PAL

Ptolemaeus Arabus et Latinus

_ (the underscore) is the placeholder for exactly one character.
% (the percent sign) is the placeholder for no, one or more than one character.
%% (two percent signs) is the placeholder for no, one or more than one character, but not for blank space (so that a search ends at word boundaries).

At the beginning and at the end, these placeholders are superfluous.

Erasmus Oswald Schreckenfuchs, In Almagesti priores tres libros annotationes

Basel, Henricus Petri, 1551 · C3r

Facsimile
Arcus
F A
A B
F T
T I
I E
E B
F T
180°

41° 42ʹ 40ʹʹ
180°

52°
180°

Chordae
120°

48° 31ʹ 54ʹʹ
60°
120°
Arcus
qui
quaeritur


52° 36ʹ 16ʹʹ
60°
120°

Solutio graduum


2880


3120



31

36
Solutio minutorum


2911


3156



60

09
Solutio secundarum


174660


189360



54

16
Multiplicatio secundarum et
tertiarum

174714


189376



120





3494280


174714


20965680



1 1 1
Divisio per primum numerum

1 8 5 8 1 4

2 0 9 6 5 6 8 0 (174714
1 2 2 2 2 2 2 0

1 1 1 1 1

189376
174714
Multiplicatio per quintum numerum

757504

189376

1325632

757504

1325632

189376
104

3 3 0 8 6 8 3 8 4 6 4
Divisio per sextum
numerum

(275723653
1 2 2 2 2 2 2 2 2 2 0
Reductio in gradus,
minuta et secundas per
60
3
3 1 5 2
3 3 1 5 5
1 4 3 2
1
Graduum, minutorum
secundarum 21 16 29
chorda
2 7 5 7 2 3 6 5 3
4 5 9 5 3 9 4
7 6 5 8 9
1 2 7 6
6 6 6 6 6 6 6 0
6 6 6 6 6 0
6 6 6 6 0
6 6 0
Arcus 20° 25ʹ 25ʹʹ
Medietas 10° 12ʹ 43ʹʹ
fere tantus est arcus TI

Exemplum secundae rationis secundum subtractionem proportionum

Cum volueris operari, duc terminum secundum auferendae proportionis in terminum primum proportionis a qua debet fieri subtractio; productum constitue numerum primum. Deinde duc terminum primum auferendae in terminum secundum alterius, quod nascitur sit secundus numerus, pro tertio numero constituas illum qui proportionatur ad numerum quaesitum: huius rei cape tale exemplum. Si cupio scire quanta sit Solis obliquatio cum abest a sectione vernali 39 gradus.

F A
A B
F T
T I
I E
E B
Arcus
180°
42° 42ʹ 40ʹʹ
180°

78°

Chorda
120°
48° 31ʹ 54ʹʹ
120°

75° 31ʹ

Solutio
432000
174714
120

271860
432000

4 3 2 0 0 0

1 7 4 7 1 4
Ordinatio

╳


2 7 1 8 6 0

4 3 2 0 0 0

4 3 2 0 0 0

2 7 1 8 6 0

4 3 2 0 0 0

1 7 4 7 1 4

8 6 4 0 0 0 0 0 0

1 0 8 7 4 4 0

1 2 9 6 0 0 0

2 7 1 8 6 0

1 7 2 8 0 0 0

1 9 0 3 0 2 0

1 0 8 7 4 4 0

1 9 0 3 0 2 0
2 7 1 8 6 0

1 8 6 6 2 4 0 0 0 0 0 0

4 7 4 9 7 7 4 8 0 4 0



1 2 0
Productum multiplicationis

9 4 9 9 5 4 9 6 0 8 0 0

4 7 4 9 7 7 4 8 0 4 0
Dispositio numeri ad divisionem
5 6 9 9 7 2 9 7 6 4 8 0 0
Productum divisionis

1 8 6 6 2 4 0 0
0 0 0 0
30° 32ʹ 28ʹʹ

28° 29ʹ Arcus
Tantus est arcus TI qui quaerebatur
14° 44ʹ 30ʹʹ dimidium