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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 869, page id 851387705:0889
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ed
dFOp. LAIV. De Calculo Centri Cravitatis.
ubique: adeoque eadem pars erit, Bitineum A Da d A, torius Superficiei Sphieri
rica; _ ABB, segmenti BBA; ex BB dD, ZOnX BBsD: e sic ubique. Pex 5C.
PrOP. 23. hujus.
Pura; Oniam habet rationem Areus BB, vel Dd, ad fuas respectire Periphe-
rias inreoras BB, vel DS; auc angulus B Ab vel D A d ad quatuor rectos: cam
habet rationem Sphaerici Cunei Suxerficies AB a b A, ad. torius Sphaerae supertici
em; Cnneique degmenti sphaerici superficies. ABb A, vel aBba, ad respectiri
Seementi sphaerici Luperticiem ABB, vel a BB; Cuneique Zona Sphaericae superfi-
cies BBdD, ad torius Zona superticiem BBd D. Et Lic ubique.
Fixponatur jam, in superticie Spharica, Triangulum Sphaericum ABD, circulo-
rum Maximorum arcubus comprehentum. Dui quidem areus concinuari, intelligan- Fi. 292
cur circulos inceoros absolvere. Hi Circuli cum line in Sphaera maximi; se mu-
cuo bisecabunt bini quilibet. EC, propres aequales ansulos cum qui, tunt, opposici
vercieales, cum qui sunt in eodem Bilineo oppotii, (Duta A== a, e a == a _, Lc
ubique;) aequalia invicem erunt quae lune in contrariis Flemisphaeriis Bilinea.
corundem Circulorum concrariis Semicirculis interjecta;) puta àa, e (quod, in
Schemare dilrupcum est ee replicatum, sed in Sphaera concinuari incellisendum elt)
AA; e similicer BB, eBB; itemDD, 88d. Sed d, eadem ratione, Oppolica
Friangula ABD, aBS, (propeer Lacera laceribus, et Angulos angulis, respectire
Tumpeis, aequalia,) erunt inricem aequalia. (Ouae elt eriam D. Samnehs Fosteri nostra-
eis Demonstracio, in Collegio Crestamense, Lonaini, Astronomia dudum Proteco.
ris; Oui hoc mihii, de Friangulo Sphaerico, Theorema Indicarie, Anno circiter
2646 aUL Z647; ut apud nolteos cum dudum receptum; ec ab FParrioro noltro,
E laris memini, primo repertum.
Si autem, ex semisuperticie Sphaerica Pu PVY = R D, (hoc eA, Facto ex Ra
dio in Peripheriam ducto) auteratur A BD criangulum; Residuum (RF- (ABD
complebune Friangula arV (hoc elt, à a L a BS; hocCA, A A = ABD; ) et
Bc7, (hoc est, BB ABD; ) _DEV, (hoc eAt, DB L ABD. ) TTOC est, Bi
linea A A + BB f DD.
ABD, = RZ. ABD. HIOC CAt, CEran
Sponendo) A A ] BB f DD - = RD = 2 A BD. Adeoque, quam habet racio-
nem, exceltus Bilineorum A A L BB L D D Supra X P, ad R Z Semisuperticiem
Sphaericam; hoc est, quam habet rationem, Fxcesus angulorum A F B F D Lupra
duos rectos, ad duos rectos; seu FxCesus areuum (angulis illis comperenrium)
Fupra semiperipheriam, ad semixeripheriam; eam habet 2 AB D duplum Prian-
suli, ad eandem se P Semituverticiem spharicam, scu duos circulos AXIOS;
plumque ABD Friangulum, ad = P P circulum in sphaera maximum.
TTocestu inrertendo (Dolito a pro aggresato arcuum, in cireulo maximo, an-
sulis A, B, D, comperencium;) uc Semiperipheria ZP, ad a = E8; tic Cireulus
in Sphaera maximus Z X P, ad (a R = = R P) criansulum sphaericum AB D. Ouod
itaque aequatur tacto ex Racdio R, in areum a = 5 P, qui conrenit Excellii ansu-
lorum A. F B F D supra duos rectos.
Elto demum Frilineum expolicum A B D, cujus lacera DL. A, DRB, SinE ar.
cus circulorum minorum P. D A, C. DB H; (lacusque B A, arcus circuli maximi.) FIP. 193
Inveniatur circuli ED A, Polus P; et circudi CDBH, polus A. Franscarque
Per A, D, circulus maximus ADa; et Der D, B, maximus LD BP; irem per P, D,
MAXIMUSPDT.
Habetur itaque (per SB, C, ) magnicudo tum integri Segmenei Superficialis
P F. D A, cum hujus Cunei seu portionis PDL A: Et (per SD.) Magnicudo
Frianguli Sphaeriei P D MI A (arcubus maximorum circutorum terminati: ) Adeo-
que et (horum difterencix) Bilinei D A magnicudo.
Similiter, (per SB, Cy) habetur magnicido cum integri seomenti ACDBHI,
cum hrujus portionis AMDKB: Fs (per SD.) Prianguli Sphaerici AMDLB:
Ergo _ (horum differentia) magnicudo Bilinei D B.
(Et similiter Faciendum eltet, ad lacus B A, I Fuister arcus cireuli minoris: Cum
vero lacus illud sic arcus Circuli maximi; id minime opus erie.)
Hlabetur aurem, ut modo dictum est, (Per S D.) Maonituce Prianguli Sphae-
rici (arcubus maximorum circulorum comprehenli) A M DTB: Unde l autera
tur Bilincum jam invencum DA, acque addacur Bilineum DB; habetur magni
iudo Trilinei expotici ABKD L. A: cujus lacera (Falcem aliqua) sunt areus mi.
ALFFFL
Auscte
norum cireulorum.