# A Short History of Initial Development of Quantum Mechanics

A timeline created using h5p. The reference book used is Lev Tarasov – Basic Concepts of Quantum Mechanics.

# An example use of H5P item for creating hotspots

Just trying out different H5P items. This item has a flower  and hotspots indicating parts of the flower.

Click on the question marks to know more..

# Galileo’s Experiments on Accelerated Motion

A short account of Galileo’s description of his own experiment on accelerated motion — a short account of it, the apparatus he used and the results he got.
The first argument that Salviati proves is that in accelerated motion the change in velocity is in proportion to the time (𝑣 ∝ 𝑡) since the motion began, and not in proportion to the distance covered (𝑣 ∝ 𝑠) as is believed by Sargedo.

“But for one and the same body to fall eight feet and four feet in the same time is possible only in the case of instantaneous (discontinuous) motion; but observation shows us that the motion of a falling body occupies time, and less of it in covering a distance of four feet than of eight feet; therefore it is not true that its velocity increases in proportion to the space. (Salviati)

Also, he proves that the increase in proportion is not of simple doubling but larger. They agree upon a definition of uniformly accelerated motion,

“A motion is said to be equally or uniformly accelerated when, starting from rest, its momentum receives equal increments in equal times. (Sargedo)

To this definition Salviati adds an assumption about inclined planes, this assumption is that for a given body, the increase in speed while moving down the planes of difference inclinations is equal to the height of the plane. This also includes the case if the body is dropped vertically down, it will still gain the same speed at end of the fall as it would gain from rolling on the incline This assumption makes the final speed independent on the profile of the incline. For example, in the figure below, the body falling along𝐶 → 𝐵, 𝐶 → 𝐷 and 𝐶 → 𝐴 will attain the same final speed.

This result is also proved via a thought experiment (though it might be feasible to do this experiment) for a pendulum. The pendulum rises to the height it was released from and not more.
After stating this theorem, Galileo then suggests the experimental verification of the theorem. of The actual apparatus that Galileo uses is an wooden inclined slope of following dimensions: length 12 cubits (≈ 5.5 m, 1 cubit ≈ 45.7 cm), width half-cubit and three-finger breadths thick . In this plank of wood, he creates a very smooth groove which is about a finger thick. (What was the thickness of Galileo’s fingers?) The incline of this plank are changed by lifting one end. A bronze ball is rolled in this groove and time taken for descent is noted.

“We repeated this experiment more than once in order to measure the time with an accuracy such that the deviation between two observations never exceeded one- tenth of a pulse-beat.

Then Galileo performed variations in the experiment by letting the ball go different lengths (not full) of the incline and “found that the spaces traversed were to each other as the squares of the times, and this was true for all inclinations of the plane”. Each variation was repeated hundreds of times so as to rule out any errors. Also, the fact that for different inclines the times of descent were in noted and were in agreement with the predictions.
Since there were no second resolution clocks to measure time, Galileo devised a method to measure time using water. This was not new, water clocks were used earlier also.

The basic idea was to the measure the amount of water that was collected from the start of the motion to its end. The water thus collected was weighed on a good balance.This weight of water was used as a measure of the time. A sort of calibration without actually measuring the quantity itself: “the differences and ratios of these weights gave us the differences and ratios of the times”

Galileo used a long incline, so that he could measure the time of descent with device he had. If a shorted incline was used, it would have been difficult to measure the shorter interval of time with the resolution he had. Measuring the free fall directly was next to impossible with the technology he had. Thus the extrapolation to the free fall was made continuing the pattern that was observed for the “diluted” gravity.

“You present these recondite matters with too much evidence and ease; this great facility makes them less appreciated than they would be had they been presented in a more abstruse manner. For, in my opinion, people esteem more lightly that knowledge which they acquire with so little labor than that acquired through long and obscure discussion. (Sargedo)

### Reference

Dialogues Concerning Two New Sciences

# Bertrand Russel’s proof of naïve realism being false

What is naïve realism you may ask? To put simply naïve realism is a belief that whatever you see with your senses is the reality. There is nothing more to reality than what your sense perceptions bring to you. It is a direct unmediated access to reality. There is no “interpretation” involved.

