MECHANICS. 
Leibnitz and other» call these mechani- 
cal curves transcendental, and dissent from 
Des Cartes in excluding them out of geome- 
try. Leibnitz found a new kind of trans- 
cendental equations, whereby these curves 
are defined ; but they do not continue con- 
stantly the same in all points of the curve, 
as algebraic ones do. 
MECHANICS, is the science which 
treats of the laws of the equilibrium and 
motion of solid bodies; of the forces by 
which bodies, whether animate or inani- 
mate, may be made to act upon one ano- 
ther; and of the means by which these may 
be increased, so as to overcome such as are 
most powerful. As this science is closely 
connected with the arts of life, and particu- 
larly with tliose which existed even in the 
rudest ages of society, the construction of 
machines must have, been practised long be- 
fore the theory upon which their principles 
depend could have been understood. Hence 
we find in use among the ancients, the le- 
ver, the pulley, the crane, the capstan, and 
many other simple machines, at a period 
when mechanics, as a science, were un- 
known. In the remains of Egyptian archi- 
tecture are beheld the most surprising 
marks of mechanical genius. The eleva- 
tion of immense and ponderous masses of 
stone to the tops of their stupendous fa- 
brics, must have required au accumulation 
of mechanical power, which is not in the 
possession of modern architects. We are 
indebted to Archimedes for the foundation 
of this science : he demonstrated, that when 
a balance with unequal arms is in equilibrio, 
by means of two weights in its opposite 
scales, these weights must be reciprocally 
proportional to the arms of the balance. 
From this general principle the mathemati- 
cian might have deduced all tire other pro- 
perties of the lever, but he did not follow 
the discovery through all its consequences. 
In demonstrating the leading property of 
the lever, he lays it down as an axiom, that 
if the two arms of the balance are equal, 
the weights must be equal, to give an equi- 
librium. Reflecting on the construction of 
the balance, which moved upon a fulcrum, 
he perceived that the two weights exerted 
the same pressure on the fulcrum as if they 
had both rested on it. He then advanced 
another step, and considered the sum of 
these two weights as combined with a third, 
and then tlie sum of the three, with a fourth, 
and so on, and perceived that in every such 
combination the fulcrum must support 
their united weight; and, tlierefore, thgt 
there is in every combination of bodies, 
and in every single body which may be 
Gotisidered as made up of a number of 
lesser bodies, a centre of pressure or gra- 
vity. This discovery Arcliimedes applied 
to particular cases, and pointed out the me- 
thod of finding the centre of gravity of 
plane surfaces, whetlier bounded by a pa- 
rallellogram, a triangle, a trapesinm, or a 
parabola. .See Centre of gravity. 
Galileo, towards the close of the sixteenth 
century, made many important discoveries 
on this subject. In a small treatise on statics, 
he proved thatit required an equal power to 
raise two different bodies to altitudes, in 
the inverse ratio of their weights, or that 
the same power is requisite to raise ten 
pounds to the height of one lumdred feet, 
and twenty pounds fifty feet. It is impos- 
sible for us to follow this great man in all 
his discoveries. In his works, which were 
published early in the seventeenth century, 
he discusses the doctrine of equable mo- 
tions in various theorems, containing the 
different relations between the velocity of 
the moving body, the space which it de- 
scribes, and the time employed in its de- 
scription. He treats also of accelerated 
motion, considers all bodies as heavy; and 
composed of heavy parts, and infers that 
the total weight of the body is proportional 
to the number of the particles of winch it 
is composed. On this subject he reasons 
in the following manner: “As the weight 
of a body is a power always the same in 
quantity, and as it constantly acts without 
interruption, the body must be continually 
receiving from it equal impulses in equal 
and successive instants of time. When the 
body is prevented from falling, by being 
placed on a table, its weight is incessantly 
impelling it downwards ; but these impulses 
are destroyed by the resistance of the ta- 
ble, which pi-events it from yielding to 
them. But where the body falls freely, 
the impulses which it perpetually receives 
are perpetually accumulating, atid remain 
in the body unchanged in every respect, 
except the diminution which they expe- 
rience from the resistance of the air : hence 
it follows, that a body falling freely is uni- 
formly accelerated, or receives equal incre- 
ments of velocity in equal times. He then 
demonstrated that the time in which any 
space is described by a motion uniformly 
accelerated from rest, is equal to the time 
in which the same space would be describ- 
ed by an uniform equable motion, with half 
the final velocity of the accelerated motion. 
