The Works of Archimedes is a collection of the surviving writings of Archimedes that he composed during the 3rd century BCE. Archimedes is hands down The Works of Archimedes is a collection of the surviving writings of Archimedes that he composed during the 3rd century BCE. Archimedes is hands down the most notable fusion of a mathematician, physicist, and engineer of Classical Antiquity. He devised mathematical formulas and proofs that are still used today, he discovered laws on various physical phenomena that are even now relevant, and invented machines and devices never seen before his time (these inventions were not discussed in the book). Reading the book, one gets to observe Archimedes' obsession with finding relations and echoing symmetrical proportions between various geometrical shapes and figures, both in two and three dimensions, while discovering ways to apply this theoretical knowledge to real-life matters.
This English translation is excellent, although the 200-page introduction was wearisome and superfluous. I believe that the translator-author had the best of intentions in providing the reader with a thorough introduction, but something should be left for the reader to explore in the principal text.
Legend has it that the last few moments before Archimedes' death he was studying geometry and drawing shapes in the dusty ground. At this time he was approached by a Roman soldier during the the siege of Syracuse. Archimedes disobeyed the soldier's orders to come with him which resulted in the soldier drawing out his sword. Archimedes reacted and plunged to protect the dust with his hands while begging the soldier and said: "Do not disturb my circles." Nonetheless, he was killed by that soldier despite the orders of the Roman Republic that he should not be harmed....more
Epicurus and his renowned school of thought teaches us to pursue happiness by relishing life's pleasures. However, not the pleasures that you might haEpicurus and his renowned school of thought teaches us to pursue happiness by relishing life's pleasures. However, not the pleasures that you might have in mind, such as living in luxury, engaging in consumerism, and indulging in sensual elations, but more learning to release one's body of pain and mind of anticipation and anxieties.
Epicurus recommends a simple and healthier lifestyle that will maximize one's happiness. Although, to achieve happiness we have to begin with structuring our lives differently, changing our habits, mindset, and perceptions of things. In particular, we should frequently surround ourselves with friends, live unseen or without attracting attention from the public eye, free ourselves from everyday affairs and politics and create or become part of close-knit self-sufficient communes, even if it means living below your means or professions. A virtuous life that will bring you peace of mind.
Epicurus' advice on faith and God is to entirely free ourselves of superstitions and never ask a God for what we can obtain ourselves as he doesn't mingle in everyday affairs.
Epicurus (341-270 BCE) is an Empiricist and The Essential Epicurus are a few fragments of works and remaining letters written to his students discussing both cosmological and ethical questions. Almost all of the Epicurean 300 written works are lost but his philosophy influenced many of the later thinkers, namely Karl Marx who did a PhD thesis on Epicurus and his philosophy. ...more
In La Géométrie (1637) I found Descartes' writing distilled and his mathematical demonstration lucid. I read the translation in English which alongsidIn La Géométrie (1637) I found Descartes' writing distilled and his mathematical demonstration lucid. I read the translation in English which alongside each page has a facsimile of the original French edition with a mid-17th century typeface design.
Descartes employs his avant-garde method of reasoning in the field of mathematics to display the method's versatility. In this unabridged edition, he presents an alternative system on how to approach, evaluate and think about mathematics. Descartes takes the ancient geometry that was constricted to a ruler and compass and transforms it into modern geometry. A geometry for which it was not necessary to draw lines, but enough to designate a letter for them. He appoints the letters a, b, and c for know values and x, y, and z for the unknown values which we use even now.
