PAL

Ptolemaeus Arabus et Latinus

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Paul of Gerresheim, Expositio practice tabule tabularum et propositionum Ptolomei pro compositione tabule sinuum et cordarum necessariarum

Brussels, BR, 1022-1047 · 196v

Facsimile

Tabula sinuum et cordarum rectificata
Arcus augmentati per dimidium gradum
Sinus seu corde mediate
Arcus augmentati per dimidium gradum
Sinus seu corde mediate
G
m
G
m
G
m
2
3
4
G
m
G
m
G
m
2
3
4
0
30
179
30
0
31
24
55
19
15
30
164
30
16
2
3
29
13
1
0
179
0
1
2
49
43
7
16
0
164
0
16
32
17
40
41
1
30
178
30
1
34
14
13
15
16
30
163
30
17
2
27
18
52
2
0
178
0
2
5
38
17
20
17
0
163
0
17
32
32
17
40
2
30
177
30
2
37
1
47
24
17
30
162
30
18
2
32
27
18
3
0
177
0
3
8
24
33
59
18
0
162
0
18
32
27
40
15
3
30
176
30
3
39
46
29
9
18
30
161
30
19
2
17
47
49
4
0
176
0
4
11
7
23
36
19
0
161
0
19
32
2
43
13
4
30
175
30
4
42
27
9
53
19
30
160
30
20
1
42
16
0
5
0
175
0
5
13
45
38
43
20
0
160
0
20
31
16
20
55
5
30
174
30
5
45
2
40
53
20
30
159
30
21
0
44
47
48
6
0
174
0
6
16
18
8
53
21
0
159
0
21
30
7
28
37
6
30
173
30
6
47
31
53
40
21
30
158
30
21
59
24
15
58
7
0
173
0
7
18
43
46
50
22
0
158
0
22
28
35
1
11
7
30
172
30
7
49
53
39
27
22
30
157
30
22
57
39
37
17
8
0
172
0
8
21
1
22
49
23
0
157
0
23
26
37
50
48
8
30
171
30
8
52
6
50
10
23
30
156
30
23
55
29
47
52
9
0
171
0
9
23
9
50
40
24
0
156
0
24
24
15
6
54
9
30
170
30
9
54
10
16
56
24
30
155
30
24
52
53
44
53
10
0
170
0
10
25
8
0
57
25
0
155
0
25
21
25
32
48
10
30
169
30
10
56
2
52
25
25
30
154
30
25
49
50
23
49
11
0
169
0
11
26
54
44
26
26
0
154
0
26
18
8
10
8
11
30
168
30
11
57
43
28
28
26
30
153
30
26
46
18
43
47
12
0
168
0
12
28
28
55
31
27
0
153
0
27
14
21
56
53
12
30
167
30
12
59
10
57
28
27
30
152
30
27
42
17
41
54
13
0
167
0
13
29
49
25
42
28
0
152
0
28
10
5
51
58
13
30
166
30
14
0
24
11
55
28
30
151
30
28
37
46
17
32
14
0
166
0
14
30
55
8
3
29
0
151
0
29
5
18
52
48
14
30
165
30
15
1
22
4
55
29
30
150
30
29
32
43
29
25
15
0
165
0
15
31
44
54
49
30
0
150
0
30
0
0
0
0

Cuiuslibet arcus propositi sinum rectum invenire: si arcus propositus fuerit maior 180 gradibus subtrahe ab eo 180 gradus et cum residuo sive cum minori propinquiori intra tabulam et accipe sinum. Intra etiam cum maiori propinquiori et illius accipe sinum. Subtrahe unum sinum ab alio et differentiam sinuum multiplica per minuta que habes infra vel ultra 30 et productum divide per 30 minuta et proveniet pars proportionalis addenda primo sinui aut subtrahenda ab eodem.

Cuiuslibet arcus cordam perfectam reperire: arcum propositum media et illius sinum rectum dupla.

Cuiuslibet arcus sinum versum reperire: si arcus fuerit minor 90 gradibus ipsum a 90 subtrahe et remanentis sinum rectum de 60 gradibus subtrahe. Si vero arcus propositus maior 90 gradibus subtrahe ab eo 90 gradus et residui sinum rectum adde 60 gradibus.