1
[A:15v]
|
ug |
|
40 |
![graffa chiusa](#micons/braces/rbra3.jpg) |
continue proportionales |
uh1 |
|
24 |
ub2 |
|
14 2/5 |
du fg3 |
|
24 |
rg4 |
|
30 |
rf |
|
6 |
bh |
|
9 3/5 |
hg |
|
16 |
f |
|
8 |
o |
|
6 |
|
|
2
Diametri
Recta 2a 64
Transversa pa kh 48
Transversa 2a au duplicata 36
Recta pa hp 27
3
aq qh tangentes peripherias5 apud puncta ha
bf6 tangens peripheria apud punctum f.
4
|
continue proportionales |
![graffa aperta](#micons/braces/lbra3.jpg) |
du |
|
24 |
au |
|
18 |
uc |
|
13 1/2 |
|
|
5
|
hp |
|
27 |
gn |
|
36 |
gx |
|
22 1/2 |
tg |
|
32 |
g9 |
|
18 |
g& |
|
9 |
|
|
6
7
|
r7f |
|
6 |
qh |
|
18 |
|
|
duplum fg cum rf scilicet 54 continue proportionalis
8
|
continue proportionales |
![graffa aperta](#micons/braces/lbra3.jpg) |
hg |
|
16 |
fg |
|
24 |
gn |
|
36 |
|
|
9
1/2 fo scilicet 5
1/2 uq scilicet 15
fu fg 45 continue proportionalia
10
|
h |
9 |
![angolare chiusa](#micons/braces/rang2.jpg) |
43 1/5 |
bh |
![graffa aperta](#micons/braces/lbra7.jpg) |
1/2 bh |
4 4/5 |
| |
kg tg hg continuis proportionalis |
equalia |
| |
gn g9 g& ***8 proportionalis |
![Radix](#micons/RDX.gif) |
5 2/5 |
![angolare chiusa](#micons/braces/rang2.jpg) |
43 1/5 |
f![psi](#micons/greek/ygreek.gif) |
1/2 hg |
8 |
|
|
Ex quibus circa hyperbolen, per numeros comprobat risulta que in conicorum theoria demonstrandum
|
hgn9 |
tg9 |
kg& |
equalia |
16 36 572 |
18 32 576 |
9 64 576 |
|
|
11
[A:16r]
|
ug |
|
122 |
![graffa chiusa](#micons/braces/rbra3.jpg) |
continue proportionales |
uh |
|
22 |
ub |
|
3 59/61 |
du fg |
|
60 |
tg |
|
61 |
rf |
|
1 |
|
|
12
Diametri10
***11 Recta 2a 88
Transversa ***12 44 kh
hp Recta 22 ***13 continue proportionales
13
bh 18 2/61
hg 100
f 2
o 1
14
qh 11
h 10 50/6114
h 9 1/615
![Radix](#micons/RDX.gif) 1 239/366
15
|
du |
|
60 |
![graffa chiusa](#micons/braces/rbra3.jpg) |
continue proportionales |
au |
|
11 |
uc |
|
2 1/60 |
|
|
16
rf 1
qh 11
duplium fg cum rf scilicet 121
continue proportionalia
17
gn 36
gx 30 1/2
g9 30
g& 25
18
bh 82 119/183
equalia
f![psi](#micons/greek/ygreek.gif) 82 119/183
Nam aq qh if tangunt peripheriam apud puncta qhf
Atque bh productam ex basi h in 1/2 bh celsitudinis vero f![psi](#micons/greek/ygreek.gif) ex basi ![Radix](#micons/RDX.gif) in 1/2 hg ***16
19
Item hp est diameter recta ad quam possunt ordinate ad diametrum kh ipsae autem lineae kpn uyx tz9 h& ponuntur aequidistantes. Ipsae autem tf linea aequidistat ipsi uq17 r nontangenti. Cumque qh possit uhy quod est 1/4 speciei. Iam propter similitudine ![triangolo](#micons/TRN.gif) lorum rg poterit ugx. Et fg poterit tg9 minus ipso ugx. Quare fg semper minor erit, quam rg. Cumque fg possit hgn erunt hgn tg9 aequalia. Quamobrem sicut tg gh sic gn g9. Et propter similitudine ![triangolo](#micons/TRN.gif) lorum sicut kg tg et rursus propter similitudinem triangolorum sicut gn g9 sic g9 g&. Quamobrem tam lineae kg tg hg