In philosophy of perception and philosophy of mind, naïve realism (also known as direct realism, perceptual realism, or common sense realism) is the idea that the senses provide us with direct awareness of objects as they really are. When referred to as direct realism, naïve realism is often contrasted with indirect realism.

Naïve Realism

To put this in other words, naïve realism fails to distinguish between the phenomenal and the physical object. That is to say, all there is to the world is how we perceive it, nothing more.

Bertrand Russel gave a one line proof of why naïve realism is false. And this is the topic of this post. Also, the proof has some implications for science education, hence the interest.

Naive realism leads to physics, and physics, if true, shows that naive realism is false. Therefore naive realism, if true, is false; therefore it is false.

As quoted in Mary Henle – On the Distinction Between the Phenomenal and the Physical Object, John M. Nicholas (ed.), Images, Perception, and Knowledge, 187-193. (1977)

Henle in her rather short essay (quoted above) on this makes various philosophically oriented arguments to show that it is an easier position to defend when we make a distinction between the two.

But considering the “proof” of Russel, I would like to bring in evidence from science education which makes it even more compelling. There is a very rich body of literature on the theme of misconceptions or alternative conceptions among students and even teachers. Many of these arise simply because of a direct interpretation of events and objects around us.

Consider a simple example of Newton’s first law of motion.

In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.

Now for the naïve realists this will never be possible, as they will never see an object going by itself without application of any force. In real world, friction will bring to halt bodies which are moving. Similar other examples from the misconceptions also do fit in this pattern. This is perhaps so because most of the science is counter-intuitive in nature. With our simple perception we can only do a limited science (perhaps create empirical laws). So one can perhaps say that learners with alternative conceptions hold naïve realist world-view (to some degree) and the role of science education is to change this.

# Rotating Earth: the proofs or significance of Leon Foucault’s pendulum – Part 1

In an earlier post, we had discussed proofs of the round shape of the Earth. This included some ancient and some modern proofs. There was, in general, a consensus that the shape of the Earth was spherical and not flat and the proofs were given since the time of ancient Greeks. Only in the middle ages, there seems to have been some doubt regarding the shape of the Earth. But amongst the learned people, there was never a doubt about the shape of the Earth. Counter-intuitive it may seem when you look at the near horizon, it is not that counter-intuitive. We can find direct proofs about it by looking around and observing keenly.
But the rotation of Earth proved to be a more difficult beast to tame and is highly counter-intuitive. Your daily experience does not tell you the Earth is rotating, rather intuition tells you that it is fixed and stationary. Though the idea of a moving Earth is not new, the general acceptance of the idea took a very long time. And even almost 350 years after Copernicus’ heliocentric model was accepted, a direct proof of Earth’s rotation was lacking. And this absence of definitive proof was not due to a lack of trying. Some of the greatest minds in science, mathematics and astronomy worked on this problem since Copernicus but were unable to solve it. This included likes of Galileo, Newton, Descartes, and host of incredibly talented mathematicians since the scientific revolution. Until Leon Foucaultin the mid-1800s provided not one but two direct proofs of the rotation of the Earth. In this series of posts, we will see how this happened.
When we say the movement of the Earth, we also have to distinguish between two motions that it has: first its motion about its orbit around the Sun, and second its rotational motion about its own axis. So what possible observational proofs or direct evidence will allow us to detect the two motions? In this post, we will explore how our ideas regarding these two motions of the Earth evolved over time and what type of proofs were given for and against it.