With this work, Descartes founded analytic geometry and laid the foundation for the development of calculus. His coordinate system we still use today to translate geometrical shapes into algebraic equations and vice versa, at last linking arithmetic and geometry into one....more
Conics, or conic sections, are when taking cross-sections of a cone or when a plane intersects a cone. Now depending on a different angle a particularConics, or conic sections, are when taking cross-sections of a cone or when a plane intersects a cone. Now depending on a different angle a particular cone is intersected we uncover various curved shapes and figures, such as circles, ellipses, parabolas, and hyperbolas. Understanding the properties of various conic sections enable us to better comprehend the quantifiable things of nature. Essentially, space-time as we know it is curved, planets revolve in an elliptical orbit, and the DNA, the fundamental component of life, spirals into a coil-shaped structure. Hence, there is more curvature in nature than the uncommon straight lines and sharp edges. Nevertheless, Apollonius utilizes Euclidean geometry to demonstrate his propositions of the conic sections, thus, employing man-made geometry to demonstrate a more nature-like geometry.
The Conics: Books I-IV (c.200BCE) were written in Alexandria, Egypt by a Greek geometrician and astronomer Apollonius of Perga (c.240BCE–190BCE). The English translation I have read is impeccable and the layout of the pages with numerous geometrical illustrations and expressions leave enough room for notes.
This is a wonderful book and I look forward to reading next La Géométrie (1637) in which Rene Descartes interprets Euclid's and Apollonius' geometrical language and theorems only to translate them into easier to follow algebraic expressions....more
The book opens with a brief dialog between Socrates, Timaeus, Hermocrates, and Critias, which swiftly retrogrades into a long monologue by Timaeus himThe book opens with a brief dialog between Socrates, Timaeus, Hermocrates, and Critias, which swiftly retrogrades into a long monologue by Timaeus himself, during which time Socrates sits quietly and listens.
Timaeus, from Locri, Italy, is a fictional character and his monologue is in fact Plato's lecture, but the philosophy presented bears a resemblance to the one of Pythagoras.
Plato (c.427-347 BCE) in Timaeus c.360 BCE discusses the origins and principles of cosmology; from the creation of the cosmos to the nature of things and humans physiology, sensory perceptions, and the well-being and maladies of the body and soul.
In Timaeus, Demiurge is the artisan that brings the cosmos from a disorderly state to an orderly harmony. The creator, Demiurge, is good and he builds a cosmos similar to himself. Timaeus' cosmos is beautiful, perfect, and a visible living being, like an organism, that is created on insightful principles in which Demiurge placed the mind into the soul and the soul into the body.
Timaeus believes that only a single spherical universe exists with a round rotating floating Earth at its center. A universe in which the Earth and all the other heavenly bodies are created and immortal and the earthly beings created but mortal.
The elements that constitute matter: water (fluid), air (gas), earth (solid), and fire (plasma) are shaped in various geometrical bodies (Platonic solids) in which the triangles they are composed of are the elementary particles of nature.
Timaeus' cosmos is mechanistic and emerged from mathematical knowledge that is governed by necessity and the divine. A universe in which energy remains constant and the observable moving image of eternal space flows to the pulse of a number that we call time.
Plato's Timaeus reads like a mythical prose poem which was apparently influenced by the “three Pythagorean books” published by Philolaus that Plato bought and Timon of Phlius said: "Well, you too, Plato, were obsessed with the desire to acquire followers; and because of it, for much money, you bought a small book, and from it, you learned to write Timaeus." Fact of fiction, we'll never know, but I like to think that Timaeus is a product of Plato's and Pythagorean philosophy....more
It's fascinating to notice in Aristotle's books, which are over two millennia old, that he is always properly citing his sources and quoting the preceIt's fascinating to notice in Aristotle's books, which are over two millennia old, that he is always properly citing his sources and quoting the preceding philosophers. In essence, he does not attempt to take any recognition for someone else's ideas and in return implements a high ethical standard of referencing his sources.
In Aristotle's On the Generation and Corruption (350 BCE) (this title in English is a bit inadequate) he discusses the characteristics of matter, the "stuff" we're made of and surrounded by. Do things come to be and pass away? Or is everything a product or a result of alteration? All this associated me with the law of conservation of energy, which states that energy is always conserved, therefore, cannot be created or destroyed or as Aristotle puts it: “the corruption of one thing is the generation of another and vice versa.”
