Two New Sciences/A History of Free Fall

by Galileo Galilei, Stillman Drake (Translator)

This is the acclaimed translation by Stillman Drake of "Discourses and Mathematical Demonstrations Concerning Two New Sciences Pertaining to Mechanics and Local Motions." It is the work written by Galileo in the last years of his life, while under house arrest by the Inquisition for suspected heresy. The two new sciences that comprise the subject of the book are the science of motion on earth and the study of the strength of materials. In presenting his findings, Galileo formulates a methodology for rigorous experimental study of natural phenomena that is the foundation for modern experimental science.

History of Free Fall, by Stillman Drake

Appended to Drake's translation and commentaries and bound in with them in the same volume is his monograph History of Free Fall: Aristotle to Galileo on the history of the discovery of the law of falling bodies, from its formulation by Aristotle to its clear statement by Galileo. Drake's painstaking research includes a close examination of Galileo's working papers which record his famous experiments with inclined planes and carefully controlled parabolic projectile paths.

Genres: Science, Physics, Philosophy, Nonfiction, Classics, History, Reference

466 pages, Paperback

First published January 1, 1638

About the author

Galileo Galilei was a Tuscan (Italian) physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations, and support for Copernicanism. Galileo has been called the "father of modern observational astronomy", the "father of modern physics", the "father of science", and "the Father of Modern Science." The motion of uniformly accelerated objects, taught in nearly all high school and introductory college physics courses, was studied by Galileo as the subject of kinematics. His contributions to observational astronomy include the telescopic confirmation of the phases of Venus, the discovery of the four largest satellites of Jupiter, named the Galilean moons in his honour, and the observation and analysis of sunspots. Galileo also worked in applied science and technology, improving compass design.

Galileo's championing of Copernicanism was controversial within his lifetime. The geocentric view had been dominant since the time of Aristotle, and the controversy engendered by Galileo's presentation of heliocentrism as proven fact resulted in the Catholic Church's prohibiting its advocacy as empirically proven fact, because it was not empirically proven at the time and was contrary to the literal meaning of Scripture. Galileo was eventually forced to recant his heliocentrism and spent the last years of his life under house arrest on orders of the Roman Inquisition.

Reviews

[Roy Lotz · Rating 4 out of 5]

But in what seas are we inadvertently engulfing ourselves, bit by bit? Among voids, infinities, indivisibles, and instantaneous movements, shall we ever be able to reach harbor even after a thousand discussions?

When most people think about the Copernican revolution, the name that comes most readily to mind—more even than that of Copernicus himself—is that of Galileo Galilei. It was he, after all, who fought most valiantly for the acceptance of the theory, and it was he who suffered the most for it—narrowly escaping the tortures of the Inquisition. It was also Galileo who wrote the most famous book to come out of the revolution: Dialogue Concerning the Two Chief World Systems, whose publication most directly resulted in Galileo’s punishment.

Some years ago I read and admired that eloquent work. But lately, after slogging my way through Ptolemy, Copernicus, and Kepler, I have come to look upon Galileo’s famous dialogue with more suspicion. For it was only through the work of Kepler that the Copernican system became unquestionably more efficient than the Ptolemaic as a method of calculating celestial movements; and though Kepler was a contemporary and a correspondent of Galileo, the Italian scientist was not aware of the German’s groundbreaking innovations. Thus the version of heliocentrism that Galileo defends is Copernicus’s original system, preserving much of the cumbrous aspects of Ptolemy—epicycles, perfect circles, and separate tables for longitude and latitude, etc.

Added to this, the most decisive advantages in favor of Copernicus’s system over Ptolemy’s—explaining why the planets’ orbits seem related to the sun’s—are given little prominence, if they are even mentioned. Clearly, a rigorous defense of Copernicanism would require a demonstration that it made calculating heavenly positions easier and more accurate; but there is nothing of the kind in Galileo’s dialogue. As a result, Galileo comes across as a propagandist rather than a scientist. But of course, even if his famous dialogue was pure publicity, Galileo would have a secure place in the annals of astronomy from his observations through his improved telescope: of the lunar surface, of the moons of Jupiter, of the rings of Saturn, of sunspots, and of the phases of Venus. But I doubt this would be enough to earn him his reputation as a cornerstone of the scientific revolution.