Even more, there was a simple geometrical fact directly opposed to the Earth’s annual motion around the Sun and there was nothing that could directly prove its diurnal rotation. (Mikhailov, 1975)

Let us consider the two components of Earth’s motion. The first is the movement around the Sun along the orbit. The simplest proof for this component of Earth’s motion is from the parallax that we can observe for distant stars. Parallax is the relative change in position of objects when they are viewed from different locations. The simplest example of this can be seen with our own eyes.
Straighten your hand, and hold your thumb out. Observe the thumb with both the eyes open. You will see your thumb at a specific location with respect to the background objects. Now close your left eye, and look at how the position of the thumb has changed with respect to the background objects. Now open the right eye, and close the left one. What we will see is a shift in the background of the thumb. This shift is related by simple geometry to the distance between our eyes, called the baseline in astronomical parlance. Thus even a distance of the order of a few centimetres causes parallax, then if it is assumed that Earth is moving around the Sun, it should definitely cause an observable parallax in the fixed stars. And this was precisely one of the major roadblock

Earth moving around an orbit raised mechanical objections that seemed even more serious in later ages; and it raised a great astronomical difficulty immediately. If the Earth moves in a vast orbit, the pattern of fixed stars should show parallax changes during the year. (Rogers, 1960)

The history of cosmic theories … may without exaggeration be called a history of collective obsessions and controlled schizophrenias.
– Arthur Koestler, The Sleepwalkers

Though it is widely believed that Copernicus was the first to suggest a moving Earth, it is not the case. One of the earliest proponents of the rotating Earth was a Greek philosopher named Aristarchus. One of the books by Heath on Aristarchus is indeed titled Copernicus of Antiquity (Aristarchus of Samos). A longer version of the book is Aristarchus of Samos: The Ancient Copernicus. In his model of the cosmos, Aristarchus imagined the Sun at the centre and the Earth and other planets revolving around it. At the time it was proposed, it was not received well. There were philosophical and scientific reasons for rejecting the model.

First, let us look at the philosophical reasons. In ancient Greek cosmology, there was a clear and insurmountable distinction between the celestial and the terrestrial. The celestial order and bodies were believed to be perfect, as opposed to the imperfect terrestrial. After watching and recording the uninterrupted waltz of the sky over many millennia, it was believed that the heavens were unchangeable and perfect. The observations revealed that there are two types of “stars”. First the so-called “fixed stars” do not change their positions relative to each other. That is to say, their angular separation remains the same. They move together as a group across the sky. Imagination coupled with a group of stars led to the conceiving of constellations. Different civilizations imagined different heroes, animals, objects in the sky. They formed stories about the constellations. These became entwined with cultures and their myths.

The second type of stars did change their positions with respect to other “fixed stars”. That is to say, they changed their angular distances with “fixed stars”. These stars, the planets, came to be called as “wandering stars” as opposed to the “fixed stars”.

Ancient Greeks called these lights πλάνητες ἀστέρες (planētes asteres, “wandering stars”) or simply πλανῆται (planētai, “wanderers”),from which today’s word “planet” was derived.
Planet

So how does one make sense of these observations? For the fixed stars, the solution is simple and elegant. One observes the set of stars rising from the east and setting to the west. And this set of stars changes across the year (which can be evidenced by changing seasons around us). And this change was found to be cyclical. Year after year, with observations spanning centuries, we found that the stars seem to be embedded on inside of a sphere, and this sphere rotates at a constant speed. This “model” explains the observed phenomena of fixed stars very well.
The unchanging nature of this cyclical process observed, as opposed to the chaotic nature on Earth, perhaps led to the idea that celestial phenomena are perfect. Also, the religious notion of associating the heavens with gods, perhaps added to them being perfect. So, in the case of perfect unchanging heavens, the speeds of celestial bodies, as evidenced by observing the celestial sphere consisting of “fixed stars” was also to be constant. And since celestial objects were considered as perfect, the two geometrical objects that were regarded as perfect the sphere and the circle were included in the scheme of heavens. To explain the observation of motion of stars through the sky, their rising from the east and setting to the west, it was hypothesized that the stars are embedded on the inside of a sphere, and this sphere rotates at a constant speed. We being fixed on the Earth, observe this rotating sphere as the rising and setting of stars. This model of the world works perfectly and formed the template for explaining the “wandering stars” also.
These two ideas, namely celestial objects placed on a circle/sphere rotating with constant speed, formed the philosophical basis of Greek cosmology which would dominate the Western world for nearly two thousand years. And why would one consider the Earth to be stationary? This is perhaps because the idea is highly counter-intuitive. All our experience tells us that the Earth is stationary. The metaphors that we use like rock-solid refer to an idea of immovable and rigid Earth. Even speculating about movement of Earth, there is no need for something that is so obviously not there. But as the history of science shows us, most of the scientific ideas, with a few exceptions, are highly counter-intuitive. And that the Earth seems to move and rotate is one of the most counter-intuitive thing that we experience in nature.
The celestial observations were correlated with happenings on the Earth. One could, for example, predict seasons as per the rising of certain stars, as was done by ancient Egyptians. Tables containing continuous observations of stars and planets covering several centuries were created and maintained by the Babylonian astronomers. It was this wealth of astronomical data, continuously covering several centuries, that became available to the ancient Greek astronomers as a result of Alexander’s conquest of Persia. Having such a wealth of data led to the formation of better theories, but with the two constraints of circles/spheres and constant speeds mentioned above.
With this background, next, we will consider the progress in these ideas.
A stabilised image of the Milky Way as seen from a moving Earth.

