453

12
I 2

30 9.83781 81 983795 32 9.83808 33 9.83821 84 9.83834 35 9.83848 86 9.83861

12

14 13 13 13 14 13 13

30 29 28 27 26 25 24

9*97776
9'97801
9*97826
9'97851
9.97877

12

I2

I 2

I 2

12 12

23 22 21 20 19 18

I 2

12

12

25

997725 10*02275 9.86056

25 9.977501

26

10°022509.86044

10'02224 9.86032
25
25

10'02 1999.86020

10°021749.86008
25
26

10°02149 9.85996

10'021239.85984

25
9'97902 10°02098 9.85972

25
9.97927

26

10.02073 9.85960 9'97953 10°020479.85948

25 997978

10'02022 9.85936

25 9998003

26

10'01997 9.85924
9.98029 10*01971 9.85912

25
9998054 10401946 9.85900
9'98079

25
10'019219-85888

I2
9998104

26
10.01896 9.85876

12
998130

10'01870 9.85864 9*98155 10.01845 9.85851

13

12 9'98180

10.018209.858391 26

I2
9'98206

25
10*017949.85827

12
9'98231
10401769 9.85815

I 2
25
998256 10*017449985803

12
9998281

26
10*01719. 9.85791

I2
9.98 307 10'01693 9.85779

25
9.98332
10:01668 9085766

13
25
9.98357

26
10'01643 9.85754

12
9.98383

10'016179.85742 25

I 2 9998408

10401592985730
25

I 2
9-98433 10.015679.85718
25

I2
9.98458

26

10.01542 9.85706 9.98484 10'01516 9:85693

13

17 16 15 14 13 12

25

SSOS

25

SOLUTION OF THE CUBIC EQUATION

23 + px + q=0,
BY TRIGONOMETRICAL TABLES.

Case L.
23 + px +9=0.

pp.
tan B =

= m.

= 8

tan A= tan : B. (1) x= F 2 cot 2 AV }p. (2) x=

=(+cot 2 A + cosec 2 AV-3)/ tp. (3) <=

- (+cot 2 A - - cosec 2 A V-3)/ }p.

2

Case II.
03 – px +q=0.

(m< 1.) sin B=m.

tan A=tan 4B. (1) x = F 2 cosec 2 AV {p. (2) x=(+ cosec 2 A + cot 2 AV-3)/ \ p. (3) x=(+ cosec 2 A cot 2 AV-3) }p.

=

(in > 1.)

Care III.
THE IRREDUCIBLE CASE.

23 – px +9=0.
cosec B=m.

A = { B.
(1) <= 2 sin AV Ip.
(2) x=+ 2 sin (60° – A) VIP.
(3) <= F 2 sin (60'+ A)/1p.