Galileo mathematics. Some major innovations he made that will

Galileo was a Polymath from Italy that lived
from 1564 to 1642 and was the oldest of his five siblings. His father, Vincenzo
Galilei, was a well-known string instrument player and composer in his time.
Vincenzo married Galileo’s mother, Giulia Ammannati,
in 1562. Galileo had three children with Marina Gamba, however, they were not
married. Because of this, Galileo enrolled both of his daughters in the convent
of San Matteo where they became nuns. His only son, Vincenzo, became a lutenist
like his grandfather.    

In 1616, Galileo was called in front of the
inquisition and warned to not promote the theory of heliocentrism. In the same
year the Catholic church barred the book “On the Revolutions of the Celestial
Spheres” by Nicholas Copernicus. This book was one of the first to introduce
the theory that the Earth orbits the Sun. It was not until 1632 that Galileo
was under investigation of the Inquisition. He published his “Dialogue on the
Two World Systems,” which contained arguments inside that supported heliocentrism.
However, according to Galileo vs The Pope, “Galileo was told then that he could consider the concept as a
hypothetical idea. He was not to present it as a reality, however, and should
not even think of it in that way.” (Hal Hellman, p 2) After his work was
published, Galileo was interrogated and asked if he believed what was
written in his book, but he refute the belief. Eventually, he was charged with
a strong suspicion of heresy and was required to light penance for his wrong
doings. The church also banned his book from being read.    

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In his seventy-seven years of life, Galileo
made a large number of discoveries in several different fields including
astronomy, engineering, physics, and mathematics. Some major innovations he
made that will not be discussed in depth in this paper are his improvement to
the geometric and military compass as well as his primitive thermometer.
Galileo improved the geometric and military compass so that cannon operators
could estimate the amount of gunpowder necessary as well as the angle of the
cannon needed for all different sizes of cannon balls. Galileo’s thermometer utilized
the density of liquids, the principle of buoyancy, and bubbles submerged in a
liquid to determine the apparatus’ surroundings.

The telescope made its first appearance in the
Netherlands during October of 1608. Hans Lipperhey was the inventor of the
telescope. The composition of the telescope was fairly basic in design; “It consisted of a convex and concave lens in a tube, and
the combination magnified three or four times.” (Albert Van Helden p. 2) Lipperhey attempted to acquire a patent for his new
invention, but he was not awarded one because “the gentlemen found the device
too easy to copy to award the patent.” (Albert Van Helden, p. 3) The telescope quickly spread all across Europe as
astronomers and lay-people alike were eager to catch a glimpse of celestial
objects up close. Although Galileo did not invent the telescope he greatly
improved its usefulness. He greatly improved the magnification from three to
four times to fifteen to twenty times. The composition was totally different
than that of the original telescope; “A typical Galilean telescope with
which Jupiter’s moons could be observed was configured as follows. It had a
plano-convex objective (the lens toward the object) with a focal length of
about 30-40 inches., and a plano-concave ocular with a focal length of about 2
inches.” (Galileo Galilei,
3)
In addition to the improved magnification, the Galilean telescope had an
additional purpose compared to the astronomical telescope. The Galilean
telescope could be used for terrestrial as well as celestial purposes without
any changes needed to be made to the object. The major difference between the
two telescopes is that the astronomical telescope gives an inverted image,
which renders it useless for use on land or sea. “Astronomers eschewed
the third convex lens (the erector lens) necessary for re-inverting the image
because the more lenses the more optical defects multiplied.” (Albert Van Helden, 5) This shows that
the Galilean telescope was superior to other telescopes at the time as it had
more magnification power as well as more uses.

One of Galileo’s biggest contributions to
science was the discovery of Jupiter’s moons. Initially, he describes them as
“three little stars, small but very bright, were near the planet; and although
I believed them to belong to the number of the fixed stars, yet they made me
somewhat wonder, because they seemed to be arranged exactly in a straight line,
parallel to the ecliptic and to be brighter than the rest of the stars equal to
them in magnitude.” (Galileo Galilei, p.
17) Although Galileo initially thought they were fixed stars in the sky, he
later observes them again and notates that the moons are in a different
orientation. Initially, there were two moons on the left and one on the right
of Jupiter. The second time the moons were observed, all three of the moons
were on the right side of the planet. Galileo notes, “on January 8th,
led by some fate, I turned again to look at the same part of the heavens, I
found a very different state of things, for there were three little stars all
west of Jupiter and nearer together than on the previous night, and they were
separated from one another by equal intervals” (Galileo
Galilei, p 18). On January 10th, Galileo observes the moons
again and only sees two on left side of Jupiter. He continues to observe and
document the position of Jupiter’s moons until March 2nd. From his
time observing the celestial objects he deduces that the movement of the
“stars” is not due to Jupiter, but that the stars are moving around Jupiter. “it
can be a matter of doubt to no one that they perform their revolutions about
this planet, while at the same time they all move as one around the center of
the world in twelve years. They revolve in unequal circles, which is evidently
the conclusion to be drawn from the fact that I have never been permitted to
see two planets in conjunction when their distance from Jupiter was great,
whereas near Jupiter two, three, and sometimes all, have been found closely
packed together.” (Galileo Galilei, p. 28) This was the first time anyone had
discovered and observed Jupiter’s moons.

Galileo also observes the surface of the earth
and describes it in some detail. He states that “Now these spots, as they are somewhat dark and of
considerable size, are plain to everyone, and every age has seen them,
wherefore I shall call them great or ancient spots, to distinguish them from
other spots, smaller in size, but so thickly scattered that they sprinkle the
whole surface of the Moon, but especially the brighter portion of it. These
spots have never been observed by anyone before me; and from my observations of
them, often repeated, I have been led to that opinion which I have expressed,
namely, that I feel sure that the surface of the Moon is not perfectly smooth,
free from inequalities and exactly spherical, as a large school of philosophers
considers with regard to the Moon and the other heavenly bodies, but that, on
the contrary, it is full of inequalities, uneven, full of hollows and
protuberances, just like the surface of the Earth itself, which is varied
everywhere by lofty mountains and deep valleys.”
(Galileo Galilei, p.7) Because
Galileo was an artist he understood the nature of lighting and how it created
shadows. Galileo exemplifies his understanding of shadows when he says, “I have
noticed that the small spots just mentioned have this common characteristic
always and in every case, that they have the dark part towards the Sun’s
portion, and on the side away from the Sun they have brighter boundaries, as if
they were crowned with shining summits.” (Galileo
Galilei, p.8) He then goes
into depth describing the cycles of the moon as well as the smaller chasms of
the moons that cannot be observed without the use of a telescope.

In conclusion, Galileo Galilei is one of the
best and most important polymaths in all of human history. He made several
advancements such as improvements to the compass, enhancements to the
telescope, as well as inventing an early form of the thermometer. In addition,
he was also an early enthusiast of the theory of heliocentrism, which was an
uncommon as well as dangerous theory to support due to the power of the
Inquisition. Although these are important improvements to society, Galileo’s
most notable contribution was his astrological discoveries. He was the first to
give a detailed, accurate description of the surface of the moon with the help
of his telescope and knowledge of lighting and shadows. Additionally, Galileo
was the first to observe and document the moons of Jupiter. He also created
accurate theories on the movement of the three moons. For the reasons stated
above, one can conclude that Galileo Galilei is one of the most innovative
minds in all of history.    

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