EXI 
vessel, out of which the air hath been 
drawn by means of the air-pump. See 
Pneumatics. 
EXHAUSTION, in mathematics, a me- 
thod in frequent use among the ancient ma- 
thematicians, as Euclid, Archimedes, &c. 
that proves the equality of two magnitudes, 
by a deduction ad absurdum, in supposing 
that, if one be greater or less than the other, 
there would follow an absurdity. 
This is founded upon what Euclid saith 
in his tenth book, viz. that those quantities, 
whose difference is less than any assignable 
one, are equal. For if they were unequal, 
be the difference never so small, yet, it may 
be so multiplied, as to become greater than 
either of them : if not so, then it is really 
nothing. This he assumes in the proof of 
the 1st proposition of book 10, which is, 
that if from the greater of two quantities, 
you take more than its half, and from the 
remainder more than its half, and so conti- 
nually, there will, at length, remain a quan- 
tity less than either of those proposed. 
On this foundation they demonstrate, that 
if a regular polygon of infinite sides be in- 
scribed in, or circumscribed about a circle ; 
the space, that is the difference between the 
circle and the polygon, will, by degrees, be 
quite exhausted, and the circle be equal to 
the polygon. 
EXHIBITION, a benefaction settled 
for the benefit of scholars in the universities, 
that are not on the foundation. 
EXIGENT, in law, a writ or part of the 
process of outlawry on civil actions. 
EXISTENCE, that whereby any thing 
has an actual essence, or is said to be. Mr. 
Locke says, “ that we arrive at the know- 
ledge of our own existence by intuition ; of 
the existence of God by demonstration ; 
and of other things by sensation. As for our 
own existence,” continues that great philo- 
sopher, “ we perceive it so plainly that it 
neither needs, nor is capable of any proof. 
I think, I reason, I feel pleasure and pain ; 
can any of these be more evident to me 
than my own existence ? If I doubt of all 
other things, that very doubt makes me 
perceive my own existence, and will not 
suffer me to doubt it. If I know I doubt, 
I have as certain a perception of the thing 
doubting, as of that thought which I call 
doubt : experience then convinces us that 
we have an intuitive knowledge of our own 
existence.” 
From the knowledge of our own exis- 
tence, Mr. Locke deduces his demonstra- 
tion of the existence of a God. 
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It has been a subject of great dispute 
whether external bodies have any existence 
but in the mind, that is, whether they really 
exist, or exist in idea only : the former 
opinion is supported by Mr. Locke, and the 
latter by Dr. Berkeley. “ The knowledge of 
the existence of other things, or things with- 
out the mind, we have only by sensation : 
for there being no necessary connection of 
real existence with any idea a man hath in 
his memory, nor of any other existence but 
that of God, with the existence of any par- 
ticular man ; no particular man can know 
the existence of any other being, but only, 
when, by operating upon him, it makes it- 
self be perceived by him. The having the 
idea of any thing in our mind no more 
proves the existence of that thing than the 
picture of a man evidences his being in the 
world, or the visions of a dream make a 
true history. It is, therefore, the actual 
receiving of ideas from without that gives 
us notice of the existence of other things, 
and makes us know that something does 
exist at that time without us which causes 
that idea in us, though perhaps we neither 
know nor consider how it does it. This no- 
tice, which we have by our senses, of the 
existence of things without us, though it be 
not altogether so certain as intuition and 
demonstration, yet deserves the name of 
knowledge, if we persuade ourselves that 
our faculties act and inform us right con- 
cerning the existence of those objects that 
affect them : but besides the assurance we 
have from our senses themselves, that they 
do not err in the information they give us 
of the existence of things without us, we have 
other concurrent reasons ; as, first, it is 
plain these perceptions are produced in us 
by external causes affecting our senses, be- 
cause those that want the organs of any 
sense never can have the ideas belonging to 
that sense produced in their minds. Se- 
condly, because we find sometimes that we 
cannot avoid the having those ideas pro- 
duced in our minds. When my eyes are 
shut I can, at pleasure, recal to my mind 
the ideas of light, or the sun, which former 
sensations had lodged in my memory ; but 
if I turn my eyes towards the sun I cannot 
avoid the ideas which the light or the sun 
then produces in me ; which shews a mani- 
fest difference between those ideas laid up 
in the memory, and such as force them- 
selves upon us, and we cannot avoid hav- 
ing ; besides, there is nobody who doth not 
perceive the difference in himself between 
actually looking on the sun and contemplat- 
