11

16

17 lemmas, and 27 corollaries. There are also 2
scholia. At the same time, I ought to remark that,
while the ^possible conclusions are innumerable, yet
after ^all premises have been iterated so as to exhaust
all the different ways of using them together with all
simpler ways, there will be no more theorems of any
particular interest, and the branch of mathematics in
question may be said to be substantially exhausted. The
theory of conics is an instance. The great geometer
Charles after he attained to a great age continued
to grind out, by the bushel basket full, such theorems
as that ^{in a plane,} the number of conics that touch five
given conics is 3264. I think that when a ma-
thematical theory has nothing new to discover but
such propositions as that it may be said to be,

1) [lemmas?], and 27 [corollsnes?]. There are also 2 [seh?].
At the sme time, I ought to remark that, while the possible cconclusions are innumerable, yet after all premises have been iterated so to as to exhaust all the different ways of using them together with all simpler ways, there will be no more theorems of any particular interest and the branch of mathematics in question may be said to be substantially exhausted. The theory of [uni?] is an instance. The great geometer Charles after he attained to a great age continued to [g?] out by the bushel basket full, such theorems as that (in a plane, text written above 'that') the number of [conies?] that touch five given [conies?] is 3264. I think that when a mathematical theory has nothing [ever?] to discover but such propositions as that it may be said to be.