is to be Sailed. They use a threefold Me∣thod
in this Affair, as they suppose this or that
to be more rightly observed.
1. The Rhumb being observed in which the
Ship was directed from the place of the first
Day, or from the place given on the Map, or
the Rhumb in which the Ship was moved, and the
quantity in the Interim of the Voyage made,
being observed. These two things being known,
the place of the Ship is found thus on the Map: [ 10]
Let the Rule, or Compass be taken, and one Shank
of it be applyed to the place of the former Day,
or from which the Ship departed; let the other
Shank be applyed to the Vicine Line, which re∣presents
the observed Quarter, or Course: Let
the Point of the Shank be noted with Chalk,
which is eminent over the place of the Depar∣ture.
Then by the Interval of the Compass, let
the Miles of the performed Voyage be taken from
the opposite Scale, and let one Foot of the Com∣pass [ 20]
be put upon the place of the Departure;
but let the Rule be moved on the Line of the
Quarter until the other Foot of the Compass touch
the noted Point of the Rule. The place of the
Map that is subject to that Point in that situa∣tion
of the Rule, is that demanded, viz. in which
the Ship then is.
But if that you determine to find out more
accurately the Point on the Map by Calculation,
or the place of the Ship it self, the Problem shall [ 30]
be this: The Latitude and Longitude of one place
being given, and the Quarter being given in which
they Sailed unto the other place, with the Voyage
performed, to find out the Latitude and Longi∣tude
of the other place. For these being found,
you may more accurately note the place of the
Ship on the Map.
2. The Quarter being observed in one known
place, to another unknown, and the Latitude of
this other, or Elevation of this Pole being ob∣served, [ 40]
to find the Situation of this other place on
the Map.
Let one Shank of the Rule be applied to the
Quarter observed near the place; and let the o∣ther
Shank be placed on the place known (or
whence the Voyage is begun) and make there on
the Shank a Mark with a Chalk; then let the
Shank applied to the Quarter be moved until the
other noted Point of the Shank applied to the
Quarter fall in on the Parallel of the observed [ 50]
Latitude. For the Point of the falling in, is the
place sought, viz. the place of the Ship. But if
that there be no Parallel of Latitude observed
on the Map, let the Degrees intercepted between
this Latitude and the Vicine Parallel,) be taken by
the interval of the Compass, on the Lateral
Line. And let the Rule in the Line of the Quar∣ter,
and one Foot of the Compass, be moved to∣gether
in this Parallel, until the other Foot of
the Compass, and the noted Shank do meet; the [ 60]
Point of the meeting sheweth the place of the
Ship. Seamen use two Pair of Compasses.
If that you will determine more accurately by
the Calculation of the place demanded on the
Map, or Earth it self, the Problem is this: The
Latitude and Longitude of one place being given,
and the Quarter in which the Navigation is ap∣pointed
to another place, and the Latitude of
this place given to find his Longitude; for the
Latitude and Longitude given is the place it
self.
3. The quantity of the Voyage performed,
from one known place to another unknown, be∣ing
observed, and the Latitude of this other be∣ing
observed, to find this other on the Maps.
Let the quantity of the Voyage performed,
be taken by the Interval of the Compass, from
the opposite Scale. Then if the Parallel through
the Degree of Latitude be observed on the Map,
let one Foot of the Compass be placed on the
noted place, the other Foot on this Parallel.
This Point shall be the place demanded. But if
the Parallel pass not through the Degree of La∣titude,
let one Shank of the Rule be applied to
the Vicine Parallel; on the other Shank let the
Degree of Latitude be noted, and let the Rule
be moved until the other Foot of the Compass
toucheth the noted Point of the Rule. The place
of the Map subject to the Point in this Situation
shall be the sought for place of the Ship.
If that a more accurate invention is required
by Calculation, the Problem shall be this: The
Latitude and Longitude of one place being given,
and the distance of the other on the Line of Na∣vigation,
and the Latitude of this, to find out
the Latitude of this other. For this being known,
when the Latitude is observed you have the Situ∣ation
of the place it self on the Maps, or Earth.
The 4th and 5th Method also of finding out
of this place is also given, viz. in which the
Longitude of the other, or sought for place is
supposed to be observed; but the Latitude is
unknown. But because that very seldom the
Longitude can be observed on the Sea, therefore
this Method is omitted, as useless. But he that
desireth more concerning this Method, let him
read Snellius, Stevens, Metius and others that
have treated at large thereof.
Proposition III.
To conjecture to what Quarter the Ship is moved,
and in what Rhumb, although the Signs be fal∣lacious.
IN this solution of the former Proposition for
the finding out the place of a Ship, those
things as noted were taken and observed, 1.
The Quarter unto which the Ship is moved, and
the Rhumb in which. 2. The way made. 3. The
Latitude of the place unto which it hath arrived.
Now therefore we must shew how these three
may be observed on the Sea, that they may be
used for the finding out the place; for if that
these be not rightly known, or observed, the
true place shall neither be found or discovered.
First therefore let us see concerning the Quarter
of the Course of the Ship, and the Rhumb.
The Pilots know the Quarter from the Com∣pass,
or Loadstone; For what Quarter, or Rhumb
of the Compass agreeth with the Line of the
conceived Longitude of the Ship, the same is
put into the Quarter of the Ship to be moved,
and to describe its Rhumb. For they seldome use