E. u. Fedoroiu: 
1( 
sin (A d) = 
cotg(;»rf) = 
cotgCy rf) = 
cotg(/ii;') = 
cotgtee') = 
cotg (d I?') = 
cotg (l-\ = 
cotg f/fl = 
cotgf;.j = 
cotg (ria ■ 
cotg t/j = 
cotg7/_i = 
cotg i/, = 
cotg i/j = 
cotg y/j = 
cotg(ga) . 
cotg(gi) = 
cotg(gc) = 
cotg(g(y) = 
colgtoc) = 
cotg ton = 
cotgtoD ' 
cotg tot?') ■ 
cotg to'/i) = 
cotgtoi/i) = 
cotgtoA') ■ 
cotgto*!) ■ 
cotgto*,) ■ 
cotg i) = 
cotg 7^, : 
cotg 1)^\ ■ 
COtgi’i : 
cotg(£.'' — £ 1 ) 
sin (7-^ — L',) 
ain {£-1 — E) 
cotg(e'n) 
cotg(f'e) 
cotg (f' 6) 
cotg (tic) 
cotg{rfc) 
cotg(rf <i‘) 
cotg (?■ c) 
Die Tabelle der Formeln der sphärischen Tetragonometrie : in Anwendung auf die Kristallographie. 
Der dritte Fall- Die GrundflHche g und die komplementüve h. 
Die Konstanten: Der Winkel (Ap) und die Wittkel G, 61. II und //j. 
Trikline Syngonie Monokline Syngonie 
(r/=,/i): !) = ■ 
Rhombische Syngonie 
= E=l 
COtgG, — cotg (i 
cotg 77, — cotg 77 
: %\n{gd)\k 
h -f cos {g li) 
" sm(p/0 
1 + A cos(gli) 
ksMiigh) 
— k + cos(//A) 
sin(p/<) 
1 — k co8 (pA) 
Äsin (gh) 
. “_A* 
2 ksinigli) 
= 2 cotg Cr — COtgCri 
= — 2 cotg (7 + 3 cotg 6r, 
= 4 cotg G — 3 cotg (r, 
= liiCotgG— COtgCr,) 
= — 4 cotg Cr + 5 cotg (r, 
s 2 cotg 77 — cotg 7/, 
= — 2 cotg 77+3 cotg 77, 
= 4 cotg-H — 3 cotg 77, 
= — 4 cotg 77 + 5 cotg 77, 
= — cotg77_scosec(j//i) sin Cr, — cotg(f//i)cos Cr, 
= — cotg 77, cosec(<//f)sin (r _3 — cotg{(/ A) cos(r_8 
= cotg 77, cosec (pA) sin G^ + cotg {g A) cos Cr, 
= cotg 77 cosec (firA)sin Cr + cotg(pA)cosCr 
= — cotg.ff_i cosec (pA) sin G-i — cotg(pA) cos Cr_i 
= cotg 77s cosec (//A)sin G_i cotg (pA") cos G_i 
= cotg 77-1 cosec (f/A) sin G, + cotg (pA) cos ö, 
= — cotgCpo)] 
= 3 cotg (p c) — 2 cotg (pp’) 
= l [cotg(pc) + 2 cotg^pp')] 
= cotg77, cosec (pA) sin (r_) + cotg(pA)cos(7_i 
= cotg77, cosec (pA) sin Cri 3 + cotg (pA) cos (rja 
= cotg77, cosec (pA) sin Crj -I- cotg (pA) cos Ctj 
= [cotg 77, sin (prf) — cotgG,sin(A(7)icosec(pA) 
= [cotg 77j sin (prf) — cotgGjSin (A(7)] cosec (pA) 
= [cotg 77, sin (p (7) — cotg Gj sin (A cZ)] cosec (p A) 
= — cotg 7/_t sin (p e') — cotg G 1 sin (A e')] cosec (p A) 
= [cotg 77, sin {pc‘) + cotg G,sin(Ae')]cosec{pA) 
= sin(pf7)sinG_i cosec(rf£*) 
= sin (Af7)sin77-i cosec^tZc) 
