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 |
|
|
|
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 |
|