Die Tabelle der Formeln der sphärischen Tetragonometrie in Anwendung auf die Kristallographie. 
der Uaupfzone und die Winkel A. ^li. li und //j. 
Der erste Fall. Die GrundflUche a uad die komplementäre Fläche h als die AusgangsHächen. Die Konstanten: Der Winkel {ab) 
Monokline Sjngonie 
Trikline Syn^fonie 
sin(A«?) = 
cotg (ac) = 
cotg (be) 
^ cotg.'lj — cotgyl 
cotg — cotg 
sin{ae) 
h 
1 k cos (n b) 
A'sin(aA) 
k + cos (fl b) 
sin (« b) 
1 — /.-cosCat) 
*,in(»tr 
coig(4e-) = - 
cotg(ce’) = 
^n{ab) 
-k^ 
2 k sin (n b) 
cotg - 1 *) =* 2 cotg A — cotg A , 
cotg J{. 1 = 2 cotg B — cotg 7/, 
cotg Aj s= — cotg Ä ^ 2 cotg 
cotg/1 .2 = 3cotgg4 — 2cotgyI, 
cotg Bf = — rntgiy 2 cotg Ä, 
cotg J{- . = 3 cotg B — 2 cotg Vy, 
colg(nc) = cotg/ycosec(n6)siii -1 cotg («/<) cos vl 
cotg(arf) = cotg /y, cosec(a^»)sinyl, + cotglai) cos.^, 
cotg («(/') = cotg yy -1 cosec(a/>) sinyl_i + cotg(a6) cos^ 
cotg {af) = cotg yy, cosec(ni) sin A -j- cotg («6) cosyl_i 
cotg(n/'’) = cotgiy I cosec(ai) sin + cotg(ai) cos.^, 
cotg(/7//,) = cotg yy, cosec (fl &) sin yl -1- cotg (n 6) cos yl 
cotg (fl r/l) == cotg li I cosec (fl b) sin yl + cotg (a b) cos A 
cotg(ai/) = 2 cotg(«. 7 ,) — cotg(flc) 
(A = yf) 
(a6)=-’; A = l 
(ai*) = ;’: s = ;] 
■^-2^ -«“i 
COtgyl, 
cotgyl, — cotg yl 
cotg yl, 
cotg.B, — cotgü 
cotg B^ 
cotg B^ 
sin (fl c) 
sin (flf) 
k 
sin(«e) 
k 
sin (fl c) 
' k ■' 
ab 
ootg 2 
1 
k 
1 
k 
l -f- Ä: cos (all) 
k&in{ab) 
ab 
cotg 2 
k 
k 
k cos (ah) 
in (ab) 
tang 2 
1 
k 
1 
k 
l ~ k cos (06) 
ysin(ai) 
, ab 
— ^ang - - 
— Ä- 
— b 
— Ä + cos (fl 6) 
siu (fl 6) 
0 
1 — t“ 
l-k> 
I — Ä» 
2 k 
2h 
2isin(a6) 
2 cotg A — cotg yl, 
— cotgyl, 
2 cotgyl — cotgyl. 
— cotg.l. 
2 Cotgy 4 — cotgyl. 
2 cotgiy — cotgif, 
— cotgiy, 
— cotgiy, 
— cotg A -\-2 cotg yl , 
2 cotgyl. 
— cotg yl ‘-i cotg yl , 
2 cotg -1, 
3 cotg..! — 2 cotgyl, 
— 2coi:gyl, 
3 cotg yl — 2 cotg yl, 
— 2 cotg yl, 
— cotg y4 + 2 cotg A , 
— cotg yy + 2 cotg yy, 
2 cotg yy, 
2 cotg jy, 
3 cotg yl — 2 cotg A , 
3 cotg B — 2 cotg yy, 
— 2 cotgiy, 
— 2 cotg yy, 
cotg cos yl 
cotgyy 
0 
0 
cotg cos Aj 
cotg/y, sin yl, 
cotgiy, sin yl, 
cotg(ac) cos.l. 
ah 
cotg ^cosyl -1 
— cotg yy. 1 sin A , 
— cotgif, sinyl_i 
— cotg (fl e) cos .1, 
860 ( 0 !») sinyl_i cotg(ö!») t 
osyl-, 
— cotg.B, sin yl, 
cotg.B, sin yl_i 
cotg (fl e') cosyl, 
cosec(a!») sin-1, -1- cotg(a6) 
cosyl. 
cotg .B_)sinyl, 
— cotgiy, sin yi, 
— cotg (fl c’) cos.l, 
cosec (fl h) sin yl -f- cotg (« !») cos yl 
cotg yy. 
cotg B^ sin yl 
cotg yy, cosec (all) 
1 cosec (fll») sin yl -1- cotg(«!») 
