 | Size | Height 278 mm, width 200 mm. | | Watermark | Pilgrim. Drake's identification: Watermark type 23. Drake's description: Crowned heald in circle 38mm. Watermark found in 1631-34. Found in manuscripts 1612-14 (floating body controversy), 1631-32 (note on Rosa Ursina). | | Comments | Written by Galileo; contains texts, drawings, tables, calculations. Relation to the Discorsi: related to 2/29-th-18. | | References | Drake 1978 497 |
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| | | Folio 62 r (final text) | | 1A | cum ab sit dimidia bc, et sit eadem ab tempus per ab, erit tota bc tempus per ambas abc. | | 1B | Accipiatur be, et sit bo media inter eb, ba, et erit ob tempus per eb et per [du]plam ipsius bd. Quod si db conficitur tempore bo, cb quo tempore conficietur fiat igitur ut db ad bo, ita cb ad aliam, quae sit, verbigratia, bn, et ostendatur [du]as ob, bn maiores esse ipsa bc, et habebitur intentum. | | 2A | Redacta est res ad hoc lemma: sit eb utcumque secta in a, et inter eb, ba media sit bo, et ut eb ad ba, ita sit ob ad bn. Dico | | 2B | eb, bo, ba, bn esse continue proportionales. Quia enim ut eb ad bo, ita bo ad ba, ratio eb ad ba erit [du]pla rationis ob ad ba: et quia ut eb ad ba, ita ob ad bn, est autem ratio be ad ba [du]pla rationis ob ad ba, erit quoque ratio ob ad bn [du]pla rationis bo ad ba. Verum ipsa ratio ob ad bn componitur ex rationibus ob ad ba et ab ad bn: ergo ratio ab ad bn est eadem cum ratione ob ad ba: ergo patet propositum. | | 3 | ab 20
ib 12
bs 15 3/10 tempus per bi
br 30
bn 38 7/17 tempus per rb
media inter cr, rb 46
tempus per rc 59
tempus per bc 20 2/5
tempus per ibc 35 1/2
Si tempus per rb esset rb, tempus per rc esset 46
mod[o] est 59. | | 4 | ab 20
bc 40
bd 50
cd 90
de 67
be 17
ec 23
abe 37
tempus per bc ex quiete in b est 44 1/3 proxime; tempus per abc 37. | | C01 | (12 * 50) : 20
12 * 50 = 600 | | C02 | 20 2/5
15 3/10
35 1/2 | | C03 | 54
38 7/17
20 10/17 | | C04 | 70 * 30 = 2100
sqrt 2100 = 45 145/170 | | C05 | 12 * 20 = 240
sqrt 240 = 15 15/50 = [15] 3/10
30 * 50 = 1500
sqrt 1500 = 38 56/136 = [38] 28/68 = [38] 7/17 | | C06 | (46 * 38 2/5) : 30 | | C07 | 46 * 38 2/5 = 368 + 1388 + 10 = 1766
1766 : 30 = 59 | | C08 | 90 * 50 = 4500
sqrt 4500 = 67 | | C09 | 40 * 50 = 2000
sqrt 2000 = 44 32/84 = [44] 8/21 | | C10 | | db | bc | cd | | | | | | 67 | 47 | 28 | 100 | 130 | 50 | 65 | | | C11 | 54_24_18_8
(12 * 24) : 54
24 * 12 = 288
288 : 54 = 5 1/3 | | C12 | 40
30 |
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