quam lineae gn g9 g& erunt in eadem proporzione continua. Unde tria ![rettangolo](#micons/RTT.gif) hgn tg9 kg& inter se aequalia sunt. [a:16v]
20
|
ug |
|
74 |
![graffa chiusa](#micons/braces/rbra3.jpg) |
continue proportionales |
uh |
|
24 |
ub |
|
7 29/37 |
fg du |
|
52 1/2 |
rg |
|
55 1/2 |
rf |
|
3 |
bh |
|
16 8/37 |
hg |
|
50 |
|
|
21
Diametri
|
64 |
kh |
|
48 |
Continue proportionale |
duplicata au |
|
36 |
hp |
|
27 |
|
|
22
f 4
o 3
23
|
du |
|
52 1/2 |
![graffa chiusa](#micons/braces/rbra3.jpg) |
continue proportionales |
qh -- au |
|
18 |
u |
|
6 6/35 |
|
|
24
|
hg |
|
50 |
![graffa chiusa](#micons/braces/rbra3.jpg) |
continue proportionales |
fg -- au |
|
52 1/2 |
gn |
|
55 1/8 |
|
|
25
|
rf |
|
3 |
![graffa chiusa](#micons/braces/rbra3.jpg) |
continue proportionales |
qh |
|
18 |
duplicata fg cum rf |
|
108 |
|
|
26
|
1/2 fo |
|
2 1/2 |
![graffa chiusa](#micons/braces/rbra3.jpg) |
continue proportionales |
1/2 uq |
|
15 |
su |
|
90 |
|
|
|
h |
|
12 6/7 |
![angolare chiusa](#micons/braces/rang2.jpg) |
productam -- 104 64/259 bh |
1/2 bh |
|
8 4/37 |
|
|
27
gh 18
h 17 1/37 scilicet 7/259
h 12 6/7 scilicet 252/259
![Radix](#micons/RDX.gif) 4 44/259
28
|
![Radix](#micons/RDX.gif) |
|
4 44/259 |
![angolare chiusa](#micons/braces/rang2.jpg) |
productam 104 64/259 f![Radix](#micons/RDX.gif) ![psi](#micons/greek/ygreek.gif) |
1/2 hg |
|
8 4/37 |
|
|
Item
|
q 36/37 |
| |
u 52 1/2 cum r. 2432 1/4 |
l 70 cum r. 4324 |
|
|
29
Ex quo calculo, circa hyperbolen, quo ad diametros, ordinatas, tangentes, quo ad lineas proportionales, ad triangola aequalia, parallma aequalia, nontangentes et aequidistantias, per numeros rationales omnia fere comprobant, quae in conicis theoriae demonstrant.
30
gn 55 1/8
gx 41 5/8
g9 39 3/8
g& 28 - 1/8
31
13 octobre 1565
32
[A:17r] Rursus ***18 descriptione hp est diametrum recta: ad quadratum possunt ordinate ad diametrum kh. Ipsae autem lineae kpn, uyx, tz9, h& punctum aequidistantes ipsa ***19 tf linea aequidistat ipsi u r nontangente. Cumque kh possit uhy quod est quadras speciei; iam propter similitudinem ![triangolo](#micons/TRN.gif) lorum rg poterit ugx et fg poterit tg920 minus ipso lo ugx. Quare fg semper minor erit quam rg. Cumque fg possit hgn propterea erunt ![rettangolo](#micons/RTT.gif) lum hgn tg9 aequalia. Quare, sicut tg--gh sic gn--g9. Et propter similitudinem ![triangolo](#micons/TRN.gif) lorum sicut kg--tg et sicut g9--g&. Tam lineae kg--tg--hg quam lineae gn--g9--g& erunt in eadem proporzione continua. Unde tria ![rettangolo](#micons/RTT.gif) ![rettangolo](#micons/RTT.gif) la hgn, tg9, kg& erunt ***21 aequalia.
14 no. 1565
33
Quamobrem sub ***22
|