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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 868, page id 851708439:0892
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LRTGONOMETRTA SPHRRICA.
BB
RV
(ZMN LMM L NN = BB = D BB -XK:: R. R L Z. = p:: 3 RR. ERV = (por
temma ) 53: anguli. FrBO 4 M N. R9: : Z. 2. =BB. 2. 93 MB.: : BB - X X.
543 An8. PIZZ -BB. BB = XX:: 2.93 An8. 59  Ans: : R g. F93 AB: : 7 93
AB. Rg. KFGO
2. 4MN. Z = B: X: Z - B:: R9. Z.9= AnC. vel M N, 3x: 3 - B:: R9. 29 AC.
2. 4M N. B f X: X: B - X:: K9. 593 Ane. vel MH. 3 M: X: 2 N:: RG.
593 AB
3. Z. F B: x: Z - B. B + Z: X: B = X:: Rg. F93 A8. Vel 3X: Z -B. 3- H:
X: 3 - N:: Rg. T93 Ane
4. B + X: X: B- X. Z + B: X: Z - B:: R9. 793 AnC. velZ - M: X: 3 -N.
3X: 3 - B:: R g. 793 AnB
CorOH: PEOPICE ZZ - X X = 4MN, si dencur Ansulus de iplius balis acque
Summa vel ditterencia crurum: invemietur per haec Theoremaca quadracum ditte-
rencix vel summae: adeoque cognicis summa ee ditterentia, cognolcencur ipta
Cruca.
Si quis loco cabularum operari velic Instrumento Proportionis Calilaea
no (quod Vostracibus Sector dicitur,) vel Giunteri Linea Locarichmica: re
Solracur Theorema primum 2m n. Bb = x x:: R. V in proporiiones has duas
7
B F X. 2N:: M. 112
vel in has 2 HI. V f X.: R V 5
1
S PHI A R IC A.
TRianeulum Sphaericum est quod consticuitur incer 3 Aicus circulorum in
SpHaCA MAXIMIOTUM.
Angulus Sphaericus est mucua Inclinatio Planorum circulorum Aneu.
lum constimencium.
Affectiones Frianeulorum Sphaericorum.
2. Si Circulus in Circulum urcunque cadac, Anguli Deinceps potici sune aqua
les duobus rectis.
2. Si Circulus Circulum secec, Anousi ad vercicem sunc aequales incer sC.
3. Major Angulus in Priangulo majori laceri opponitur.
4. Tlolcelis Frianguli qui ad batin tunc anguli, incer se Cune aequales; de vicistim
S Prianguli duo anguli aequales incer se tuerime oppolica eis lacera erune aequalia.
5. Friangula mucuo AEquilarera Tunc ee mucuo Aiquiangula.
6. Si 2 Friangula habuetinc2 lacera e Angulum comprehentum respective x
qualia: Crune Priangula quond reliquas parces (nempe reliquos Angulos de cerrium
lacus) inricem aqualla.
lia: erune ee reliqua lacera de angulus in Priangulis invicem aequalia.
6. Ommis Frianguli a qua ris lacera certio Tune majora. Nlam Areus circul
maximi est breristimum incer 2 puncta spacium in Sphaerae
Superticie; uc linea recta in plano.
9. Omne lacus Frianguli Sphaeciei est minus Semicirculo.
Puca DB est minus Semicirculo DBC.
20. Anguli ad SCMICITCHIOEM ExErEMA OppOTICi, TunC in.
ter (C aequales (D ==C): quippe iiidem planis consticue.
TT. Si crurum anguli cujulris in Priangulo summa sic major aequalis vel minoe
Semicirculo: angulus ad balem incernus eric respective major aequalis vel minor
angulo externe oppolico: Adeoque angulorum duorum ad balem incernorum sum-
ma et major aequalis vel minor 2 Rcctis. Dem: S1 DB + Ba lu = = =DBC,
erit
+
608
f21. B F R.. B.
N. C:: R. V
2. st 2 Friangula cios angulos de lacus sillesscelm habuerine respectire aqua-