1But the curve-line A C B, is greater than the two right-lines A C,
and C B; therefore, à fortiori, the curve-line A C B, is much
greater than the right line A B, which was to be
and C B; therefore, à fortiori, the curve-line A C B, is much
greater than the right line A B, which was to be
SALV. I do not think that if one ſhould ranſack all the
logiſms of the world, there could be found one more commodious
than this, to give an example of the moſt ſolemn fallacy of all
fallacies, namely, than that which proveth ignotum per ignotius.
logiſms of the world, there could be found one more commodious
than this, to give an example of the moſt ſolemn fallacy of all
fallacies, namely, than that which proveth ignotum per ignotius.
SALV. Do you ask me how ſo? The unknown concluſion
which you deſire to prove, is it not, that the curved line A C B, is
longer than the right line A B; the middle term which is taken
for known, is that the curve-line A C B, is greater than the two
lines A C and C B, the which are known to be greater than A B;
And if it be unknown whether the curve-line be greater than the
ſingle right-line A B, ſhall it not be much more unknown whether
it be greater than the two right lines A C & C B, which are known
to be greater than the ſole line A B, & yet you aſſume it as known?
which you deſire to prove, is it not, that the curved line A C B, is
longer than the right line A B; the middle term which is taken
for known, is that the curve-line A C B, is greater than the two
lines A C and C B, the which are known to be greater than A B;
And if it be unknown whether the curve-line be greater than the
ſingle right-line A B, ſhall it not be much more unknown whether
it be greater than the two right lines A C & C B, which are known
to be greater than the ſole line A B, & yet you aſſume it as known?
SALV. As the two right lines are greater than A B, (as may be
known by Euclid) and in as much as the curve line is longer than
the two right lines A C and B C, ſhall it not not be much greater
than the ſole right line A B?
known by Euclid) and in as much as the curve line is longer than
the two right lines A C and B C, ſhall it not not be much greater
than the ſole right line A B?
SALV. That the curve-line A C B, is greater than the right
line A B, is the concluſion more known than the middle term,
which is, that the ſame curve-line is greater than the two
lines A C and C B. Now when the middle term is leſs known
than the concluſion, it is called a proving ignotum per ignotius.
But to return to our purpoſe, it is ſufficient that you know the
right line to be the ſhorteſt of all the lines that can be drawn
tween two points. And as to the principal concluſion, you ſay,
that the material ſphere doth not touch the ſphere in one ſole
point. What then is its contact?
line A B, is the concluſion more known than the middle term,
which is, that the ſame curve-line is greater than the two
lines A C and C B. Now when the middle term is leſs known
than the concluſion, it is called a proving ignotum per ignotius.
But to return to our purpoſe, it is ſufficient that you know the
right line to be the ſhorteſt of all the lines that can be drawn
tween two points. And as to the principal concluſion, you ſay,
that the material ſphere doth not touch the ſphere in one ſole
point. What then is its contact?
SALV. And the contact likewiſe of another ſphere equal to the
firſt, ſhall be alſo a like particle of its ſuperficies?
firſt, ſhall be alſo a like particle of its ſuperficies?