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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis (shelfmarks Leibn. Marg. 100:1/2, Stück 2; Leibn. Marg. 100:1/2)
# Folio 876, page id 851708439:0900
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76
LRTGONOMETRTA SFHAHA.
In Triangulo quovis Sphaerico DCB, 2 laceribus DB, BC, de anpulo B cont
Prehenlo, dacis: invenire angulos reliquos D, C.
et 232 Cr. 23XCr:: TZL
3L Ll.
ul
33Z Cr. S3XCr:: r= L. B.
Fig. 19.
Dem. Sint A, E, C, poli lacerum DB, DC, BC. ErGO areUS AP = L. D, de ac.
cuS R. G = L C, _ areuS AG = 180 = LB. SUIDPONACME ArCUS LO = areui
E C = = aECUI EP. Tum si puncta G A O K P Scereopraphice projiciantur, recla
A R. CxIC = F, 3L D, _ AC = r, ZB, e AO = F, 3X L. L. _ AP = Y, 3L. Ll
cricque OG P lemicireulus d polo F deleripeus per C. Cenerum aucem ejus pula n.
Tum Cumpra Ba = BC = BL, de ducta DIAIEITO BI AB, d D K H B m II SHI:
exit DB = SB, _ m K = m H. _ PA = DL. SICNOTDS, FrIC an SY Z~DL. y.
aADL. KZa2SC. ErBOL. Y. Sy:: DL,. 82:: L. K. Sa. FrgO L. SIIK∞. Sed
puncta saHco Tunc in circuli peripheria, cujus Diameter est s a. trgo L. n cH =
(22S1I = -LL, SD =) R∞Y. EEGO LR ∞HI = p aN =- 1. ErgO II =-M c = MR.
Lcem nK. L. K:: (con. coR: :) T, LDS2. L, LDSL. 1. C. Z, SIn CF. X SIn CF.::
F, 3ZCr. T, 3XOr. ErgO (eriam pari racionC) Z Sin L. L. Z SIN LL:: PZ ZLL.
TZ X LL. Sed Z Sin er. Z SIn CF. :: (Z SIn LL. Z SIN LL::) Y, ZLLE. I3
ZL L. 2. 6. AK. AH:: AP. AO. FrGO _ a K F 5N HL. 5A K = 32 HL:: 3 AP F 3AO.
3AP = ZAO. 2. C. Am. M c:: AN. nC. Sed d L. mNco = L. G AN. (DMipDC B
elt polus cam circuli minoris a CL, quam maximi AG: e D est polus circuli mI-
noris cujus radius a c, e circuli maximi ducti per A F P. ) KrgO (per Z 6. K.uCl.)
ANmco ZaAnG. Ideoque aN HI c ZA AOC. _ An K coZ A A P G. FrGONC.
AHI:: AG. AO. _ RC. AK:: ACi. AP. ScdlADROZADL. K: et aS nc =A
DLK. ErGODN. 2C:: VL. (L R =) aH. d S2. Ac:: dL. (L 1 =) AK. Fr∞ODR.
DL:: (2c. X HL:: CFaL) A G. A O. d S 2. dL:: (N∞. X K:: CFAL) AO. AP. 10. 5, ZCV.
53XCY:: T Z L VerVCalIS. Y, ZX lil. e 293L61. 2, ZX CY:: Y L LVOIE. X, 3Cllao
CO ROL L A R LV M I.
In Prianculo quovis Sphaerico AFC.
F, 3baC. Y, 3ZCr:: T, EX CT. T, E X segmencorum balis, quae tiune per ar-
cum perpendicularem ab H demistum. Dico AG. A B:: AO. A d. PUTa Cn M
circulum OC P in Sphaera secare areum A C in puncto a. LrgO arcUS A d M
disterencia segmentorum balis A Ci; de postquam creulus projectus tuerie, punctum
a jacebic in peripheria OGP, cruque recta A d cangens lemiIS acCuS Ad: C
(propier punctum A extra circulum OAGP) AC. AP:: AO. Ad.
COROL L. A R TV M II.
19 bal. 19 36C1-. 23 to lt. L Z KCC.
Sed LF. AG = arcuI DB, _ LAO F. = BC.
COAOL
AG. AB: : 8 a- 8L. (UE SupCA.)