Overview Level of Folio 62 r


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


Overview Level of Folio 62 r