Aristotle accepts Empedocles' notion that matter is composed of the four elements: earth, being the heaviest, then water, air, and the lightest, fire. But unlike Plato's elements that have a particular shape, Aristotle's elements do not differ in shape, and there are a limited number of them, not infinity, as Democritus claims.
Although, its Democritus' concept and description of matter that is more in line with today's modern science. Democritus states that matter is made of small, invisible, indivisible, uncreated, moving, and indestructible atoms and between them lies a void. Aristotle disagrees with this notion but does show admiration for Democritus and his work.
In my view, this book was more insightful than Aristotle's On the Heavens but less compelling than his Physics or Metaphysics. In any case, I look forward to reading more of Aristotle in the future....more
"I wish to provide an interpretation of nature that will rest on a certain foundation laid out by none other than myself, so that I may know to what e"I wish to provide an interpretation of nature that will rest on a certain foundation laid out by none other than myself, so that I may know to what extent I can believe in that interpretation."
Lomonosov states that the way experimentation is conducted in his time accompanied by mathematical expression is an insufficient method for understanding nature. He argues that in order to comprehend the characteristics and behavior of nature, we must employ all of our senses, including our chemical senses: taste and smell. Rather than simply observing and recording nature's phenomena, we must mix nature's elements, dissolve and separate them, while cooling and heating them, in order to fully comprehend the matter by which we are surrounded. Lastly, we should not sever philosophy from science as the freedom of philosophizing on nature is an effective tool to interpret things.
If this was a novel, which it is not, Lomonosov would be our narrator, and the central character his love for chemistry.
Corpuscular Philosophy: Selected Works (1738-1765) is written by Mikhail Lomonosov (1711-1765) a Russian polymath who's known, among other things, for discovering the law of conservation of mass in chemical reactions and the atmosphere of Venus.
Prior to reading this book, I didn't know much about Corpuscular Theory. But when I hear the words Corpuscular Theory, two names and one image comes to mind; Descartes and Newton for the former, and a stream of particles for the latter. Even though the original Corpuscular Theory was mostly abandoned but later, from the 18-20th century, to some extent, was revived and redefined.
Lomonosov begins with the assumption that all matter is made up of imperceptible and indivisible physical particles where each particle possesses a force of inertia. These particles are in constant rotational, translational, and oscillating motion. All of Lomonosov's descriptions of particles associated me with 20th-century atomic physics.
He argues that all observable bodies consist of corpuscles, where heat is contained in the internal movements of these bodies. He defines a corpuscle as a set of elements that make up a small mass that is round in shape, where between the corpuscles lies an interspace filled with an imperceptible fluid matter. The corpuscles are in constant motion, some indivisible and others colorful, continually being created and decomposed. These illustrations reminded me of what we know today as molecules, compounds, cells, and photons. Also, what we refer to today as "gravitational waves", Lomonosov refers to it as "gravitational fluid".
Lomonosov presents in these 22 selected works the fundamental principles of chemistry. He is an exquisite writer who capable of adapting his style of writing and adjusting his tone in writing that suits the occasion. For instance, in his scientific papers, he is lucid and concise. In his letter to, Leonhard Euler, he uses an unassertive tone like a humble student would when writing to their mentor in the 18th century. His speech to the Russian Imperial Academy of Sciences is poetic and one of confidence, inspiration, and authority. While his open letter to a Leipzig journalist, a book critic, is harsh and sardonic as the journalist "groundlessly" criticized one of his theories. Lomonosov is a versatile and accomplished individual and writer and I look forward to reading more of his work, perhaps, I would be most interested in reading his biography....more
Rene Descartes claims that a trustworthy correspondence does not exist between our sensations and that what is causing them. Therefore, our five exterRene Descartes claims that a trustworthy correspondence does not exist between our sensations and that what is causing them. Therefore, our five external senses can often deceive our internal common sense which will consequently affect how we perceive things and as a result lead us to draw faulty conclusions. Hence, Descartes replaces the unreliable method of deducing truth through our physical senses, with rationalism.