# Why philosophy is so important in science education

This is a nice article whicH I have reposted from AEON…

Each semester, I teach courses on the philosophy of science to undergraduates at the University of New Hampshire. Most of the students take my courses to satisfy general education requirements, and most of them have never taken a philosophy class before.
On the first day of the semester, I try to give them an impression of what the philosophy of science is about. I begin by explaining to them that philosophy addresses issues that can’t be settled by facts alone, and that the philosophy of science is the application of this approach to the domain of science. After this, I explain some concepts that will be central to the course: induction, evidence, and method in scientific enquiry. I tell them that science proceeds by induction, the practices of drawing on past observations to make general claims about what has not yet been observed, but that philosophers see induction as inadequately justified, and therefore problematic for science. I then touch on the difficulty of deciding which evidence fits which hypothesis uniquely, and why getting this right is vital for any scientific research. I let them know that ‘the scientific method’ is not singular and straightforward, and that there are basic disputes about what scientific methodology should look like. Lastly, I stress that although these issues are ‘philosophical’, they nevertheless have real consequences for how science is done.
At this point, I’m often asked questions such as: ‘What are your qualifications?’ ‘Which school did you attend?’ and ‘Are you a scientist?’
Perhaps they ask these questions because, as a female philosopher of Jamaican extraction, I embody an unfamiliar cluster of identities, and they are curious about me. I’m sure that’s partly right, but I think that there’s more to it, because I’ve observed a similar pattern in a philosophy of science course taught by a more stereotypical professor. As a graduate student at Cornell University in New York, I served as a teaching assistant for a course on human nature and evolution. The professor who taught it made a very different physical impression than I do. He was white, male, bearded and in his 60s – the very image of academic authority. But students were skeptical of his views about science, because, as some said, disapprovingly: ‘He isn’t a scientist.’
I think that these responses have to do with concerns about the value of philosophy compared with that of science. It is no wonder that some of my students are doubtful that philosophers have anything useful to say about science. They are aware that prominent scientists have stated publicly that philosophy is irrelevant to science, if not utterly worthless and anachronistic. They know that STEM (science, technology, engineering and mathematics) education is accorded vastly greater importance than anything that the humanities have to offer.
Many of the young people who attend my classes think that philosophy is a fuzzy discipline that’s concerned only with matters of opinion, whereas science is in the business of discovering facts, delivering proofs, and disseminating objective truths. Furthermore, many of them believe that scientists can answer philosophical questions, but philosophers have no business weighing in on scientific ones.
Why do college students so often treat philosophy as wholly distinct from and subordinate to science? In my experience, four reasons stand out.
One has to do with a lack of historical awareness. College students tend to think that departmental divisions mirror sharp divisions in the world, and so they cannot appreciate that philosophy and science, as well as the purported divide between them, are dynamic human creations. Some of the subjects that are now labelled ‘science’ once fell under different headings. Physics, the most secure of the sciences, was once the purview of ‘natural philosophy’. And music was once at home in the faculty of mathematics. The scope of science has both narrowed and broadened, depending on the time and place and cultural contexts where it was practised.
Another reason has to do with concrete results. Science solves real-world problems. It gives us technology: things that we can touch, see and use. It gives us vaccines, GMO crops, and painkillers. Philosophy doesn’t seem, to the students, to have any tangibles to show. But, to the contrary, philosophical tangibles are many: Albert Einstein’s philosophical thought experiments made Cassini possible. Aristotle’s logic is the basis for computer science, which gave us laptops and smartphones. And philosophers’ work on the mind-body problem set the stage for the emergence of neuropsychology and therefore brain-imagining technology. Philosophy has always been quietly at work in the background of science.
A third reason has to do with concerns about truth, objectivity and bias. Science, students insist, is purely objective, and anyone who challenges that view must be misguided. A person is not deemed to be objective if she approaches her research with a set of background assumptions. Instead, she’s ‘ideological’. But all of us are ‘biased’ and our biases fuel the creative work of science. This issue can be difficult to address, because a naive conception of objectivity is so ingrained in the popular image of what science is. To approach it, I invite students to look at something nearby without any presuppositions. I then ask them to tell me what they see. They pause… and then recognise that they can’t interpret their experiences without drawing on prior ideas. Once they notice this, the idea that it can be appropriate to ask questions about objectivity in science ceases to be so strange.
The fourth source of students’ discomfort comes from what they take science education to be. One gets the impression that they think of science as mainly itemising the things that exist – ‘the facts’ – and of science education as teaching them what these facts are. I don’t conform to these expectations. But as a philosopher, I am mainly concerned with how these facts get selected and interpreted, why some are regarded as more significant than others, the ways in which facts are infused with presuppositions, and so on.
Students often respond to these concerns by stating impatiently that facts are facts. But to say that a thing is identical to itself is not to say anything interesting about it. What students mean to say by ‘facts are facts’ is that once we have ‘the facts’ there is no room for interpretation or disagreement.
Why do they think this way? It’s not because this is the way that science is practised but rather, because this is how science is normally taught. There are a daunting number of facts and procedures that students must master if they are to become scientifically literate, and they have only a limited amount of time in which to learn them. Scientists must design their courses to keep up with rapidly expanding empirical knowledge, and they do not have the leisure of devoting hours of class-time to questions that they probably are not trained to address. The unintended consequence is that students often come away from their classes without being aware that philosophical questions are relevant to scientific theory and practice.
But things don’t have to be this way. If the right educational platform is laid, philosophers like me will not have to work against the wind to convince our students that we have something important to say about science. For this we need assistance from our scientist colleagues, whom students see as the only legitimate purveyors of scientific knowledge. I propose an explicit division of labour. Our scientist colleagues should continue to teach the fundamentals of science, but they can help by making clear to their students that science brims with important conceptual, interpretative, methodological and ethical issues that philosophers are uniquely situated to address, and that far from being irrelevant to science, philosophical matters lie at its heart.

