c correspondencem curra parii
culam:) Adeoque illarum quadrata ; quae quadracis aequalibus A2 (PEOP.
1222 2