DOI Seite / Zitierlink:
https://doi.org/10.11588/diglit.20658#0364
( 350 )
BOOK VL
OP PROJECTION,
CHAP. I.
OF THE ORTHOGRAPHIC AND STEREOGRAPHIC PROJECTION OF THE SPHERE, AND THE
METHOD OF DRAWING UNIVERSAL MAPS.
BY the projection of the sphere on a plane is meant the representation of the several
points or places of the surface of the sphere, and of the circles thereon described, upon a
transparent plane placed between the eye and the sphere ; or such as they appear to the eye at
a given distance. Projection is therefore only a particular case of perspective, and subject to
the laws thereof.
The chief use of the projection of the sphere is the construction of planispheres, maps and
charts, which are said to be of this or that projection, according to the several situations of
the eye, and the perspective plane, with regard to the meridian, parallels of latitude, and other
points or places to be represented.
The most usual projection of maps of the world, is that on the plane of the meridian, which
exhibits aright sphere, the first meridian being the horizon; the next is the projection on the
plane of the equator, which has the pole in the centre, from which proceed the meridians like
the radii of a circle; and thus represents a parallel sphere.
The projection of the sphere is usually divided into orthographic and stereo graphic; to which
may be added the gnomonic, on which dialling is founded.
The orthographic projection is that in which the surface of the sphere is drawn upon a plane
cutting it in the middle; the eye being placed at an infinite distance, vertically to one of the
hemispheres. The laws of this projection are—1. That the rays coming from the eye being at
an infinite distance, and making the projection, are supposed to be parallel to each other and
all perpendicular to the plane of projection.
2d. A right line perpendicular to the plane of projection is-foreshortened and projected into
a point, where it meets the said plane.
3d. A right line not perpendicular, but either parallel or obliquely inclined to the projection,
is projected into a right line comprehended between perpendiculars let fall from the extremities
of the original line.
4th. The projection of any line is greatest when this line is parallel to the plane of projection.
5th. From this it appears that a liaie parallel to the plane of the projection is projected into a
right
BOOK VL
OP PROJECTION,
CHAP. I.
OF THE ORTHOGRAPHIC AND STEREOGRAPHIC PROJECTION OF THE SPHERE, AND THE
METHOD OF DRAWING UNIVERSAL MAPS.
BY the projection of the sphere on a plane is meant the representation of the several
points or places of the surface of the sphere, and of the circles thereon described, upon a
transparent plane placed between the eye and the sphere ; or such as they appear to the eye at
a given distance. Projection is therefore only a particular case of perspective, and subject to
the laws thereof.
The chief use of the projection of the sphere is the construction of planispheres, maps and
charts, which are said to be of this or that projection, according to the several situations of
the eye, and the perspective plane, with regard to the meridian, parallels of latitude, and other
points or places to be represented.
The most usual projection of maps of the world, is that on the plane of the meridian, which
exhibits aright sphere, the first meridian being the horizon; the next is the projection on the
plane of the equator, which has the pole in the centre, from which proceed the meridians like
the radii of a circle; and thus represents a parallel sphere.
The projection of the sphere is usually divided into orthographic and stereo graphic; to which
may be added the gnomonic, on which dialling is founded.
The orthographic projection is that in which the surface of the sphere is drawn upon a plane
cutting it in the middle; the eye being placed at an infinite distance, vertically to one of the
hemispheres. The laws of this projection are—1. That the rays coming from the eye being at
an infinite distance, and making the projection, are supposed to be parallel to each other and
all perpendicular to the plane of projection.
2d. A right line perpendicular to the plane of projection is-foreshortened and projected into
a point, where it meets the said plane.
3d. A right line not perpendicular, but either parallel or obliquely inclined to the projection,
is projected into a right line comprehended between perpendiculars let fall from the extremities
of the original line.
4th. The projection of any line is greatest when this line is parallel to the plane of projection.
5th. From this it appears that a liaie parallel to the plane of the projection is projected into a
right