Subrena E Smith
This article was originally published at Aeon and has been republished under Creative Commons.

# Thomas Kuhn on the role of textbooks in science education

The single most striking feature of this [science] education is that, to an extent wholly unknown in other fields, it is conducted entirely through textbooks. Typically, undergraduate and graduate students of chemistry, physics, astronomy, geology, or biology acquire the substance of their fields from books written especially for students.

Thomas Kuhn The Essential Tension
Here Kuhn is trying to show us the nature of science education which is usually divergent from the historical processes and events which led to the currently accepted theories. Most of the textbooks rather show the content matter which makes sense conceptually in a rationally organised manner. Of course, the ideal goal, at least in the physical sciences, is to create a hypothetico-deductive model in which a given theory, its predictions, explanations and implications can be derived from some basic definitions and axioms. For example, an introductory text on motion in physics usually starts with definitions and assumptions usually of a mass point, and/or operations that are defined on it. The text does not describe the historical conditions in which this conceptual approach arose, rather it adapts a very pragmatic pedagogical approach. It defines the term and ends it there, but in this process, it redefines the conceptual history. This approach assumes that there is no pedagogical merit or role in introducing a concept in its historical context. This perhaps is also linked to Poppers distinction of the context of discovery and the context of justification. What we see is a rational reconstruction of historical processes to make sense of them in a straightforward manner.

