f. u. Fedorow: 
Die Tabelle der Formeln der sphärischen Tetragonometrie in Anwendung auf die Kristallographie. 
Der zweite Fall. Die Grundfläche f und die komplementäre Fläche f‘ als die Ausgangsflächen. 
Die Konstanten: Der Winkel ff' nicht io der Hauptzone and die Winkel F, F\, F' und F\. 
Trikline Syngonie 
^ cotg F, “^otg F 
cotg Fl — cotg 7*’' 
sin if' c) = sin {fc)lk 
h 4- cos (//■') 
sin (/?■■) 
cotg (f‘ c) « 
. ff. l+*cos(^') 
colK(/-»)= 
1 (fvi —i + cos (/;■■) 
. «,'-1 1— *COS(//'') 
colg(/c)= 
, 1 “ 
C0tK('^^) = 2A3in {/?■■) 
cotg F- 1 ■* 2 cotg F — cotg Fl 
cotg F'-i = 2 cotg F — cotg 7''i 
cotg 7'*, = — cotg F + 2 cotg 7'’, 
cotg 7'’_2 = 3 cotg F — 2 cotg 
cotg 7' j = — 2 cotg /*' + 8 cotg 7-’, 
cotg F-a “ 1 cotg F — 8 cotg F, 
cotg {fe) «= cotg F' cosec (ff ) sin F -f- cotgOf') cosF 
cotg(/‘rf) cotg Fi coacc (//■■) sin F, + cotg Of') cos F, 
cotg (fd‘) «= — cotg FL, cosec (fi' ) sin F-, — cotg (f ') cos F_ 
cotg(/'n) = cotg/‘’| cosec Of') sinF-, -j- cotg(/f') cosF-i 
cotg(/7i) = cotg Fl, cosec (/?■') sinF, + cotg(/f ') cosF, 
cotg!/“«/) — cotg Fi cosec (/n sin F -f- cotg (;?'') cosF 
cotg i//!') “ — cotg F-i cosec (ff') sin F 4- cotg{^'') cos F 
cotgl/A) »* cotgF' cosec{//’‘)sin7^ 4- cotg(^4cosF, 
cotg(7y‘) = cotg 7*’' cosec (//*■) sin F_2 — cotg(//‘) cosi-’-e 
Cütg(i^^,) =* cotg 7=8 cosec sin F, 4- colg(/f)oonF^ 
cotg ( fh\) a= — cotg F.a cosec (ff‘) sin F-, — cotg (ff') cosF_, 
cotgO^/i,) = cotg 7''; cosec (//■') sinF, -4- cotg(/?') cosF, 
cotg(/'^;:) = — cotg Fl, cosec(//'')sinF_8 — cotg (/?'') cos7'’_3 
cotg C — [cotg F' sin (cf) — cotg Fsin (cf)] cosec 
cotgC, = [cotg Fi s\n(cf) — cotgF-, sm(c/'0] cosec Of') 
cotgC’-j = [cotg Fl, sin (cO — cotgF, sin (c/“')] cosec(ff') 
cotg 7i'' e= [cotg F' sin (c' f) 4- cotg F sin (c'/“)] cosec (ff') 
cotg(7;^' — 7^i) = [cotg/-’i sin{c'/4 4" cotgF_iain{eY')] cosec(^’') 
cotg(7;,’li — 7^') = [cotg7‘-, s\n(e‘f) 4* cotgF.: sin (e'/“')] cosec (//*') 