Descartes' universe is mechanistic and the human body a machine. He asserts that the universe plays by the rules of his Three Laws of Nature which are surprisingly similar to Newton's Three Laws of Motion published 50 years later. In Descartes' universe, everything is comprised of matter made of tiny particles called corpuscles that are similar to atoms. He believes that the universe is a perfect solid in which motion is conserved with no empty spaces, anywhere, not even between the particles as previously (and now) thought. Just as we are unable to observe the air around us that doesn't mean the space we're surrounded by is empty. Therefore, Descartes claims that emptiness is filled with some type of matter as well. Perhaps he was referring to what we call today dark matter or dark energy?
The World and Other Writings (1629-1633) is written in a simple and approachable language with comprehensible everyday life examples. Thus, not as densely written as his Discourse on Method and Meditations on First Philosophy. This book covers several subjects: cosmology, physics, anatomy, physiology, and more. I found his chapters on the phenomena of reflection and refraction of light most original through the example of the rainbow. Descartes also correctly assumes the existence of other planetary systems and that they border one another and our Solar system. Of course, some of the science is dated as the book was written 400 years ago, same as the science we rely on today will perhaps be dated 400 years in the future, but that should not stop us from reading it....more
Immanuel Kant is proof that one does not have to be an exceptional mathematician or a scientist to comprehend and unravel the origins and evolution ofImmanuel Kant is proof that one does not have to be an exceptional mathematician or a scientist to comprehend and unravel the origins and evolution of the cosmos.
Universal Natural History and Theory of the Heavens (1755) explores our silent and orderly cosmic structure and the mechanical principles of its celestial bodies that are constrained to self-governing laws of nature.
Kant claims that the universe developed from raw material and out of primordial chaos. A universe with a common mid-point around which the suns and their planets revolve. He believes that we must live in a limitless cosmos without borders with infinite planetary systems, as we cannot have a Devine eternity without spatial infinity. We occupy an expanding universe that will continuously develop and create new planetary systems and galaxies; a universe in which creation is never completed but repeated.
Although the planetary systems of our universe will eventually decay and collapse, nevertheless, the creation of new planetary systems will make up for their loss. Just as nature, which began in chaos, was capable of bringing itself into beautiful structural order, it can, over and over again, after its destruction, rise from its ashes into a collective harmony. Much of Kant's vision of the universe is in line with the modern view of the cosmos.
Kant correctly presumes that other planets, within our Solar system, exist beyond Saturn (Uranus was discovered in 1781 and Neptune in 1846). Kant also made a pivotal contribution to our understanding of nebulas.
He even entertains the idea that most planets will be or are inhabited, and that the quality of the inhabitant's material composition and level of spirituality increases proportionally with the distance from their sun.
There is a nice flow to this writing and a comprehensible thought process. He is capable of conveying a single thought in numerous expressions. If you want to learn the mechanics of the heavenly bodies, from this period in time, you should read Newton and Kepler, but if you desire to learn about the cosmos, as a whole, without being bogged down with mathematical formulas, Kant is the way to go....more
Immanuel Kant examines the characteristics and behavior of matter and how information that we acquire about matter is predominantly derived from our eImmanuel Kant examines the characteristics and behavior of matter and how information that we acquire about matter is predominantly derived from our experiences or observations by way of our senses. However, Kant claims, that the foundation that determines and makes it possible to arrive at empirical knowledge of matter lies in metaphysics. Therefore, some a priori concepts of space, time, and mathematics already exist in our minds that we are born with and subsequently these concepts predetermine how we comprehend things. So the way we perceive matter and the material world is through these built-in ideas, and through these hardwired spectacles, we experience things and arrive at what we know as knowledge. Hence, the knowledge we acquire in the natural sciences is grounded in metaphysics.
Furthermore, Kant perceives matter as something infinitely divisible, although through experience can never be endlessly divided. A matter capable of being compressed to infinity, but not expanded to infinity as the matter would eventually lose its density and leave an empty universe. But the cosmos will not end-up empty, Kant argues, owing to the balance between the repulsive and attractive forces that maintain a clockwork universe.
