Overview Level of Folio 103 v

 Size Height 270 mm, width 195 mm. Watermark Siren. Drake's identification: Watermark type 25. Drake's description: Siren in 39mm circle, crown above. Watermark found in 1632. Comments Written by Galileo; contains text, calculations, drawing. Relation to the Discorsi: related to 3/13-pr-06. References Caverni 1972 561
 Folio 103 v (final text) 1A Tabula altitudinum semiparabolarum infra elevationem gr[adus] 45, quarum impetus est semper idem, nempe sublimitas cum altitudine 10000. 1B Sit impetus datus semper idem, nempe bd ex altitudine et sublimitate composita linea db 10000; et quia, dimidia amplitudo, nempe bf, mediat inter altitudinem et sublimitatem, intelligatur db divisa ita, ut [rectangulum] partium sit aequale [quadrat]o fb. Quod si db divisa sit bifariam in e, erit [quadratum] be aequale [rectangulo] partium ipsius db et [quadrato] ae; si ergo a [quadrato] be dematur [quadratum] fb (seu dicas [rectangulum] illi aequale, a partibus contentum), remanebit [quadratum] ea, cuius radix dempta ex eb, relinquet ba altitudinem quaesitam. Amplitudo autem bc iam calculata est ad singulos gradus elevationis. C01 G. 1. 349 = 174 1/2 + 174 1/2 174 1/2 * 174 1/2 = 696 + 1218[0] + 174[00] + 174 = 30450 25000000 - 30450 = sqrt 24969550 = 495[0] sqrt 24969550 = 4996 C02 G. 4. 1391 = 695 + 696 695 * 696 = 4170 + 6255[0] + 4170[00] = 483720 25000000 - 483720 = 24516280 sqrt 24516280 = 4950 5000 - 4950 = 50 C03 Gr7 2419 = 1209 + 1210 1209 * 1210 = 12090 + 2418[00] + 1209[000] = 1462890 25000000 - 1462890 = 23527110 sqrt 23527110 = 4850 5000 - 4850 = 150 C04 Gr. 10. 3420 = 1710 + 1710 1710 * 1710 = 17100 + 1197[000] + 171[0000] = 2924100 25000000 - 2924100 = 22075900 sqrt 22075900 = 4698 5000 - 4698 = 302 C05 G. 14. 4694 = 2347 + 2347 25[000000] - 5519409 = 19480591 2347 * 2347 = 16429 + 9388[0] + 7041[00] + 4694[000] = 5508409 25[000000] - 5508409 = [19491591] sqrt 19980591 = 4413 5000 - 4413 = 587 5000 - 4415 = 585 sqrt 19491591 = 441[4] C06 Gr. 2. 698 = 349 + 349 349 * 349 = 3141 + 1396[0] + 1047[00] = 121801 25000000 - 121801 = 24878199 sqrt 24878199 = 4987 5000 - 4987 = 13 C07 G. 5? . 1736 = 868 + 868 868 * 868 = 6944 + 65208[0] + 944[00] = 753424 25000000 - 753424 = 24246576 sqrt 24246576 = 4924 5000 - 4924 = 76 C08 Gr. 8. 2756 = 1378 + 1378 1378 * 1378 = 11024 + 9646[0] + 4134[00] + 1378[000] = 1898884 25[000000] - 1898884 = 23101116 sqrt 23101116 = 4816 sqrt 23101116 = 4806 5000 - 4806 = 194 C09 G. 11. 3746 = 1873 + 1873 1873 * 1873 = 5619 + 13111[0] + 14984[00] + 1873[000] = 3508129 25[000000] - 3508129 = 21491871 sqrt 2149187 = 4646 5000 - 4646 = 354 C10 G. 15 5000 = 2500 + 2500 2500 * 2500 = 6250000 25[000000] - 6250000 = 17500000 sqrt 17500000 = 4324 5000 - 4324 = 676 C11 G. 3 1044 = 522 + 522 522 * 522 = 1044 + 1044[0] + 2610[00] = 272484 25000000 - 272482 = 24727516 sqrt 24727516 = 4972 5000 - 4972 = 28 C12 G. 6. 2079 = 1039 + 1040 1039 * 1040 = 41560 + 1039[000] = 1080560 25[000000] - 1080560 = 23929440 sqrt 23929440 = 4892 5000 - 4892 = 108 C13 G. 9. 3090 = 1545 + 1545 1545 * 1545 = 7725 + 6180[0] + 7725[00] + 1545[000] = 2387025 25[000000] - 2387025 = 22612975 sqrt 22612975 = 4755 5000 - 4755 = 245 C14 G. 12. 4067 = 2033 + 2034 2033 * 2034 = 8132 + 6099[0] + 4066[000] = 4135122 25[000000] - 4135122 = 20864878 sqrt 20864878 = 4568 5000 - 4568 = 432 C15 G. 16 5300 = 2650 + 2650 2650 * 2650 = 132500 + 1590[000] + 530[0000] = 7022500 25[000000] - 7022500 = 17977500 sqrt 17977500 = 4239 5000 - 4240 = 760 C16 Gr. 13. 4383 = 2191 + 2192 2191 * 2192 = 4382 + 19719[0] + 2191[00] + 4382[000] = 4802672 25[0000000] - 4802672 = 20197328 sqrt 20197328 = 4494 5000 - 4494 = 506 C17 G. 17 5592 = 2796 + 2796 2796 * 2796 = 16776 + 25164[0] + 19572[00] + 5392[000] = 7817616 25[000000] - 7817616 = 17182384 sqrt 17182384 = 4145 5000 - 4145 = 855

 Overview Level of Folio 103 v