1which depart from two points marked upon another right line, are
then wider above than below, when the angles included between
them upon that right line are greater than two right angles; and
if theſe angles ſhould be equal to two right angles, the lines would
be parallels; but if they were leſs than two right angles, the lines
would be concurrent, and being continued out would
ly interſect the triangle.
then wider above than below, when the angles included between
them upon that right line are greater than two right angles; and
if theſe angles ſhould be equal to two right angles, the lines would
be parallels; but if they were leſs than two right angles, the lines
would be concurrent, and being continued out would
ly interſect the triangle.
SIMP. Without taking it upon truſt from you, I know the
ſame; and am not ſo very naked of Geometry, as not to know a
Propoſition, which I have had occaſion of reading very often in
Ariſtotle, that is, that the three angles of all triangles are equall to
two right angles: ſo that if I take in my Figure the triangle ABE,
it being ſuppoſed that the line E A is right; I very well conceive,
that its three angles A, E, B, are equal to two right angles; and
that conſequently the two angles E and A are leſſe than two right
angles, ſo much as is the angle B. Whereupon widening the lines
A B and E B (ſtill keeping them from moving out of the points A
and E) untill that the angle conteined by them towards the parts
B, diſappear, the two angles beneath ſhall be equal to two right
angles, and thoſe lines ſhall be reduced to parallels: and if one
ſhould proceed to enlarge them yet more, the angles at the points
E and A would become greater than two right angles.
ſame; and am not ſo very naked of Geometry, as not to know a
Propoſition, which I have had occaſion of reading very often in
Ariſtotle, that is, that the three angles of all triangles are equall to
two right angles: ſo that if I take in my Figure the triangle ABE,
it being ſuppoſed that the line E A is right; I very well conceive,
that its three angles A, E, B, are equal to two right angles; and
that conſequently the two angles E and A are leſſe than two right
angles, ſo much as is the angle B. Whereupon widening the lines
A B and E B (ſtill keeping them from moving out of the points A
and E) untill that the angle conteined by them towards the parts
B, diſappear, the two angles beneath ſhall be equal to two right
angles, and thoſe lines ſhall be reduced to parallels: and if one
ſhould proceed to enlarge them yet more, the angles at the points
E and A would become greater than two right angles.
SALV. You are an Archimedes, and have freed me from the
expence of more words in declaring to you, that whenſoever the
calculations make the two angles A and E to be greater than two
right angles, the obſervations without more adoe will prove
neous. This is that which I had a deſire that you ſhould
ly underſtand, and which I doubted that I was not able ſo to make
out, as that a meer Peripatetick Philoſopher might attain to the
certain knowledg thereof. Now let us go on to what remains.
And re-aſſuming that which even now you granted me, namely,
that the new ſtar could not poſſibly be in many places, but in one
alone, when ever the ſupputations made upon the obſervations of
theſe Aſtronomers do not aſſign it the ſame place, its neceſſary
that it be an errour in the obſervations, that is, either in taking the
altitudes of the pole, or in taking the elevations of the ſtar, or in
the one or other working. Now for that in the many workings
made with the combinations two by two, there are very few of
the obſervations that do agree to place the ſtar in the ſame
tion; therefore theſe few onely may happily be the
ous, but the others are all abſolutely falſe.
expence of more words in declaring to you, that whenſoever the
calculations make the two angles A and E to be greater than two
right angles, the obſervations without more adoe will prove
neous. This is that which I had a deſire that you ſhould
ly underſtand, and which I doubted that I was not able ſo to make
out, as that a meer Peripatetick Philoſopher might attain to the
certain knowledg thereof. Now let us go on to what remains.
And re-aſſuming that which even now you granted me, namely,
that the new ſtar could not poſſibly be in many places, but in one
alone, when ever the ſupputations made upon the obſervations of
theſe Aſtronomers do not aſſign it the ſame place, its neceſſary
that it be an errour in the obſervations, that is, either in taking the
altitudes of the pole, or in taking the elevations of the ſtar, or in
the one or other working. Now for that in the many workings
made with the combinations two by two, there are very few of
the obſervations that do agree to place the ſtar in the ſame
tion; therefore theſe few onely may happily be the
ous, but the others are all abſolutely falſe.
SAGR. It will be neceſſary then to give more credit to theſe
few alone, than to all the reſt together, and becauſe you ſay,
that theſe which accord are very few, and I amongſt theſe 12,
do find two that ſo accord, which both make the diſtance of the
few alone, than to all the reſt together, and becauſe you ſay,
that theſe which accord are very few, and I amongſt theſe 12,
do find two that ſo accord, which both make the diſtance of the
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