Archimedes Texts

SALV. I see that you understand the businesse very well. I be
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 insen
sible, in respect of the Firmament (or Starry Sphere;) and con
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, pas
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 a
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 Ma
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 afore
said distance, and angles be exactly taken.

SIMP. So that if the Rules dependent on Geometry and Astro
nomy be true, all the fallacies and errours that might be met with
in attempting to investigate those altitudes of new Stars or Co
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 them
selves to parallels, if so be the recession should be infinite, which