cosyl 
cotg iy_i 
— cotgiy, sin A 
— cotg^, cosec (al») 
2 cotg (o;/,) — cotg(ac) 
2 cotg (fl//,) — cotg (fl c) 
2cotg(air,) 
2 cotg {(i;;,) 
Rhombilche Syngonie 
sin (fl e) 
a «A 
cotg 2 
ab 
«^otg ,, 
ab 
t->g-2 
ab 
“ tang 
0 
— cotg A , 
— cotg 
2 cotg .'I, 
— 2 cotg yl, 
2 cotg.l, 
“ 2cotgyI, 
0 
— cotg COSvlj 
ab 
tniig ^ cosvJ, 
ab 
— tang cosyl, 
cotg.l, cosec(aÄ) 
-- cotg .1, co.sec(a//) 
otg(oy,) 
cotg.l, 
cotg yy, 
sin (fl c) 
k 
1 
k 
k 
1 
k 
— k 
\ — k> 
2k 
— cotg-l, 
— cotg yy, 
2 cotg yl, 
— 2 cotg -1, 
2 cotg yy, 
— 2 cotg yy, 
0 
cotg yy, sin .1, 
— cotg.ß, sin..!, 
cotgyy, sin yl, 
-- cotg yy, sin .1, 
cotg yy, 
— cotg yy, 
“OOtg((l</,) 
cotg («;;■) = — 2 cotgCaj,) + 3 cotg (ac) 
— 2 cotg (ö^i) 4* 3 cotg (fl c) 
-2cotg(a^,) + 3 cotg (ac) 
“ 2cotg(ai/,) 
— 2cotg(as/,) 
2cotg(o.((,) 
— 2cotg(rt.v,) 
cütg(fl/i) = cotg yy cosec (fl 1») sin ylj -1- cotg (a/>) cosyl, 
cotg.l cosec (fl!*) sin yl, 4" cotg(fl!») cosyl, 
cotg .B sin yl, 
0 
cot}.' ^ni) COS .1, 
cotg(a/)) cos.l, 
0 
cotg(fl/t') — cotg //co^ec (hA) sin y/ - 2 -j- cotg(aA) cos.l^j 
cotgyl cosec (fl A) sin yl _2 4" cotg(aA) cos-l _2 
cotgiisln .!— 2 
0 
— cotg(flA) cos.l. 
— cotg(flA) cos .1, 
0 
cotg(flA,) = cotg yy cosec(flJ) sin yl, 4- cotg(ai) cos. 
1, 
cotg.l cosec (fl 6) sin .1, 4* cotg(aA) cos.l, 
cotgiy .sin yl, 
(i 
cotg {ab) cos.l. 
cotg(aA) cosyl, 
n 
cotg(aA|) = cotgiy cosec (fl !») sin .1 _) cotg(flA)cosyl_i 
cotg.l cosec(aA) sin.l-i 4* cotg(aA) cos.l_i 
cotgiy sin yl_i 
0 
— cotg (fl A) cos .1, 
— cotg(aA) cos.l. 
0 
cotgii' a= [cotgiy sin (fl c) — cotgyl sin(!»p)] cosec(fl!») 
0 
cotgiy sin (flc) 
— cotgyl cos (fl c) 
0 
0 
0 
cotgi?, =: [cotgiy, siu (ne) — cotgyl i .sin (!»«)] cosec (n 6) 
1 (cotg .1 — cotg .1 _i) sec 
cotgiy, sin (fl p) 
— cotgyl, CO.S (fl c) 
2cotg yl, cosec(«A) sin (Ap) 
. , ab 
cotg.l, sec 
2 cotg .1, cos (fl p) 
cotgi'.’-i = Icotgi)' 1 sin(flr‘) — cotgyl, sin(!»r)] CüS6c(n!») 
1 (cotg .1 _ 1 cotg -1)SBC 
cotg iy_j sin (flp) 
— cotg-l, cos(ac) 
— 2 cotg .1, cosec (flA) 8in(Ap) 
— cotg A , sec 
— 2 cotg .1, cos(up) 
cotgiC' — [cotg yy sin (fl r) -|- cotgyl sin(Ae')l coseo(flA) 
c„t.ioosec?‘ 
cotg /y sin (flp) 
cotg.l cos (fl p) 
0 
0 
0 
colgK; 5= [cotgyy, sin(fle') r cotgyl, sm(!»p‘)] cosBc(nA) 
cotg.l, cosec 
cotgiy, sin (flp) 
cotgyl, cos (fl p) 
2 cotg.l, cosec (fl A) sin (Ap') 
cotg.l, cosec 
2 cotg . 1 , cos (fl p) 
cotgi^'-i — [cotg/y isin(fle’) + cotgyl.isin(6e')lcosec(a!') 
ah 
cotg.l _i cosec 
cotg iy _2 sin (fl f) 
cotgyi_3 COs(«p) 
— 2 cotg . 1 , cosec (fl A) sin (Ap') 
— cotgyl, cosec”^^ 
— 2 cotg-l, co.s(öp) 
In diesen TuWllen werden die Bozeichnutigen der 
Vinkel ir 
der regulären Kntwicklung durch Unterdrücken der iwvte 
unteren Zahl verkürzt. Also 
Aic 
. H. nnttatt: Ai 
An 
An 
A-n heihi ea 
A,3 d_,j| yt-ii 
ü A 
A\ 
ylj yl-i 
A~, mw. 
A~J 
