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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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PFOp. XV
De Calculo CantriCravitatis.
TLEM; (pFOpter A C = C A; ) ParabOIET. a.
cus rectum erir aequale ipti Cia =R: FF
(propter Bb = V C = x) eric B5 = b a = 
Adeoque Semiparabolae complementum B à S
(urpoie circumseripri Parallelosrammi BB AS
Exiens) - 
ErgO; ParaboIX SeGmentIM AV B = AVS
=AaS = BA5 = v R -, R + . Acque
hoc demum in Z R ductum; exhibet ZV R 2
=SR3 = L4 Semiseomenti Circularis ABV
Momentum respectu rectae Aa; vel Semiqua
drantalem Ongulam correspondentem: Ejusque duplum, V R 2 - = 3 = Z ∞3
= V R = = 23 = ZV R2 - Zs R  Z522; UE PEIUS, 5 Y
Acque hinc similiter elicientur, tum Sectorum B C A, B a A, Momenca Peu Pemi-
quacrancales Ingula respectu rectae Aa, cum Cenrrorum praricaris inde distantia;
ExteragUE VE PrIUS.
Fademque adhuc alias sic investisantur.
Si incelligatur Sphaeran vel Sector Sphaerieus, (puta BC B ex conrertione Secto. WV
ris circularis BC A cirea Aa factus,) ex numero intinitis Pyramidulis (juxta Fis. 159.
det. T. Cap. 4.) contlari: Ouorum omnium communis verrex Tic C Centrum; 8x 260.
communis alcicudo Circuli Sphaeraere Radius; Balesque compleant iplam superti-
ciem Sphaericam, vel Sectoris Sphaerici: Superticiem curram, (puca B A B quae ar
eus B A, circa Aa conrersione deseribitur:) Fric (propier, Pyramides Prilimatum
super cildem balibus aeque altorum Friences, per prop. 6 hujus;) Sector Sphari-
cus BC B a, aequalis superticiei Sphaerica sesmenco B AB in Friencem Radii
ducto.
Tlabetur aurem Superticiei Sphaerica sesmentum illud B AB, s ducatuE AECuS
A B = a in Peripheriam ejusdem arcus Centro graricaris deseriptam, per Z2 hu-
ius. Fst aurem ejusdem AB arcus Cemrum GravICaLIS, Duta C (in H18. 16F, 162.) Fi8
162
in recta C. S arcus axC; rectaque CC = = R, (per 24 huju s.) Rectaque 5, = = C, 167
(uc SO. oltensum cst:) Acque (proprer similia Friangula) Vr CS = R, ad
5. = 1C hc CC = = _, ad = = Cc diltanciam Ceniri eravicais Arcubo AB, ab
Aa; Adcoque   est Peripheria juldem neera convectione cicca M a deleripra
In quam itaque si ducatur AB = a, habetur Sphaerica Superticiei segmentum
BAB = =: vel (PTOPIeT C = Z VR,) Superticiei Sphaeriea seomentum
BAB = ∞4
Vel ctiam (per L3 hujus;) Propter incesram sphaerae superticiem quatuor Circu. Pix
lis maximis xequalem; hoc elt, 2 R P: acque abseiltum lesmencum ABB, in Ca 150
ratione ad toram, qua elL ipsius alticudo AV = V, ad Aa = 2 R: FFIE UEA a = 2R, 160.
ad AV = v, Sic tora superticies Sphaerica 2 RP, ad iptius segmencum B AB = ~Z.
uE prius.
Ouod irague superticiei Sphaerieae segmentum, in ; R ductum, exhibet Sectorem
Sphaericum BCB A = Z V R P: Adeoque semiquadrantalem Ongulam, seu Plani
BC A momentum respectu Aa, ZV R 2. Idem, quod supra, S O repercum est.
Caeteraque hinc, ut ibidem, deducentur.
Exhibuimus icaque Semicireuli Partiumque iptius exposicarum, cum Magnicudi-
nes, cum Momenta respectu rectarum aliquor expolitarum; corumque distanciam
Ceneri graricaris d rectis illis. AdeOqUE PeT prOP. 26. Cap. PrXced. (propter datas
COrum
2.