Overview Level of Folio 125 v

 Size Height 278 mm, width 200 mm. Comments Written by Galileo; contains text, calculations, tables. Relation to the Discorsi: statement and elaboration of 3/14-pr-07. References Caverni 1972 531-532, 562-563
Folio 125 v (final text)
1A Altitudines semiparabolarum, quarum eadem sit amplitudo, reperire.
1B Id autem absolvitur per dimidiam tangentem arcum elevationis datae semiparabolae.
1C Inventa, ex dictis, altitudine, sublimitates singularum semiparabolarum, quarum eadem sit amplitudo, facile reperies. Nam, cum dimidia amplitudo mediet inter altitudinem et sublimitatem, diviso [quadrato] mediae amplitudinis per altitudinem, habebimus sublimitatem, quae postea, addita altitudini, exibet impetum.
1D Fabricemus ergo tabulam sublimitatum, sitque semper dimidia a[m]plitudo semiparabolae 5000. Eius [quadratum] semper idem 25000000. Elevatio sit gr[adus] 1, tangens ipsius 174 1/2, qualium tangens gr[adus] 45 est 10000.
2 tangens gr[adus] 1, 174 1/2. Eius dimidium 87 1/4: per hunc numerum divide [quadratum] 25000000.
3 Tabula
C01
 Elevationes Altitudines Sublimitas Gr: 1 87 287356 Gr. 2 175 1/2 142450 3 262 95802
C02 Gr.1 174 1/2
C03 91
91
92
93
95
95
96
98
98
99
101
103
103
106
107
108
111
114
113
95
98
C04 Gr. 4
10000000 : 349 = 28653
50000000 : 349 = 143266
143062
C05 995?
1529[00]
162899
172299
C06 500000000 : 87 = 574758
286533 [* 2 =] 573066
C07
 88 88 87 87 77 77 88 88 138 89 89 88 88 89 95 89 84 90 91 91 91 91
C08 Gr. 4
699 [: 2 =] 349 1/2
50000000 : 699 = 71531
C09 G. 5.
50000000 : 875 = 57285
50000000 : 875 = 57142
C10 G. 6.
50000000 : 1051 = 47573
C11 G. 7.
1225 [: 2 =] 614
25000000 : 614 = 40716
C12 G. 8.
50000000 : 1405 = 35587
C13 G. 9.
1584 [: 2 =] 797
25000000 : 31368
25000000 : 792 = 31565
C14 G. 10
50000000 : 1763 = 28367
C15 G. 11.
1944 [: 2 =] 972
25000000 : 972 = 25720
C16
C17 G:12.
2125 1/2 [: 2 =] 1063
25000000 : 1063 = 25[?]
25000000 : 1063 = 23518
C18 G. 13.
2303 [: 2 =] 1154
25[000000] : 1154 = 21701
50000000 : 2309 = 21654
25000000 : 1154 = 24[?]
C19 701 - 654 = 47
2125 : 2 = 1062
C20 25000000 : 87 = 287356
100000000 : 349 = 286533
C21 Gr. 2. dimid[?]
349.
25[000000] : 175 1/2 = 50000000 : 351
50000000 : 351 = 142450
C22 G. 3
524 [: 2 =] 262
25000000 : 262 = 95802
C23 G. 31.
50000000 : 6009 = 8336
C24 G. 32
50000000 : 6249 = 8001
C25 G33
6494 [: 2 =] = 3247
25000000 : 3247 = 7699
C26 G34
50000000 : 6245 = 7413
C27 G. 35.
50000000 : 7002 = 7141
C28 G. 36.
5000000 : 7265 = 6882
C29 G37.
7536 [: 2 =] 3768
25000000 : 3768 = 6635
C30
 Gr.1 174550 174657 Gr. 2 349207 87 174871 Gr. 3 524078 87 175191 Gr. 4 699269 88 175617 Gr. 5 874886 88 176804 Gr. 6 1051042 88 176804 Gr. 7 1227846 89 177562 Gr. 8 1405408 178436 Gr. 9 1583844 Gr. 10
C31 G. 14.
2493 [: 2 =] 1246
5000000 : 2493 = 20056
C32 G. 15.
2679 [: 2 =] 1339
5000000 : 2679 = 18663
C33 G. 16.
2867 [: 2 =] 1484
5000000 : 2867 = 17405
C34 G. 17
3057 [: 2 =] 1529
5000000 : 3057 = 16355
C35 Gr. 18.
3249 [: 2 =] 1629
5000000 : 3249 = 15390
C36 G. 19.
3443 [: 2 =] 1722
5000000 : 3443 = 14522
C37 Gr. 20.
3640 [: 2 =] 1820
25000000 : 1820 = 13736
C38 Gr. 21
3839 [: 2 =] 1919
5000000 : 3829 = 13024
C39 G. 22.
4040 [: 2 =] 2020
25000000 : 2020 = 12376
C40 G. 23
4245 [: 2 =] 2123
5000000 : 4245 = 11778
C41 G. 24
4452 [: 2 =] 2226
25000000 : 2226 = 11230
C42 G. 25
4663 [: 2 =] 2332
5000000 : 4663 = 10722
C43 G. 26.
5000000 : 4877 = 10253
C44 G. 27
5000000 : 5095 = 9812
C45 G. 28
5000000 : 5317 = 9404
C46 G. 29
5000000 : 5543 = 9020
C47 G. 30
5000000 : 5774 = 8659

 Overview Level of Folio 125 v