cotg(cc) =» cotgF cosec (/^c) sinC 4” cotgiyc) cos 6' 
cotg{crf) = cotg 7* cosec (/“c) sin C 4* cotg(/'c) cosC 
cotg (c e') = — cotg 7*' cosec (f e‘) sin E' 4- cotg (f c') cos E ‘ 
cotg (fl r') = — cotgF-i cosec (/■«') sin F' 4 - cotg (/"c') cosF', 
cotg (h (') “ — cotg /•’, cosec (/* e’) sin F' + cotg (/>’) cos F' 
sin(7!,’ — E^) = sin (/"e) sin 7’- cosec(cf) 
sin (F_i — F) = sin (/'c) sin F' cosec (ce) 
Monokline Syngonie Rhombiache sjogonig 
(F=F') 
or') = " = 
cotg F, 
cotg F, — cotg F 
cotgF, 
cotg 7’ 
cotgFi — cotgF' 
cotg F, 
cotg 7’i 
cotg 7' 
siaf 
sin(fc)/i 
s\n(fe)jk 
sin(/’c)/Ä: 
sin^- 
sin (f c)lk 
cotg| 
k 
k 
k + cosOf ') 
sinW') 
cotg 
k 
cotgf- 
1 
k 
1 
k 
1 + i cos (/?■') 
i sin (Jf‘) 
cotg 
l 
k 
-tang| 
— k 
— k 
— t H- cos(ff‘) 
sin iff‘) 
— tang ^ 
— k 
tang^ 
1 
k 
1 
k 
I — k cos (ff‘) 
k sin (ff ) 
t“'ig ^ 
1 
k 
0 
1—*» 
l-k' 
l-k* 
0 
\-k* 
2 k 
2k 
2 k sin (ff') 
2 k 
2 cotg F — cotg F, 
— cotg F, 
2 cotg F — cotg F, 
— cotg F, 
— cotg 7’, 
— cotg 7’, 
2 cotg F — cotg F, 
2 cotgF' — cotgF 
— cotg Fl 
— cotg Fl 
— cotg 7’, 
— cotg 7’; 
— cotg F 4- 2 cotg F, 
2 cotg F, 
— cotg F 4- 2 cotg 7 , 
2 cotg 7’, 
2 cotg F^ 
2 cotg F, 
3 cotg F — 2 cotg 7’, 
— 2 cotg F, 
3 cotg F — 2 cotg F, 
— 2 cotg F, 
— 2 cotg F^ 
-3cotg>, 
— 2 cotg F 4- 3 cotg F, 
3 cotg F, 
— 2 cotgF 4- 3 cotg 7', 
3 cotg F, 
3 cotg F, 
3 cotg F, 
4 cotg F — 3 cotg F, 
— 3 cotgF, 
4 cotg F — 3 cotg 7’, 
— 3 cotg F, 
— 3 cotg F, 
— 2 cotg F, 
cotg ^ cos F 
cotg F' 
0 
0 
0 
0 
. ff' r 
cotg 2 cos 7' , 
cotg Fi sin F, 
cotg F| sin F, 
cotgFi cosec {/? ') sin 7’, 4- cotg{^')cosF, 
cotg fj- cos F^ 
cotg 74 sin 7’, 
— cotg ^ cos F_, 
— cotg FL, sinF, 
cotgFi sinF_, 
cotg Fl cosec (ff"') sin 7’, -j- cotg (ff) cos F, 
cotg ^ cos 7’, 
cotg 7'’1 sin 74 
cotgF, cosec 0?*') sinF-i 4* cotgOf' ) cosF_, 
cotgF, sinF, 
cotg F; sin F-i 
cotg 74 cosec (/? ') sin F, — colg(;f') cos 7’, 
tang ^ cos 7', 
cotg 74 sin 7', 
cotg F-i cosec(ff‘) sin F, 4” cotg(/? 
