What advancements did Galileo make in the history of telescopes?
Although Galileo did not invent telescope, He made his own telescope and used it to observe the sky, stars, moon, planets, and many other things.
His observations and records of the Moon's hills and craters, the four moons orbiting Jupiter, Venus's crescent phases, the Milky Way's stars, and much more confirmed Copernicus's theory of a universe centered on the sun.
Wikipedia lists Hans Lippershey of the Netherlands as one of the inventors, however he was not given a patent because two other lens manufacturers at the time counterclaimed ownership of the technology.
The following year, Galileo invented a far simpler way to join the two lenses in a refracting telescope, and the Venetian senate doubled his salary based solely on this discovery.
After that, he made even more improvements to them. Before his work, the magnification that could be obtained with telescopes at the time was only about three times; Galileo's improvements increased this to about 33 times.
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Galileo Galilei made significant advancements in the history of telescopes by improving their design and making astronomical observations. He enhanced the magnification power, allowing him to observe celestial bodies in greater detail. Galileo observed Jupiter's moons, discovered the phases of Venus, and identified sunspots. His observations provided evidence supporting the heliocentric model of the solar system.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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