= cotgG, cosec (c'p) sin £; + cotg(c'p) cosT?; 
= cotg7r_i cosec(c'p)sin7?i + cotg (c'p) cos Ti’i 
= 2 cotg (e' c) — cotg (c* a) 
= — cotgG _i cosec Cp <7)sin71 — cotg(prf)cosD 
= cotgG, cosec (prf) sin 7) + cotg(pd)cos7) 
= cotgG cosec (prf)sinD + cotg(pd)cosD 
= — cotgG, cosec (pc’) sin (£'— £i) + cotg(pr')cos(£'— 7^i) 
sin(prf) 
cotg ~ ^ 
lang '[j 
0 
2 cotg G — cotg G, 
— 2 cotgG + 3cotg(», 
4 cotgG — 3 cotg(r, 
J (4 cotg(f — cotgG,) 
— 4 cotgG + 5 cotgG, 
2 cotgG — cotg (i, 
— 2 cotgG + 3 cotg(r, 
4 Cotg(r — 3 COtg(r, 
— 4 cotgG + 5 COtg(r, 
— cotgG _3 cosec (pA) sin G, — cotg(pA)cosG, 
— cotgG, cosec (pA) sinG.a — cotg(pA) cosG _3 
cotg cos G, 
sin(prf) 
L 9^^ 
cotg-^ 
pA 
cotg-^ 
. tO» 
— taug-., 
tang 
0 
gli 
cotg ^2 . 
’ 2 
ts(r 
cotg (rg cosec (pA) sin (r_i + COtg(pA)cOS (r_i 
cotg G_i cosec(pA)8in Gj + cotg(pA) cosG, 
^ [cotg (p '•) — cotg (p 0)1 
3 cotg (po — 2 cotg (pp') 
KcotgCpfi + 2cotg(pp')] 
cotgG, cosec (pA) sin G_i + cotg(pA) cos(r. i 
cotgG, cosec (pA) siii(Ti8 + cotg(pA) cos (»i» 
cotg(r, cosec (pA) -sinGj + cotg (pA) cos (rj 
0 
2 (— cotgö + cotgG,) sec 
I ^ 
2(cotg(r — cotg(r,)sec'^^ 
j. /. 9^^ 
— COtg(r-ii cosec 
L t pA 
cotg»r, cosec ^ 
sin G_i cosec (tZr) 
2 cotgG — cotg(/, 
— 2cotgG +3cotg(», 
4 cotg(r — 3cotg(/, 
\ (-1 COtg(r — COtg(f,) 
— 4cotg(f + öcotgG, 
2 cotgG — cotg(T, 
— 2cotg(f + 3 cotg(f, 
4 cotg(r — 3 cotg(»', 
— 4 cotgG + 5 cotgG, 
— cotg(r _3 cosec (pA) sin (r, — cotg(pA) cos (», 
— cotg(r’, cosec (pA) sin G^ 3 — cotg(//A)cos (»_3 
L '//' , . 
cotg ,, cos(», 
cotg cos 7 ; 
— cotg cos (V _1 
cosec (pA) sin (r_i + cotg(pA) cosG_| 
_j cosec (pA) sinG, + cotg(pA) cos(ry 
cotg(2pc) 
3 cotg (pc) — 2 cotg(ppO 
\ [cotg (pc) + 2cotg(pp')] 
cosec (pA) sin G_i + cotg(pA) cos(r_i 
I COSecipA) sin (rj 3 + cotg(pA) C0S(ri3 
, cosec(pA)sin (/5 + cotg(pA) cos(r 5 
0 
2(— cotgG + cotgG,) 
cotgG, 
cotg(/ 
cotgG, 
cotgG 
cotg( 
2 (Cütgfr — COtg(r,), 
isec 
* /r P7i 
- COtg(r,| cosec 
cotgG, c 
sin G_i sin cosec (rfc) 
COtg(r, ! 
!C ~ sin E\ + taug c{is7i’| 
0 
— cotg (c'a) 
cotg£]' 
cotgfT,’’ — £;) 
cotg(£l, - E]) 
0 
sinG_isin^ cosec((Zc) 
pA 
'2 
cotg ( r, sec sin 7?i + tang cos E'i 
0 
— cotg(c'fl) 
cotg£| 
cotg(£' — £,’) 
cotg(/il, — 7?I) 
0 