') cos F^ 
cotg Fl, sinF, 
— cotgFi sinF, 
— cotg74cosec(/f')siaF, 4- cotg(ff')cosF^ 
-tang ^'cos7', 
— cotg 7'i sin F^ 
cotg F, cosec (ff‘) sin F 4- cotg (ff ) cos F 
— cotg 7^-2 cosec (ff') sin F 4- cotg (ff‘) cos F 
cotgF cosec (/?■') sinF, 4" cotg(^'') cosF^ 
— cotgF cosec (ff) sin F-i — cotg(F0 cosF_2 
cotgF, cosec (/?■') siiiF, 4" cotg(F‘) cos7’, 
— cotg F_8 cosec (ff) sin F_i — cotg(/f ') cos7’_, 
cotgF, cosec (ff) sin 7’, + cotg(/f IcosF, 
— cotgF-, cosec(yf')sinF_s — cotg(//‘') cosF_3 
0 
cotg 7'i 
— cotg F'-i 
cotgF' sinF, 
— cotg 7’' sinF, 
cotg F'a sin F, 
— cotg Fa sinF, 
cotg Ft sin F, 
— cotgFli sinF, 
cotgF' sin{cf) 
2 cotgFi sin F 
2 cotg Fl sin F 
ü 
0 
3 cotg F\ sin 
3 cotgFi sinF_, 
cotg Fi sin F, 
cotg Fl sin F-a 
— cotgF cos (cf) 
2 cotg 7’i cosec(ff') 
2 cotg Fi cosec (ff ) 
cotg (/?’') cos 
cotgO'7') cos F\ 
3 cotg 7’1 cosec(ff')s\T\ 7’,4- cotg(/f')cos7’ 
3 cotg Fl cosec(/f)sin7', 4- cotg (^’')cos F^ 
cotgFi cosec (/?'‘)sin 7’, 4* cotg(//'') cosF, 
cotgFi cosec (/?') sin F, cotg (//’') cos 7’, 
0 
2 cotg F. cosec (ff) 
2 cotg 7 , cosec (ff) 
cotg (/;■') cos 7', 
cotgl// ') cos 74 
[ 3 cosocf/T*') + cotgf/7 ‘)l cos 7’, 
[3 cosec (//■') 4- cotg (//■')] cos 7’, 
cotg F, cosecf/?’')8in 74 4* cotg (/f') cos 7<’, 
cotg 74 cosec (ff) sin 7’, cotg (// ') cos 7', 
0 
2 cotg 74 
2 cotg F\ 
0 
0 
3 cotg 7'! sin 
3 cotg 74 sin 74 
Cfitg 7‘'i sin 7’’, 
cotg 74 sin 7’, 
0 
ä {colgF, — cotgF-, )sec ^ 
cotgFij sin (cf) 
— ColgF-! COS(,Cf) 
2 cotg F, cosec (ff‘) .sin (cf) 
cotg 74 sec 2 
2 cotg 74 cos (cf) 
1 (cotg F-I — cotgF,)sec -~ 
cotgF_2 sm(cß 
— cotg 7’j cos(c/') 
— 2 cotg F, cosec (//') sin (cf) 
— cotg 74 sec ^ 
— 2 cotg 7', co8(c7) 
cotgF cosec ^ 
cotg F' sin (cf) 
cotgF cos (c/4 
0 
0 
0 
cotgF, cosec ^ 
cotg Fi sin (c f) 
cotgF, cos (c/o 
2 cotg 74 cosec (ff) sin (e'f) 
cotg F, cosec 
2 cotg 7’, cos(cf) 
cotgF-i cosec ^ 
— cotgFls sin(c/’) 
cotgF, cos(c/‘) 
2 cotg 7’, cosec (ff') sin (c' f) 
cotg 7’, cosec ^2 
2 cotg 7’, co8(r/') 
cotgF cosec ^ 
cotg(c/') cos C 
cotg (cf) cos (J 
0 
0 
ü 
cotg F, cosec 
cotg 7’, cosec (c/’) sin C 4- cotg(c/') cosC 
cotgF, cosec (c/')sin C 4- cotg(c/') cosC 
cotg 7’, cosec(c/') 
cotg 74 cosec 
cotg 7*', cosec (c/) 
— cotg 7' sec sin F'4-tang^^ cosF' 
coig(cf) cos C 
cotg (c/o cosC 
0 
0 
0 
— cotgF-i sec*'^ ^ sinF' 4- tang^^ \osF' 
cotgF, cosec(cf) sin (7 4" cotg(c/') cosC 
- cotgF-i cosec(/'c)smC4-cotg(/‘c)co8C 
cotg 74 cosec («' f) 
cotg 7’, sec ^ 
cotg 74 sec(fe) 
— cotg F, sec sin F' 4" tang ^ cos F' 
— cotgF,cosec(c/')sinC 4" coig(cf)cosC 
— cotg F, cosec (f c) sin C 4- cotg (f c) cos C 
— cotg F, cosec (e' f) 
ff 
— cotg 7’, sec 2 
— cotg 7’, socCc/") 
sin sin F cosec (ce) 
sin{/c) • cosec (cc) 
sin (f c) sin F cosec (c e) 
sin (f c) 
.(//■') 
2 
sinl/c) 
sin ^ ^ sin F - cosec (cc) 
cos(/c) sin F' cosec (cc) 
cos (f c) cosec (c c) 
cos (f c) 
.(ff) 
2 
C08(/'C) 
