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

The

tion of a

tick, to prove the

right line to be the

ſhorteſt of all lines.

tion of a

tick, to prove the

right line to be the

ſhorteſt of all lines.

The Paralogiſm

of the ſame

tetick, which

veth ignotum per

ignotius.

of the ſame

tetick, which

veth ignotum per

ignotius.

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.

SIMP. How ſo?

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?

SIMP. I do not yet very well perceive wherein lyeth the

lacy.

lacy.

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?

SIMP. It ſhall ſo.

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?

SIMP. It ſhall be a part of its ſuperficies.

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?

SIMP. There is no reaſon vvhy it ſhould be othervviſe.

SALV. Then the tvvo ſpheres vvhich touch each other, ſhall

touch vvith the tvvo ſame particles of a ſuperficies, for each of them

agreeing to one and the ſame plane, they muſt of neceſſity agree

in like manner to each other. Imagine now that the two ſpheres

touch vvith the tvvo ſame particles of a ſuperficies, for each of them

agreeing to one and the ſame plane, they muſt of neceſſity agree

in like manner to each other. Imagine now that the two ſpheres

[in Fig. 6.] whoſe centres are A and B, do touch one another:

and let their centres be conjoyned by the right line A B, which

paſſeth through the contact. It paſſeth thorow the point C, and