This book provides the answer. Here is Galileo’s real scientific masterpiece—one of the most important treatises on mechanics in history. Rather inconveniently, its title is easy to confuse with Galileo’s more famous dialogue; but in content Two New Sciences is an infinitely more serious work than Two Chief World Systems. It is also a far less impassioned work, since Galileo wrote it when he was an old man under house arrest, not a younger man in battle with the Catholic authorities. This inevitably makes the book rather more boring to read; yet even here, Galileo’s lucid style is orders of magnitude more pleasant than, say, Kepler’s or Ptolemy’s.

As in Two Chief World Systems, the format is a dialogue between Simplicio, Sagredo, and Salviati (though Galileo cheats by having Salviati read from his manuscript). Unlike the earlier dialogue, however, Simplicio is not engaged in providing counter-arguments or in defending Aristotle; he mostly just asks clarifying questions. Thus the dialogue format only serves to enliven a straightforward exposition of Galileo’s views, not to simulate a debate.

The book begins by asking why structures cannot be scaled up or down without changing their properties. Why, for example, will a small boat hold together if slid down a ramp, but a larger boat fall to pieces? Why does a horse break its leg when it falls down, but a cat can fall from the same distance entirely uninjured? Why are the bones of an elephant proportionately so much squatter and fatter than the bones of a mouse? In biology this is known as the science of allometry, and personally I find it fascinating. The key is that, when increasing size, the ratio of volume to area also increases; thus an elephant’s bones must support far more weight, proportionally, than a mouse’s. As a result, inventors and engineers cannot just scale up contraptions without providing additional support—quite a counter-intuitive idea at the time.

Galileo next delves into infinities. This leads him into what is called “Galileo’s paradox,” but is actually one of the defining properties of infinite sets. This states that the parts of an infinite set can be equal to the whole set; or in other words, they can both be infinite. For example, though the number of integers with a perfect square root (4, 9, 16…) will be fewer than the total number of integers in any finite set (say, from 1-100), in the set of all integers there is an infinite number of integers with a perfect square roots; thus the part is equal to the whole. Galileo also takes a crack at Aristotle’s wheel paradox. This is rather dull to explain; but suffice to say it involves the simultaneous rotation of rigid, concentric circles. Galileo attempts to solve it by postulating an infinite number if infinitesimal voids in the smaller circle, and in fact uses this as evidence for his theory of infinitesimals.

As a solution to the paradox, this metaphysical assertion fails to do justice to its mathematical nature. However, the concept of infinitely small instants does help to escape from of the Zeno-like paradoxes of motion, to which Greek mathematics was prone. For example, if you imagine an decelerating object spending any finite amount of time at any definite speed, you will see that it never comes to a full stop: the first second it will travel one meter, the next second only half a meter, the next second a quarter of a meter, and so on ad infinitum. The notion of deceleration taking places continuously over an infinite number of infinitely small instants helped to escape this dilemma (though it is still unexplained how a thing can be said to “move” during an instant).

Galileo had need of such concepts, since he was writing long before Newton’s calculus and too early to be influenced by Descartes’s analytical geometry. Thus the mathematical apparatus of this book is Greek in form. Galileo’s calculations consist exclusively of ratios between lines rather than equations; and he establishes these ratios using Euclid’s familiar proofs. Consequently, his mechanics is relational or relativistic—able to give proportions but not exact quantities.