# Science Education and Textbooks

What are the worst possible ways of approaching the textbooks for teaching science? In his book Science Teaching: The Role of History and Philosophy of Science pedagogue Michael Matthews quotes (p. 51) Kenealy in this matter. Many of the textbooks of science would fall in this categorisation. The emphasis lays squarely on the content part, and that too memorized testing of it.

Kenealy characterizes the worst science texts as ones which “attempt to spraypaint their readers with an enormous amount of ‘scientific facts,’ and then test the readers’ memory recall.” He goes on to observe that:
Reading such a book is much like confronting a psychology experiment which is testing recall of a random list of nonsense words. In fact, the experience is often worse than that, because the book is a presentation that purports to make sense, but is missing so many key elements needed to understand how human beings could ever reason to such bizarre things, that the reader often blames herself or himself and feels “stupid,” and that science is only for special people who can think “that way” … such books and courses have lost a sense of coherence, a sense of plot, a sense of building to a climax, a sense of resolution. (Kenealy 1989, p. 215)

What kind of pedagogical imagination and theories will lead to the textbooks which have a complete emphasis on the “facts of science”? This pedagogical imagination also intimately linked to the kind of assessments that we will be using to test the “learning”. Now if we are satisfied by assessing our children by their ability to recall definitions and facts and derivations and being able to reproduce them in writing (handwriting) in a limited time then this is the kind of syllabus that we will end up with. Is it a wonder if students are found to be full of misconceptions or don’t even have basic ideas about science, its nature and methods being correct? What is surprising, at least for me, that even in such a situation learning still happens! Students still get some ideas right if not all.
A curriculum which does not see a point in assessing concepts has no right to lament at students not being able to understand them or lacking conceptual understanding. As Position Paper on Teaching of Science in NCF 2005 remarks

‘What is not assessed at the Board examination is never taught’

So, if the assessment is not at a conceptual level why should the students ever spend their time on understanding concepts? What good will it bring them in a system where a single mark can decide your future?

# Round Earth: The Proofs

## What is the evidence for a round Earth?

In this post, we explore some of the evidence for proving that the Earth is indeed spherical in shape (if not a perfect one), and not a flat one. Though in the current age we can all point to the images of Earth taken from space  (like the one shown below)

In the age of satellites is easy for us to dismiss the doubting minds who think that the Earth is not flat. But this was always not so. Apart from the evidence from the space age, people in the past had good evidence and arguments for believing that the Earth was indeed spherical in shape and not flat or any other shape. Somehow this misconception that all ancient people considered that the Earth was flat, was generated in nineteenth-century science books.

## Ancient evidence

It is commonly believed that people till very recently believed that the Earth is flat and that some European explorers, by circumnavigating the Earth, proved that it was round. But this is not correct. Ancient Greeks already knew about the spherical shape of the Earth, and it forms the basis of many cosmological models that they built. This, in turn, had implications for the philosophical worldview of the ancient
Aristotle presents us with one of the first evidence for the roundedness of the Earth. For the ancient Greeks, the circle and the sphere presented the perfect form in nature. This was also tied to their worldview in which the celestial and terrestrial was demarcated from each other. The celestial bodies, which included the planets and stars were supposed to be perfect. There were seven planets known to the ancients, which included the Sun and the Moon. The planets were supposed to be spherical themselves revolving with a constant speed in circular orbits around the Earth. One of the core assumptions was that the heavens are unchangeable. So anything that was considered celestial was by definition (a) perfect (spherical or circular), (b) unchangeable (constant). So any mechanism that explained celestial phenomenon had to include these two concepts.

The cosmology of the ancient Greeks then was built upon these basic assumptions which were non-negotiable for them. This lead to the formation of various models based on the basic theme of a fixed Earth and planets on circular orbits moving constant speeds. Due to these assumptions and also due to some observed phenomena, led to the conclusion that Earth should also be indeed spherical.
Let us look at the arguments given by Aristotle in this regard. This is from Book II of On the Heavens.