The Metaphysical Foundations of Natural Science is written in the late 18th century, where by that time much of the mechanical physics has been laid out by scientists such as Newton, his contemporaries and predecessors, and mathematics had become so complex that left relatively little room for philosophers to contribute and difficult to catch-up and this new reality was noticeable in this book. Not that you can compare the two, but I found Kant's Universal Natural History and Theory of the Heavens that he wrote at 31 years of age, a more fascinating natural science book than the Metaphysical Foundations of Natural Science that he wrote 30 years later....more
On the Heavens (350 BCE) is Aristotle's take on "cosmology". Aristotle’s universe is spherical, one, and finite in scale. It is vast in volume and masOn the Heavens (350 BCE) is Aristotle's take on "cosmology". Aristotle’s universe is spherical, one, and finite in scale. It is vast in volume and mass but does not stretch to infinity, and no time or space, not even emptiness, exists beyond it. So, there are no multiple universes (the multiverse) in Aristotle's world. His interpretation of the cosmos is that it was not created, so it is unborn, and it is imperishable, therefore, eternal. Where all the bodies and elements that move in perfect circular motion are reserved only for the heavens and the straight lines and their variants for our sublunary world. A world in which the heavy elements and bodies naturally move downwards, toward the center, and the light ones, move upwards, away from the center.
Everything in Aristotle's universe serves a purpose and nothing in it is excessive or meaningless. He claims that the Earth is small, round, motionless, and composed of and enveloped by the four elements; earth, air, fire, and water and that the Earth sits in the center of the universe where all the heavenly bodies, made up of the pure fifth element, aether, revolve around it.
I would say that the absolute majority of Aristotle's description of the universe is not in line with the discoveries made in cosmology and astronomy in the last half of the millennium. But who can blame him? We don't feel the Earth's rotation, and when we look at the sky, in all directions, it does seem as if we are in the center of something. Furthermore, all the planets and the Sun appear like they are revolving around us. Hence, Aristotle's viewpoint is a rational and logical one that he deduced from observation through his senses. But it seems that we can't depend on our delicate senses and rationality to unravel the cosmos?
Aristotle is also overly critical of his predecessors Pythagoras, Anaxagoras, Democritus, Empedocles, and Plato and their concept of the universe, but it was these individuals' descriptions of the cosmos, utilizing their mathematics, imagination, mysticism, and reasoning that modern cosmology can find their roots, not in Aristotle's cosmos.
The Epitome of Copernican Astronomy (1621) has a slight textbook feel and format in which, Kepler, simulates a discussion with the reader, where the rThe Epitome of Copernican Astronomy (1621) has a slight textbook feel and format in which, Kepler, simulates a discussion with the reader, where the reader poses the questions and Kepler presents his answers and explanations of celestial mechanics.
He confesses that only a few copies of his Astronomia Nova (1609) were sold as the content was wearisome and the book came with a hefty price tag. So he ended up taking the advice of friends and wrote this book that can be considered a summary of his previous works and a supplement to Aristotle's On the Heavens. Therefore, in order to reach a wider reading audience he simplifies the language used and excluded all the heavy geometrical calculations.
Kepler developed his astronomy on Copernicus' hypotheses, Tycho Brahe's observations, and William Gilbert's philosophy of magnetism, even though he barely mentions Copernicus’ work in this summary. He also inspired and provided a foundation for, Newton, to devise his law of universal gravitation. The term gravity is not used, yet he refers to it as an inborn force and an immaterial form, but the term inertia was first introduced in this book.
He frequently brings up and compares his theories with those of the ancient Greek mathematicians and compares his astronomical findings with the ones of his contemporaries, especially with the observations that were ”made with the help of the Belgian telescope”.