This did not stop Galileo from anticipating much of Newton’s system. He establishes the pendulum as an exemplar of continually accelerated motion, and shows that pendulums of the same length of rope swing at the same rate, regardless of the height from which they fall. He asserts that an object, once started in motion, would continue in motion indefinitely were it not for friction and air resistance. He recounts experiments of dropping objects of different masses from the same distance, and seeing them land at the same moment, thus disproving the Aristotelian assertion that objects fall with a speed proportional to their mass. (Unfortunately, there is scant evidence for the story that Galileo performed this experiment from the Leaning Tower of Pisa.) Galileo also makes the daring asserting that, in a vacuum, all objects would fall at the same rate.

There are still more riches to be excavated. Galileo asserts that pitches are caused by vibrating air, that faster vibrations causes higher pitch, and that consonant harmonies are caused by vibrations in regular ratios. He exhaustively calculates how the time and speed of a descending object would differ based on its angle of descent—straight down or on an inclined plane. He also shows that objects shot into the air, as in a catapult, descend back to earth in a parabolic arc; and he shows that objects travel the furthest when shot at 45 degrees. In an appendix, Galileo uses an iterative approach to find the center of gravity of curved solids; and in an added dialogue he discusses the force of percussion.

As you can see, this book is too rich and, in parts, too technical for me to appraise it in detail. I will say, however, that of all the scientific classics I have read this year, the modern spirit of science shines through most clearly in these pages. For like any contemporary scientist, Galileo assumes that the behavior of nature is law-like, and is fundamentally mathematical; and with Galileo we also see a thinker completely willing to submit his speculations to experiment, but completely unwilling to submit them to authority. Far more than in the metaphysical Kepler—who speculated with wild abandon, though he was a scientist of comparable importance—in Galileo we find a true skeptic: who believed only what he could observe, calculate, and prove. The reader instantly feels, in Galileo, the force of an exceptionally clear mind and of an uncompromising dedication to the search for truth.

[Bryan · Rating 5 out of 5]

Very briefly: this book is the authoritative English translation of Galileo's masterpiece, after a long history of notoriously poor and incomplete translations. My copy is well-worn from study.

Galileo's Two New Sciences (originally: Discorsi e dimostrazioni matematiche, intorno a due nuove scienze) was first published in Italian in 1638. However, the publication was rushed at the end -- Galileo had gone blind, and would die a few years later in 1642. So many pieces that Galileo intended for publication, and which he dictated to his students at the end, didn't make it into print. Most English translations have been based on a (1914) edition which was missing these pieces.

Fortunately, the translation that Drake has produced in this book is based on a complete edition of Galileo's original Italian work, put together by Antonio Favaro (Le Opere di Galileo Galilei, 1898, Edizione Nazionale, Florence). The page-numbers of the Italian edition are included in this edition by Drake, for easy cross-referencing to Galileo's original language. Many of Galileo's manuscript notes have also been included as footnotes.

In addition, Drake has revised many of the faulty English translations here. As a historian and philosopher of science, Drake has shown in many places that these faulty translations have at times led to incorrect and incoherent interpretations of Galileo's work. These mistakes have been corrected in the present edition.

All in all, this book is a great purchase. First, it's a masterpiece, and a must-read for all philosophers and scientists. Second, it's the most authoritative English translation, designed for both students and scholars. It's hard not to thoroughly enjoy this book.

[Xander · Rating 2 out of 5]

This is Galilei's second Dialogue and this book is not on world systems but on his scientific work, more particularly on his law of free fall and on projectile motion.

(I read parts of this book as additional source material in a physics course, so don't take this review too literally.)

Galilei wrote Two New Sciences in his dying days, while suffering from illness and his lifelong house arrest by the Church. Since he wasn't allowed to publish on astronomy anymore - this was considered to inflammatory to Christian tastes - he decided to publish on physics.

Almost everybody knows the infamous inclined planes which Galilei used to study motion of falling objects. His (consequently discovered) law of free fall is one of the ingredients that Isaac Newton would use to synthesize a whole new mechanical world system in his Principia.

