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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 6
# Folio 34v, page id 00068208:0070
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ignoratur locus ubi loxodromia secat aequatorem, cum ipsa logam loxodro
mia ad huc ignoreture. Opus est ergo calculo quodam Algebraico ad transcen
denta applicuto, ad hoc determinandum sit puncum unud it alterum 3t
datur differentia latitudinis 1n3h, et longitudinis. 1929. Quaentu loxodromia
ol2 13C. seu angulus polEt quaeritur et punctur At quo loxodio mia quaesita si con
tinuetur secalit aequatorem.  uae sita assumamus tanquam inventa, et sit:
 A
du et
a
2e 
e n
A3qustresit y et A2
x sit (y)
n ad
det
et
v sit sinus complementi latitudinis Ait, et () sit sinus complementi
latitudinis A3h.
erit y aegu qui du sunt datis.  eta liv
sit((∞) sint horum duorum sinnum logarithmi, erit:
 3 e
aequa b lIVI. Datur autem differentia
y aequ.  lv unt ulo
a
am ea .
longitudinum seu, 123. Quae vocetur Z. ergo
y aequ. bd (V) - b Iv. seu
e a
a.C
a
5
(V)= lv
fiet.
11
o
. P: a
seu tangens languli loxod donniae est ad
sinum totum,
li congi
ut differeutia louetua  differem
Unde habemus theadema praeclarum:
e
augens anguli hexodromiae est ad finum
quas habent punca 
totum, ut
arcus differentiae longitudinume est ad differentiam. baga
dctarum rationum
interlogarithmoram hyperbolicoru iptanum complement
latitudinum quas habent eaedemtextrema
21d
ee
i
Huic theoremati si adutu pr a nobis nunc primum invento
de theorema supra demonstratum; et injum caltis notum:
et
n
pec.
si addatur
la
secans anguli loxodromiae est ad sinum totum uboquantitas
on veido
loxodro miae seu ritinerit
xtremorum
vorbu
est ad
in a retutu
differmitiamlatitudinum
un 3 alvam
u
ineum
sufficient ista ad cursum navis dirigendum, nec aliis
e
.
 mapnis. indinebit: gubernalorquam t
pus
reqvago aetum
tabulis aut
sinum Canone
Errgonometrico cum suis
communi et Logaritmisa nappisquencommunibus, dint
esa
ta
atitudinum longitudinamus
s
dn
nt
 ). 
 tt
in quibus
ptum
tet nulli
promontoria et loca periculosa sint bene descrisita
e utaraet
in iis rhombi notentur. illud famen, opus erit it indis
uia
observata
declinatione magnetica. cngulus onthombus verificetur,
quotras licet