The shape of the heaven is of necessity spherical; for that is the shape most appropriate to its substance and also by nature primary.
Part 11
With regard to the shape of each star, the most reasonable view is that they are spherical. It has been shown that it is not in their nature to move themselves, and, since nature is no wanton or random creator, clearly she will have given things which possess no movement a shape particularly unadapted to movement. Such a shape is the sphere, since it possesses no instrument of movement. Clearly then their mass will have the form of a sphere. Again, what holds of one holds of all, and the evidence of our eyes shows us that the moon is spherical. For how else should the moon as it waxes and wanes show for the most part a crescent-shaped or gibbous figure, and only at one moment a half-moon? And astronomical arguments give further confirmation; for no other hypothesis accounts for the crescent shape of the sun’s eclipses. One, then, of the heavenly bodies being spherical, clearly the rest will be spherical also.

In Part 13 of the book Aristotle talks about the shape of the Earth.

There are similar disputes about the shape of the earth. Some think it is spherical, others that it is flat and drum-shaped. For evidence they bring the fact that, as the sun rises and sets, the part concealed by the earth shows a straight and not a curved edge, whereas if the earth were spherical the line of section would have to be circular. In this they leave out of account the great distance of the sun from the earth and the great size of the circumference, which, seen from a distance on these apparently small circles appears straight. Such an appearance ought not to make them doubt the circular shape of the earth. But they have another argument. They say that because it is at rest, the earth must necessarily have this shape. For there are many different ways in which the movement or rest of the earth has been conceived.

Here we see the cognisance of the fact that the curvature tends to be linear when see it is too large. Aristotle then goes on to discard the ideas by Anaximenes, Anaxogoras and Democritus who claim that flatness of the Earth is responsible for it being still. He argues, even a spherical Earth can remain at rest. The Earth being at rest and it being spherical are related. In Part 14 he takes this discussion further. The first argument uses the symmetry of weight distribution.

Its shape must necessarily be spherical. For every portion of earth has weight until it reaches the centre, and the jostling of parts greater and smaller would bring about not a waved surface, but rather compression and convergence of part and part until the centre is reached.

He further argues using reasoning of additional weight distribution how a spherical Earth can still be

If the Earth was generated, then, it must have been formed in this way, and so clearly its generation was spherical; and if it is ungenerated and has remained so always, its character must be that which the initial generation, if it had occurred, would have given it. But the spherical shape, necessitated by this argument, follows also from the fact that the motions of heavy bodies always make equal angles, and are not parallel. This would be the natural form of movement towards what is naturally spherical. Either then the earth is spherical or it is at least naturally spherical.

After this, he looks at evidence from lunar eclipses to reason that Earth is indeed spherical.

The evidence of the senses further corroborates this. How else would eclipses of the moon show segments shaped as we see them? As it is, the shapes which the moon itself each month shows are of every kind straight, gibbous, and concave-but in eclipses the outline is always curved: and, since it is the interposition of the earth that makes the eclipse, the form of this line will be caused by the form of the earth’s surface, which is therefore spherical.

Finally Aristotle takes into account the fact that stars change their positions in the sky relative to the horizon when we move to North or South, indicating that we are indeed on a spherical surface. This will not happen on a flat surface.

Again, our observations of the stars make it evident, not only that the earth is circular, but also that it is a circle of no great size. For quite a small change of position to south or north causes a manifest alteration of the horizon. There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves northward or southward. Indeed there are some stars seen in Egypt and in the neighbourhood of Cyprus which are not seen in the northerly regions; and stars, which in the north are never beyond the range of observation, in those regions rise and set. All of which goes to show not only that the earth is circular in shape, but also that it is a sphere of no great size: for otherwise the effect of so slight a change of place would not be quickly apparent.

Another evidence which can be seen since antiquity is that the masts of the ships on ocean became visible first on the horizon, the ship appear later. This can be simply explained by assuming that the surface of the ocean is curved too.

Thus we have seen the ancient evidence for a spherical Earth. It was well known and well established fact, both theoretically and empirically.
Images from:
All About The Telescope – P. Klushantsev
A Book About Stars and Planets – Y. Levitan
Physics for The Inquiring Mind – Eric Rogers.