During the time he wrote this book, Kepler, was frequently forced to leave his residence due to the consequences of what came to be known as The Thirty Years' War, but he did not now allow this, and other life struggles, to prevent him from continuing his research and writing. So it's Kepler's perseverance that is equally inspiring as his discoveries. This is my third book by Kepler and I think it's time for me to move on to other thinkers of the scientific revolution....more
The universe is an embodiment of symmetrical patterns and rhythmical movements, where the celestial bodies stroke against the sky to conduct a cosmic The universe is an embodiment of symmetrical patterns and rhythmical movements, where the celestial bodies stroke against the sky to conduct a cosmic harmony of musical sounds.
Kepler proposes that the five regular solid figures are in a proportional distance relationship with the six, then known, planets and behave as a structure for our solar system.
Kepler also explores the audio space of our planetary system in which the Sun is the composer and the source of musical harmony amongst the planets. He finds that the ratio between the two extremes motions of an elliptical orbit (perihelion and aphelion) correlate to a different harmonic interval and that a pair of any two planets will always strive for a perfect consonance. Where the "movements of the heavens are nothing except a certain everlasting polyphony" orchestrated by the Creator.
While reading Harmonices Mundi you get the sense that, Kepler, vision of the universe is an idealistic one, and his approach to philosophy is more Platonic or Pythagorean, rather than Aristotelian, even though his laws of planetary motion were derived from observations by the senses, therefore, are based on empirical evidence i.e. which is more Aristotelian. At times it felt like I was reading about an esoteric science that is substantiated by mathematics expressions. Although, the numerous propositions discussed have not been confirmed or are incorrect, except for one, that is mentioned at the end of the book: the time it takes any one of our planet’s to revolve around the Sun, squared, is proportional to the planet’s average distance from the Sun, cubed. This came to be known as Kepler’s third law of planetary motion. The book is too dense in content and not as clear as I would like it to be, therefore, somewhat difficult to follow but that should be expected when indulging into the mystical realm of the cosmos....more
This is an impressive succinct summary of human evolution: from the first hominid species to the Homo sapiens.
Even though the development of the humaThis is an impressive succinct summary of human evolution: from the first hominid species to the Homo sapiens.
Even though the development of the human family is a complex non-linear process with numerous unanswered questions and missing elements, Tattersall, finds a way to present the story of evolution that a layman can easily follow and comprehend the terminology of the various historical periods and the sciences employed in mapping the hominids lineage.
Tattersall is a leading scientist in the field of paleoanthropology, through which perspective he mostly presents his arguments, but he is aware that "Science is thus inherently a system of provisional, rather than absolute, knowledge." and therefore is not imposing his opinion on the reader. Nevertheless, he makes a point that "Unlike religious knowledge, which is based on faith, scientific knowledge is grounded in doubt."
In The World from Beginnings to 4,000 BCE we learn that human species are not as fine-tuned to their environments as we might think they are, but they are an adaptable kind. The ancient Homo is not the "caveman" depicted in motion pictures, but a species that spent most of their time out in the open. We discover that the Neanderthals burials of their dead might suggest empathy for the deceased, and the early toolmakers such as the Homo habilis 1.9 million years ago might give us an insight into when our precursors became planners. Also, it's perhaps not the larger brains that allowed hominids to migrate outside of Africa, but our bipedal predecessors' capability and endurance to walk, persistently, hour after hour, day after day.
Even though this book was published recently, in 2008, much has changed in this filed with the introduction of the whole-genome sequencing of ancient DNA and if you are curious to find out more, please check out David Reich's Who We Are and How We Got Here (2018).
All in all, Tattersall's approach is sensible and his arguments are well-presented in an even-handed manner. Big thanks to Sense of History and Marc for introducing me to this author and book.
I have always found the night sky intriguing and calming, and as a result, I have even named my first daughter "night" in Arabic. But you can for onlyI have always found the night sky intriguing and calming, and as a result, I have even named my first daughter "night" in Arabic. But you can for only so long gaze up into the endless space and glittering stars before you begin to question, "What is it all?" and "How does it work?".
