_Thales_ was the first we know of who predicted eclipses. He pointed out
the advantages that must arise from a due observation of the little bear
or polar star; and taught that the earth was round, and the ecliptic in
an oblique position.
_Pytheas_ also, by accurate observations at Marseilles, more than 300
years before Christ, determined the obliquity of the ecliptic, by means
of the solstitial shadow of the sun upon a dial. He found the height of
the gnomon was to the length of the shadow as 600 to 213⅛; whence he
concluded, that the obliquity of the ecliptic was 23° 49′. When Gassendi
was at Marseilles with the celebrated Peiresc, he reiterated the
experiment, and found it very just.
_Thales_ went to the Egyptians to be instructed in geometry, and himself
instructed them in that science. He showed them how to measure the
pyramids by the length of their shades, and to determine the measure of
inaccessible heights and distances, by the proportion of the sides of a
triangle. He demonstrated the various properties of the circle; he
discovered, respecting the isosceles triangle, that the angles at its
base were equal; and he was the first who found, that in right lines
cutting one another, the opposite angles are equal.
_Anaximander_, the successor of Thales, was the inventor of the
armillary sphere, and of sun-horologes, or dials; he was likewise the
first who drew a geographical map.
_Pythagoras_ was the first who gave sure and fundamental precepts in
music. Struck by the difference of sounds which issued from the hammers
of a forge, but came into unison at the fourth, and fifth, and eighth
percussions, he conjectured that this must proceed from the difference
of weight in the hammers; he weighed them, and found he had conjectured
right. Upon this he wound up some musical strings, in number equal to
the hammers, and of a length proportioned to their weight; and found,
that at the same intervals, they corresponded with the hammers in sound.
Upon this principle he devised the monochord; an instrument of one
string, capable of determining the various relations of sound. He also
made many fine discoveries in geometry.
_Plato_ by his studies in mathematics was enabled to devise the analytic
method, or that geometric analysis, which enables us to find the truth
we are in quest of, out of the proposition itself which we want to
resolve. He it was who at length solved the famous problem, respecting
the duplication of the cube. To him also is ascribed the solution of the
problem concerning the trisection of an angle; and the discovery of
conic sections.
_Hipparchus_ discovered the elements of plane and spherical
trigonometry.
_Diophantes_, who lived 360 years before Jesus Christ, was the inventor
of algebra. It was from this science that the ancients drew those long
and difficult demonstrations which we meet with in their works. They are
presumed to have aimed at concealing a method which furnished them with
so many beautiful and difficult demonstrations; and to have preferred
the proving of their propositions by reasonings _ad absurdum_, rather
than hazard the disclosure of the means by which they arrived more
directly at the result of what they demonstrated. We meet with strong
traces of algebra in the 13th book of Euclid. From the time of
Diophantes, algebra made but small progress, till that of Vietus, who
restored and perfected it, and was the first who marked the known
quantities by the letters of the alphabet. Descartes afterwards applied
it to geometry.
_Aristarchus_ was the first who suggested a method of measuring the
distance of the sun from the earth, by means of the half section of the
moon’s disk, or that phasis of it wherein it appears to us when it is in
its quadratures.
_Hipparchus_ was the first who calculated tables of the motion of the
sun and moon, and composed a catalogue of the fixed stars. He was also
the first who, from the observation of eclipses, determined the
longitude of places upon earth: but his highest honour is, that he laid
the first foundations for the discovery of the precession of the
equinoxes.
_Archimedes_ discovered the square of the parabola, the properties of
spiral lines, the proportion of the sphere to the cylinder, and the true
principles of statics and hydrostatics. His sagacity is evident from the
means he adopted to discover the quantity of silver that was mixed along
with the gold, in the crown of king Hieron. He reasoned upon the
principle, that all bodies immerged in water lose just so much of their
weight, as a quantity of water equal to them in bulk weighs. Hence he
drew this consequence, that gold being more compact must lose less of
its weight, and silver more; and that a mingled mass of both, must lose
in proportion to the quantities mingled. Weighing therefore the crown in
water and in air, and two masses, the one of gold, the other of silver,
equal in weight to the crown; he thence determined what each lost of
their weight, and so solved the problem. He likewise invented a
_perpetual screw_, valuable on account of its being capable to overcome
any resistance; and the _screw_ that still goes by his own name, used in
the elevating of water. He alone defended the city of Syracuse, by
opposing to the efforts of the Romans the resources of his genius. By
means of machines, of his own construction, he rendered Syracuse
inaccessible. Sometimes he hurled upon the land forces stones of such
enormous size, as crushed whole phalanxes of them at once. When they
retired from the walls, he overwhelmed them with arrows innumerable, and
beams of a prodigious weight, discharged from catapults and balistæ. If
their vessels approached the fort, he seized them by the prows with
grapples of iron, which he let down upon them from the wall, and rearing
them up in the air, to the great astonishment of every body, shook them
with such violence, as either to break them in pieces, or sink them to
the bottom. When they kept at a distance from the haven, he focalized
fire from heaven, and wrapped them in sudden and inevitable
conflagration. He once said to king Hieron, “Give me but a place to
stand upon, and I will move the earth.” The king was amazed by the
declaration, and Archimedes gave him a specimen of his power by
launching singly by himself a ship of a prodigious size. He built for
the king an immense galley, of twenty banks of oars, containing spacious
apartments, gardens, walks, ponds, and every convenience required by
regal dignity. He constructed a sphere, representing, the motions of the
stars, which Cicero esteemed one of the inventions which did the highest
honour to human genius. He perfected the manner of augmenting the
mechanic powers, by the multiplication of wheels and pullies; and
carried mechanics so far, that his works surpass imagination.