| 1. | CosL CosZd= CosM CosN |
| 2. | CosL SinZd CosB'r - Sin L Sin B'r = CosN SinM |
| 3. | CosL SinZd SinB'r + Sin L Cos B'r = Sin N |
| 4. | SinEq SinN + CosEqCosBrq CosN = Cos B'r'q Cos E'q' |
| 5. | CosEq Sin Brq CosM-Sin Eq CosN SinM + Cos Eq CosBrq Sin N Sin M= Sin B'r'q Cos E'q' |
| 6. | CosEq SinBrq Sin M +Sin Eq CosN CosM-CosEq CosBrq SinN CosM = Sin Eq' |
| 7. | CosM CosN = CosLq CosZdq |
| 8. | CosM SinN CosBrq- SinM SinBrq = SinLq CosZdq |
| 9. | CosM SinN SinBrq + SinM Cos Brq = SinZig |
| 10. | Sin Brq CosN = SinB'rq CosZdq |
| 11. | CosBrq CosM - SinBrq SinN SinM = CosB'rq CosZdq |
| 12. | CosEg CosBgr CosN - SinEg SinN = CosE'g CosB'gr |
| 13. | CosEg SinBgr CosM+ SinEg CosN SinM + CosEg CosBgr SinN SinM = CosE'g Sin B'gr |
| 14. | SinEg CosN CosM + CosEg CosBgr SinN CosM -CosEg SinBgr SinM = SinE'g |
| 15. | SinB'ur CosM = SinBur CosL |
| 16. | CosB'ur CosN +Sin B'ur SinM SinN = CosBur CosL |
| 17. | Tan E'q's = SinE'q' / Cos E'q' CosB'r'q |
