1ſtanding of which, I ought firſt to advertiſe you, that when ever
the new Star, or other Phænomenon is near to the earth, turning
with a Diurnal motion about the Pole, it will ſeem to be farther
off from the ſaid Pole, whilſt it is in the lower part of the
an, then whilſt it is above, as in this Figure [being fig. third of
this Dial.] may be ſeen. In which the point T. denotes the
tre of the Earth; O the place of the Obſervator; the Arch VPC
the Firmament; P. the Pole. The Phænomenon, [or appearance]
moving along the Circle F S. is ſeen one while under the Pole by
the Ray O F C. and another while above, according to the Ray
O S D. ſo that the places ſeen in the Firmament are D. and C. but
the true places in reſpect of the Centre T, are B, and A,
ſtant from the Pole. Where it is manifeſt that the apparent place
of the Phænomenon S, that is the point D, is nearer to the Pole than
the other apparent place C, ſeen along the Line or Ray O F C,
which is the firſt thing to be noted. In the ſecond place you muſt
note that the exces of the apparent inferiour diſtance from the Pole,
over and above the apparent ſuperiour diſtance from the ſaid Pole,
is greater than the Inferiour Parallax of the Phænomenon, that is, I
ſay, that the exceſſe of the Arch C P, (the apparent inferior
ſtance) over and above the Arch P D, (the apparent ſuperior
ſtance) is greater then the Arch C A, (that is the inferiour
lax.) Which is eaſily proved; for the Arch C P. more exceedeth
P D, then P B; P B, being bigger than P D, but P B. is equal to
P A, and the exceſſe of C P, above P A, is the arch, C A,
fore the exceſſe of the arch C P above the arch P D, is
er than the arch C A, which is the parallax of the Phænomenon
placed in F, which was to be demonſtrated. And to give all
vantages to the Author, let us ſuppoſe that the parallax of the ſtar
in F, is the whole exceſſe of the arch C P (that is of the inferiour
diſtance from the pole) above the arch P D (the inferiour
ſtance.) I proceed in the next place to examine that which the
obſervations of all Aſtronomers cited by the Authour giveth us,
amongſt which, there is not one that maketh not againſt himſelf
and his purpoſe. And let us begin with theſe of Buſchius, who
findeth the ſtars diſtance from the pole, when it was ſuperiour, to be
28 gr. 10 m. and the inferiour to be 28 gr. 30 m. ſo that the
ceſſe is 0 gr. 20 m. which let us take (in favour of the Author) as
if it all were the parallax of the ſtar in F, that is the angle T F O.
Then the diſtance from the Vertex [or Zenith] that is the arch
C V, is 67 gr. 20 m. Theſe two things being found, prolong the
line C O, and from it let fall the perpendicular T I, and let us
conſider the triangle T O I, of which the angle I is right angle,
and the angle I O T known, as being vertical to the angle V O C,
the diſtance of the ſtar from the Vertex, Moreover in the triangle
the new Star, or other Phænomenon is near to the earth, turning
with a Diurnal motion about the Pole, it will ſeem to be farther
off from the ſaid Pole, whilſt it is in the lower part of the
an, then whilſt it is above, as in this Figure [being fig. third of
this Dial.] may be ſeen. In which the point T. denotes the
tre of the Earth; O the place of the Obſervator; the Arch VPC
the Firmament; P. the Pole. The Phænomenon, [or appearance]
moving along the Circle F S. is ſeen one while under the Pole by
the Ray O F C. and another while above, according to the Ray
O S D. ſo that the places ſeen in the Firmament are D. and C. but
the true places in reſpect of the Centre T, are B, and A,
ſtant from the Pole. Where it is manifeſt that the apparent place
of the Phænomenon S, that is the point D, is nearer to the Pole than
the other apparent place C, ſeen along the Line or Ray O F C,
which is the firſt thing to be noted. In the ſecond place you muſt
note that the exces of the apparent inferiour diſtance from the Pole,
over and above the apparent ſuperiour diſtance from the ſaid Pole,
is greater than the Inferiour Parallax of the Phænomenon, that is, I
ſay, that the exceſſe of the Arch C P, (the apparent inferior
ſtance) over and above the Arch P D, (the apparent ſuperior
ſtance) is greater then the Arch C A, (that is the inferiour
lax.) Which is eaſily proved; for the Arch C P. more exceedeth
P D, then P B; P B, being bigger than P D, but P B. is equal to
P A, and the exceſſe of C P, above P A, is the arch, C A,
fore the exceſſe of the arch C P above the arch P D, is
er than the arch C A, which is the parallax of the Phænomenon
placed in F, which was to be demonſtrated. And to give all
vantages to the Author, let us ſuppoſe that the parallax of the ſtar
in F, is the whole exceſſe of the arch C P (that is of the inferiour
diſtance from the pole) above the arch P D (the inferiour
ſtance.) I proceed in the next place to examine that which the
obſervations of all Aſtronomers cited by the Authour giveth us,
amongſt which, there is not one that maketh not againſt himſelf
and his purpoſe. And let us begin with theſe of Buſchius, who
findeth the ſtars diſtance from the pole, when it was ſuperiour, to be
28 gr. 10 m. and the inferiour to be 28 gr. 30 m. ſo that the
ceſſe is 0 gr. 20 m. which let us take (in favour of the Author) as
if it all were the parallax of the ſtar in F, that is the angle T F O.
Then the diſtance from the Vertex [or Zenith] that is the arch
C V, is 67 gr. 20 m. Theſe two things being found, prolong the
line C O, and from it let fall the perpendicular T I, and let us
conſider the triangle T O I, of which the angle I is right angle,
and the angle I O T known, as being vertical to the angle V O C,
the diſtance of the ſtar from the Vertex, Moreover in the triangle