SALV. I ſee that you underſtand the buſineſſe very well. I
lieve that you do likewiſe comprehend, that, in regard the ſtar B
is lower than C, the angle which is made by the rayes of the
ſight, which departing from the two places A and E, meet in C,
to wit, this angle A C E, is more narrow, or if we will ſay more
acute than the angle conſtituted in B, by the rayes A B and
E B.
lieve that you do likewiſe comprehend, that, in regard the ſtar B
is lower than C, the angle which is made by the rayes of the
ſight, which departing from the two places A and E, meet in C,
to wit, this angle A C E, is more narrow, or if we will ſay more
acute than the angle conſtituted in B, by the rayes A B and
E B.
SIMP. This I likewiſe underſtand very well.
SALV. And alſo, the Earth beine very little and almoſt
ſible, in reſpect of the Firmament (or Starry Sphere;) and
ſequently the ſpace A E, paced on the Earth, being very ſmall in
compariſon of the immenſe length of the lines E G and E F,
ſing from the Earth unto the Firmament, you thereby collect that
the ſtar C might riſe and aſcend ſo much and ſo much above the
Earth, that the angle therein made by the rayes which depart
from the ſaid ſtationary points A and E, might become moſt
cute, and as it were abſolutely null and inſenſible.
ſible, in reſpect of the Firmament (or Starry Sphere;) and
ſequently the ſpace A E, paced on the Earth, being very ſmall in
compariſon of the immenſe length of the lines E G and E F,
ſing from the Earth unto the Firmament, you thereby collect that
the ſtar C might riſe and aſcend ſo much and ſo much above the
Earth, that the angle therein made by the rayes which depart
from the ſaid ſtationary points A and E, might become moſt
cute, and as it were abſolutely null and inſenſible.
SIMP. And this alſo is moſt manifeſt to ſenſe.
SALV. Now you know Simplicius that Aſtronomers and
thematicians have found infallible rules by way of Geometry and
Arithmetick, to be able by help of the quantity of theſe angles
B and C, and of their differences, with the additional knowledg
of the diſtance of the two places A and E, to find to a foot the
remoteneſſe of ſublime bodies; provided alwayes that the
ſaid diſtance, and angles be exactly taken.
thematicians have found infallible rules by way of Geometry and
Arithmetick, to be able by help of the quantity of theſe angles
B and C, and of their differences, with the additional knowledg
of the diſtance of the two places A and E, to find to a foot the
remoteneſſe of ſublime bodies; provided alwayes that the
ſaid diſtance, and angles be exactly taken.
SIMP. So that if the Rules dependent on Geometry and
nomy be true, all the fallacies and errours that might be met with
in attempting to inveſtigate thoſe altitudes of new Stars or
mets, or other things muſt of neceſſity depend on the diſtance A E,
and on the angles B and C, not well meaſured. And thus all thoſe
differences which are found in theſe twelve workings depend, not
on the deſects of the rules of the Calculations, but on the errours
committed in finding out thoſe angles, and thoſe diſtances, by means
of the Inſtrumental Obſervations.
nomy be true, all the fallacies and errours that might be met with
in attempting to inveſtigate thoſe altitudes of new Stars or
mets, or other things muſt of neceſſity depend on the diſtance A E,
and on the angles B and C, not well meaſured. And thus all thoſe
differences which are found in theſe twelve workings depend, not
on the deſects of the rules of the Calculations, but on the errours
committed in finding out thoſe angles, and thoſe diſtances, by means
of the Inſtrumental Obſervations.
SALV. True; and of this there is no doubt to be made. Now
it is neceſſary that you obſerve intenſely, how in removing the Star
from B to C, whereupon the angle alwayes grows more acute, the
ray E B G goeth farther and farther off from the ray A B D in
the part beneath the angle, as you may ſee in the line E C F,
whoſe inferiour part E C is more remote from the part A C, than
is the part E B, but it can never happen, that by any whatſoever
immenſe receſſion, the lines A D and E F ſhould totally ſever from
each other, they being finally to go and conjoyn in the Star: and
onely this may be ſaid, that they would ſeparate, and reduce
ſelves to parallels, if ſo be the receſſion ſhould be infinite, which
it is neceſſary that you obſerve intenſely, how in removing the Star
from B to C, whereupon the angle alwayes grows more acute, the
ray E B G goeth farther and farther off from the ray A B D in
the part beneath the angle, as you may ſee in the line E C F,
whoſe inferiour part E C is more remote from the part A C, than
is the part E B, but it can never happen, that by any whatſoever
immenſe receſſion, the lines A D and E F ſhould totally ſever from
each other, they being finally to go and conjoyn in the Star: and
onely this may be ſaid, that they would ſeparate, and reduce
ſelves to parallels, if ſo be the receſſion ſhould be infinite, which
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