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Liber
IV.
DE
NAVIGATIONE
L I BE R
Q
V AR T
V
s.
De Loxodromiis.
f/
A M
f/
¡
S
faimtia Loxpdromica videat11r dtflicili>
,
earamq11e theoria
Jit–
perare cnpacitatem naucleromm communi11m
,
q11i falam praxin JPeélare debeml
q11ia tamm nihil in hac m11terta demonjlrare pojfitm, q11in inttllig11t11r n11t11-
r11
tlliH4 linu, q1tam d1iélu e¡11falem rombi pixulis n1111tice, fi1pr11 Jiiperficiem
telluris demmt navli
,
totam hanc doUrinam ad fua principia revocabo. Id
eo /ubentim (ncio, q11od jit hic Lyditu lapÜ
t¡tto 11omutl/.e praxes
a
mtt!tis pamm in Geo–
metría verfatis ptopomwt11r,
&
t¡11te 11liq11andu
a
vero ablied11nt. Ta/is atttem erit ordo htt–
f
ut
libri. Primo pr.emittam nonmdla Theoremala q11ib1u Loxodromi11mm 11at11ram explicabo,
tttm docebo methodum ji1pp11tandamm
tab1~lamm.
Ter;10 ufeu tradam ad direélionem n11-
vigii
,
fala 11tendo additione
,
&
ftbtraE11011e. .f2.!!_11r10 fa!vam omma problemata na1,tic11,
per
jiAIM
,
tangentes
,
&
fecantes
,
detegamq11e errores q11i in h11c materia per medmm pa–
ralld11m committ11nt11r,
&
q11ten11m verA corretlto debeat adh1beri. HtU ergo methodos do*
{ltortbtu propono, factliores_
&
geometrictU libro feq11enti propójittmis. Si enim n111tclemm infli–
t11end1tm fii(ctperem
,
nollem mm arithmetws calmlir mtrtcare, in q11ib1is
11ifi
Jit exerctta–
tifamus potejl in gravtf¡mos errores impingere; faltU praxes goometrictH ea(q11e fac1ll1mtU ei
proponerem. Ji2!!)a tamen Jap1enlibtU,
6-
injipientib11s debitor ji1m, in hoc libro praxes arith–
metiou difjicit1ores propono. In feq11enti Gcometriuu
&
faaiiores tr11dittm1S.
il1lll1ltlD!l'llil1lNJl!11iJWJIJ.tilj1JTirlilW,il1ll.lll1l1Hfllml!l!llllJlllJ
P R O P O S I T I O
l.
Theorema.
De
narnra
lint.t loxodroniic.t
,
quam
dtf<
ribit
11avu
d11ifo e¡ufdem Rhombi
pi:ddu
n11mic4.
Linea loxodromica otiginem Íuam dncir , ex
pra:cipuo navigationum inlhumemo Ícil1ccr ex
paxidc namica. Clarnm c'.iim efl qnod fi fcqna–
mur.eundem rumbum obllquum pixidis nau1ica:
v~rbi
gratii Sudoflum , linea quam decurrer
na~
vis cum omnibns mcridianis ang11l11m graduum
~; c~mprehender;
qua:timus igimr qua:na111
fic ·
1lla lmea , qua: cum omnibus meridianis angu–
lum femireél:um ef!icit,
Diximus fupra rofam pixidis naudcá: exhibere
horizonrem ,
&
lineas romborum
elfo
commu–
nes
feéHo~es ver~icalimn;
cum plano horizonris,
quz pro uídem c1rculis aíli.1mi poffinr. Noran–
dum
ra~en
eundem maximum circulum qui ref–
pell:u al1cujus regionis verricalis alicujus mune–
re
f~ng!1ur
, reípeél:u alterius regionis alrerius
vemc~hs
munere fungi ; verbi gra1ia fi
íolvo
maffilia per Sudeftum, íeu 45 venicalem , dum
1~ulr.llln
progreffus infiíl:endo ícmper eidem ver–
t'.c~li
, randem hic circulus non amplius cum me–
.r1d1ano
a~gu_lum_ eu1~de.m
dncier ,
&
coníequcn–
rer non tndicabtmr a lmea Sudcfü , qua: aliam
vemcalem oílender; quare fi imperarum
¡¡,
111
femper fequar eandem lioeam Sudefii , inirio in-
!iftam circulo verricaii, qui erat
4;
reípeél:u il•
lius horizontis
e
quo profcéhis fom , hunc au-
1em poftea de[eram , q11ia cum a\io meridiano
ad quem ícilicet perveni., non efficit angulum
~
5 gradumn; íed minorem • qnare
fi
dirigar íem–
per eadem linea pixidis nautica:, non pcrcurram
maximum circulum; fed aliam linea111 curvam.
H.ecd1ffic11lrns jam olim Nonio propofira foic
a
celtbri nauclcro in hnnc modum : Rumbus
Orienialis Íen Efl, exhibet circulmn maximum ,
íed duo circuli
fe
bifariam Íecanr
(per
11.r.The...
dofi1)
igitur circulus maximus quem rombus
Ef1u
repra:Íentat, fecat a:q11inoétialem circulmn
A
Q'.iod manife!lum eft ex
eo
quod
~o\
dic.zqlJiM•
ll:ii oriatur in ea linea, ncmpc onatur m rombo
Efl