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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)
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PRTGONOMETRTA SPMLLLA.
eric BA = =- = BC, ideoque L (C) D = = -- L B AC, _ L. D F L. D AB = -
(h B AC F D AB =
2
Coroll. Si crus Triansuli IPoscelis sic = = = Ouadrance; erir angulus ad
balem = - - -
+2. Omnis Frianguli lacerum summa est circulo minor. Nam B A = BC f AC.
Froo DB L D A f BA -= DBC. F DAC.
23. Anguli Sphaerici mentura elt Circuli Arcus, inter crura de lexiptus a vertice
ansuli uc volo, et incerrallo gractuum 90.
24. Priansuli CEID laterum poli n x m
conlticuunt Priangulum quod respectu AGTID
appelletur Supplementale; propterea quod Sup.
plementa ansulorum et lacerum Prianguli
CHID sunc aqualia laceribus et ansulis Pri-
anguli NYX N.
Dem. A punctis CFTD canquam polis de.
seribantur 3 Circuli maximi Z AY, R PM N,
XBNZ; Tum YM == 90 = AX; PFODICE
AC poluM arCUS FIGT, e Z, F, PolOS aECUS
GA. ErSO MX = = AY = Supplemento ar-
cuS CA = Suppl. L HCD. Sic Z N est 90
=BX. ErgO NX =BZ = SuppI. (arCuS
BF =) LHID C. Item N P elt 90 =M R.
ErGONM = F R = Suppl. L. DTIC.
Nocandum hic, aN FM inter 3 POlOS proxiores ConIMuM, ConCtarC, CX 3
ansulis de lateribus qua sunt aequalia respectire laceribus ee angulis a GTTD ex
cepto latere maximo NIM quod est Supplemencum L maximi LI; de L F. elt
Cuppl. lateris maximi D.
F5. Frianculi cujulris cres anguli TunC = 2 1 8 -6 1. Nam NX F ZM
F NML = 4 - (PeT 12.) 2. c. 2 - -D, + 2 1 - 6, +2 1 - H = 4 -. LXBC
2 1 =D, +G, F TI. 2. Angulorum internorum limul ec externorum summa
elt = 6 -1. Eroo summa internorum est - 6 -1.
26. Frianguli angulus quilibet cum ditterentia reliquorum est =2-1. Nam
ZN ZM F MN. 2. C. 2 1 -D =2 - C, + 2  -TI. ErgoC F TID
27. Si 2 Friangula sine mutuo aequiangula, sunc eriam mutuo aequilatera. Sint
enim Friangula dara A, B, es Friangula iplis Supplementalia, a B. FrsO cum
AZB, erunc (per 24) an B, aequilatera FrSO (per 5) _ZB. ErgO (Pex 14)
A, B, sunt aequilatera.
18. Si circulorum maximorum areus diverti ducan-
tur ab eodem superticiei puncto in circulum dacum,
maximus areus is erir qui cransir per polum cireuli dati,
et huic propior major erit remotiore. Ut lic P polus
circuli C xD, et er polus circuli DP C, erir AD= AB
= AF = AC. e arcus B= C = BP = BD.
29. Circulus maximus per cireuli maximi polos du-
ctus, facit cum ipso ansulos Rectos: es vicererta l
circulus maximus (i circulo maximo perpendicularis
cransic per ipsius volos. L. PBD =- s -= P C D = P DB = x AC
20. Si ad Priansuli basem anguli sine similes B. P. Uterque aCutIS UE in AF. A F,
vel ucerque obculus ur in aB A C: perpendicularis a vertice A demisla cadet in
era Priangulum. Sin anguli ad basem sint dissimiles ut in AB AF L. B elt acu-
tuS (quippe L. P BF. est rectus,) e L. A est obtusis: perpendicularis cadit extra,
Ouineciam liquet ex eodem Schemate 9. quomodo Priansuli Rectanguli Am.
biguicaces Solrancur. Nimirum.
SO~ VF XO N F 5.
= Si prus anguli recti sIE = = d0: erit inidem angulus OppoLCuS = = 90.
Sic in ABDA, D A = arcu quadrantali D P, e L DB A est = IDBP. EF
in aBCA, LCBA est L sCBP, ut AC. = quadrancali areu PC.
RFPEY 3
2. LFOUE