1on upon the Earths motion; for from the Earth in A it ſhall be
ſeen according to the ray A E, with the elevation of the angle
E A C; but from the Earth placed in B, it ſhall be ſeen
cording to the ray B E, with the elevation of the angle E B C,
bigger than the other E A C, that being extern, and this
tern and oppoſite in the triangle E A B, the diſtance therefore
of the ſtar E from the Ecliptick, ſhall appear changed; and
likewiſe its altitude in the Meridian ſhall become greater in the
poſition B, than in the place A, according as the angle E B C
exceeds the angle E A C, which exceſſe is the quantity of the
angle A E B: For in the triangle E A B, the ſide A B being
continued to C, the exteriour angle E B C (as being equal to
the two interiour and oppoſite E and A) exceedeth the ſaid
gle A, by the quantity of the angle E. And if we ſhould take
another ſtar in the ſame Meridian, more remote from the
ptick, as for inſtance the ſtar H, the diverſity in it ſhall be
greater by being obſerved from the two ſtations A and B,
ding as the angle A H B is greater than the other E; which
gle ſhall encreaſe continually according as the obſerved ſtar ſhall
be farther and farther from the Ecliptick, till that at laſt the
greateſt mutation will appear in that ſtar that ſhould be placed in
the very Pole of the Ecliptick. As for a full underſtanding
of we thus demonſtrate. Suppoſe the diameter of the Grand
Orb to be A B, whoſe centre [in the ſame Figure] is G, and
let it be ſuppoſed to be continued out as far as the Starry Sphere
in the points D and C, and from the centre G let there be erected
the Axis of the Ecliptick G F, prolonged till it arrive at the ſaid
Sphere, in which a Meridian D F C is ſuppoſed to be deſcribed,
that ſhall be perpendicular to the Plane of the Ecliptick; and
in the arch F C any points H and E, are imagined to be taken,
as places of fixed ſtars: Let the lines F A, F B, A H, H G,
H B, A E, G E, B E, be conjoyned. And let the angle of
ference, or, if you will, the Parallax of the ſtar placed in the
Pole F, be A F B, and let that of the ſtar placed in H, be the
angle A H B, and let that of the ſtar in E, be the angle
A E B. I ſay, that the angle of difference of the Polar ſtar F, is
the greateſt, and that of the reſt, thoſe that are nearer to the
greateſt are bigger than the more remote; that is to ſay, that the
angle F is bigger than the angle H, and this bigger than the angle
E. Now about the triangle F A B, let us ſuppoſe a circle to be
ſcribed. And becauſe the angle F is acute, (by reaſon that its baſe
AB is leſſe than the diameter DC, of the ſemicircle D F C) it ſhall
be placed in the greater portion of the circumſcribed circle cut
by the baſe A B. And becauſe the ſaid A B is divided in the
midſt, and at right angles by F G, the centre of the
ſeen according to the ray A E, with the elevation of the angle
E A C; but from the Earth placed in B, it ſhall be ſeen
cording to the ray B E, with the elevation of the angle E B C,
bigger than the other E A C, that being extern, and this
tern and oppoſite in the triangle E A B, the diſtance therefore
of the ſtar E from the Ecliptick, ſhall appear changed; and
likewiſe its altitude in the Meridian ſhall become greater in the
poſition B, than in the place A, according as the angle E B C
exceeds the angle E A C, which exceſſe is the quantity of the
angle A E B: For in the triangle E A B, the ſide A B being
continued to C, the exteriour angle E B C (as being equal to
the two interiour and oppoſite E and A) exceedeth the ſaid
gle A, by the quantity of the angle E. And if we ſhould take
another ſtar in the ſame Meridian, more remote from the
ptick, as for inſtance the ſtar H, the diverſity in it ſhall be
greater by being obſerved from the two ſtations A and B,
ding as the angle A H B is greater than the other E; which
gle ſhall encreaſe continually according as the obſerved ſtar ſhall
be farther and farther from the Ecliptick, till that at laſt the
greateſt mutation will appear in that ſtar that ſhould be placed in
the very Pole of the Ecliptick. As for a full underſtanding
of we thus demonſtrate. Suppoſe the diameter of the Grand
Orb to be A B, whoſe centre [in the ſame Figure] is G, and
let it be ſuppoſed to be continued out as far as the Starry Sphere
in the points D and C, and from the centre G let there be erected
the Axis of the Ecliptick G F, prolonged till it arrive at the ſaid
Sphere, in which a Meridian D F C is ſuppoſed to be deſcribed,
that ſhall be perpendicular to the Plane of the Ecliptick; and
in the arch F C any points H and E, are imagined to be taken,
as places of fixed ſtars: Let the lines F A, F B, A H, H G,
H B, A E, G E, B E, be conjoyned. And let the angle of
ference, or, if you will, the Parallax of the ſtar placed in the
Pole F, be A F B, and let that of the ſtar placed in H, be the
angle A H B, and let that of the ſtar in E, be the angle
A E B. I ſay, that the angle of difference of the Polar ſtar F, is
the greateſt, and that of the reſt, thoſe that are nearer to the
greateſt are bigger than the more remote; that is to ſay, that the
angle F is bigger than the angle H, and this bigger than the angle
E. Now about the triangle F A B, let us ſuppoſe a circle to be
ſcribed. And becauſe the angle F is acute, (by reaſon that its baſe
AB is leſſe than the diameter DC, of the ſemicircle D F C) it ſhall
be placed in the greater portion of the circumſcribed circle cut
by the baſe A B. And becauſe the ſaid A B is divided in the
midſt, and at right angles by F G, the centre of the