An introductory text-book of logic - Mellone, Sydney - Rare Books at ...

82 IMMEDIATE INFERENCE.
the geometrical converse. The geometrical converse is
the simple converse of an A proposition, and it is not
logically inferrible from the latter, but has to be proved
independently. Thus the geometrical converse of
"
all
equilateral triangles are "
equiangular is
"
all equiangular
triangles are equilateral." In every case it will be found
that an independent proof is necessary for the geomet
rical converse. Euclid usually adopts the indirect proof,
by reductio ad absurdum (as in I. Prop, vi., &c.),
in the
course of which the truth of the original proposition is
appealed to.
We now add some examples illustrating the process of
conversion. Every proposition to be converted must first be
reduced to strict logical form.
(1) "There is no excellent beauty that hath not some
strangeness in the proportion."
(a) Excellent beauty
(b) [a thing] without strangeness in the proportion ;
1
(c) denied of every instance of the subject.
" No excellent beauty is a thing without
Hence SeP,
strangeness in the proportion."
"
Converse PeS, Nothing without strangeness in the pro
portion is excellent beauty."
(2)
"
It is a poor centre of a man s actions, himself."
(a) A man s self
(b) a poor centre of his actions ;
(c) affirmed of every case of the subject.
Hence SaP, "A man s self in every case is a poor centre
of his actions."
Converse PiS, "Something which is a poor centre of a
man s actions is himself."
(3) "Mercy but murders, pardoning [/>.,
those that kill."
(a) Mercy which pardons those that kill
(b) a murderous thing ;
(<r)
affirmed of every instance of the subject.
For the proper order of logical analysis see 4.
if it pardons]