After more than 3,000 years of recorded astronomical observations, Pierre-Simon Laplace (1749-1827) in The System of the World (1824) presents the final touches on his predecessor's works and on celestial mechanics (a term Laplace coined) as a whole. This is all prior to the introduction of the theory of relativity, quantum mechanics, and the modern view of cosmology that was set in motion at the turn of the 20th century.
Laplace's outstanding contributions to mathematics and astronomy earned him the status of a Nobleman and was often referred to as the French Newton. Besides just presenting his scientific findings, Laplace expresses his love for astronomy, his irritation with astrology, and Earth's and human's insignificance and position in the vastness of space. He introduces the readers to his nebular hypothesis and in the final part of the book, Laplace shares a well-balanced summary of the history of astronomy and its most prominent contributors. This was well-done.
With Laplace's final chapter, I will also temporarily pause my exploration of the original works of geometry, astronomy, and what can be considered now the classical view of physics. I wish to move on and read other books on this topic but from the 20th and 21st centuries. For those of you interested in exploring the development of heavenly mechanics these are the original works I would recommend:
This is a mastodon of paperbacks. It comes in at 1.5 kg and 30 cm tall. Only towards the end of my read did I get accustomed to holding it properly anThis is a mastodon of paperbacks. It comes in at 1.5 kg and 30 cm tall. Only towards the end of my read did I get accustomed to holding it properly and sitting suitably (while seated, a sturdy tabouret to push off of with your feet comes in handy and your lap, to help take some pressure off your hands).
Astronomia Nova was written in Latin in 1609 and wholly translated and published into English in 1992 or 383 years later. It took long enough, but Donahue's translation is immaculate and impeccable.
The author, Johannes Kepler (1571-1630), was a German astronomer, physicist, mathematician, and a key figure of the scientific revolution. While diligently working on creating a new and more accurate blueprint of our planetary system, he had to deal with his mother, Katharina, being accused of and imprisoned for witchcraft, which at the end, cost her life.
In this book, Kepler, presents his findings on the motion of Mars and takes the reader, step-by-step, in reconfirming heliocentrism and compares his results with those of Brahe, Copernicus, and Ptolemy. It was Kepler that first discovered that the planets move in an oval or elliptical orbit (Kepler's 1st Law) with the sun at the focus (Kepler first coined the word 'focus' in 1604). Also, the sun-planet line sweeps out equal area in equal time (Kepler's 2nd Law). Furthermore, planets are not objects on rotating spheres but free flowing bodies.
Kepler even stated the sun rotates around its axis: "the sun, although it stays in one place, rotates as if on a lathe". He wrote this several years prior to Galileo's telescopic observation. While reading this book you get the sense of Kepler's strong insight of the essence of nature's behavior, perhaps, a trait from his "witch" mother who was a healer and herbalist? As if he was also driven by symmetry, he was looking for reciprocity, proportionality, and uniformity in everything.
You can't mention, Kepler, without introducing his mentor Tycho Brahe, who Kepler says that Brahe asked him while on his death bed "that I demonstrate everything in his hypothesis". But due to Kepler's discoveries (and possibly their sour relationship) the vow was not kept.
Kepler's work was also a foundation and inspiration behind Newton's laws of universal gravitation. Kepler describes gravitation as a "kind of pressure upon, and counter-pressure from, that air" and that there is a "power residing in the sun, which moves all the planets" and the "immaterial species residing in the sun itself, possessing inestimable strength, seeing that it is the primary activity of every motion in the universe."
Kepler, fuses the geometrical and mathematical equations and hypotheses with physical causes which resulted in a new type of astronomy the Astronomia Nova.
The missing half a star is due to the lack of clarity in certain chapters. Even, Donahue, in his introduction, says that Kepler's Latin "valued style more than clarity". Also, I rounded it down to four stars, since at times, reading the numerous calculations, does become tedious, which, Kepler, admits it himself: "If this wearisome method has filled you with loathing, it should more properly fill you with compassion for me, as I have gone through it at least seventy times, at the expense of a great deal of time".
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