Anyway, falling objects and projectile motions are the objects of this second Dialogue. And I have to admit that I found this book less readable than Siderius Nuncius or Dialogues concerning Two Chief World Systems. There is a lot more mathematics in this book, and a lot less dialogue; hence, it feels somewhat forced at times.

But then again, I didn't read the whole book, just big, loose parts as additional information. I cannot really recommend this book; it's less important as an historical document (compared to his two earlier mentioned works) and it's less accessible (again, compared to his other two works).

As a closing remark, I have to add that this edition is rather cheap. It looks like it's printed to get easy money; the translation is correct, but there are no introductory notes, no references, no end notes, etc. Also, I find it strange that this book - which is definitely a stand-alone work - is not added on Goodreads (I added this edition, since there are no alternatives available). Strange...

[Ethan · Rating 4 out of 5]

Definitely a new genre for me, but I loved the challenge of trying to understand some of the math and physics, some of which definitely went over my head. The dialogue format was also especially enjoyable. Didn’t read every part but did finish large portions of the stuff actually written by Galileo. Will probably be revisiting this again at some point.

[Arkar Kyaw · Rating 4 out of 5]

The satanic bible which eventually unleashed the horde of demons known as new mathematicians and "scientists" such as Issac Newton.

[Roberto Rigolin F Lopes · Rating 5 out of 5]

We are in 1632, Galileo is showing us how to do science using a novel method to reason over natural phenomena. He reuses Plato’s dialogs to develop his ideas, perhaps trying to maximize the reach of his book by adopting a common format at that time. Or, I love to guess, he is criticizing ancient philosophy by reasoning over relations, numbers and experiments, therefore, challenging Plato on his own game. As a result, he is igniting the scientific revolution by laying down the scientific method and firing up classical physics. All within a quite entertaining book, even if compared to Kepler (too religious) and Newton (too tedious; his own words). Galileo makes references to Archimedes (-212), Euclid (-300) and Aristotle (-322) remiding us that the middle ages were not very productive on scientific knowledge. Some fifty years later, Newton had many more experiments to refer to and developed these ideas further in his “Philosophiae Naturalis Principia Mathematica” (1687) which put Physics on solid foundations.

[Brian Maicke · Rating 4 out of 5]

This is a great book to start with for those interested in the scientific classics. Written as a dialogue and in the vernacular rather than Latin, Dialogues is a much more accessible read than the Copernicus text I started with. There is still a bit of geometry that may be off putting to some readers, but even those without a science background should be able to follow the discussion if they have an interest.

[Tyler · Rating 4 out of 5]

I quite enjoyed this work. It's a work primarily, first and foremost, on physics. However, there are other items discussed, especially in the first day interlocutors, which borders on just pure mathematics/geometry. With this section I have a large problem, with these demonstrations, Galileo attempts to show that a point, taken infinitely, composes a line. However, as per Euclid's first definition of Elements, a point is that which has no breadth or width or depth, in other words no dimension. So how can something with no point, taken infinitely, compose a line? Certainly this is up for debate, but to formalize the definition of it is something ridiculous. In particular, to show that a point has a magnitude, he uses a mathematical proof of a bowl and a right angled cone to show that all the way up to the point, the area of the rim of the bowl equals the cone that is being asymptotically shrunk to the point. However, one just needs to think for one second and realize that since a point is that which has no dimension, there is no way that at the moment that right angled cone meets a point, is it equal to the rim of the bowl. So there is a clear objection to that entire line of reasoning in the first day interlocutors. As for the second day interlocutors, here is where the work turns into something like Archimedes' propositional proofs or Apollonius, there is one problem with Galileo's proofs however: he never, unlike many of the ancients and some of his contemporaries, references the earlier mathematicians when making proofs. You have to go about the process of trying to connect the dots on your own. This had led me, at various times, to be rifling through Euclid, trying to demonstrate that certain relations work, or actually hold, and at one time, had me actually proving something different than Galileo because it was a more sound way to prove it. At the very beginning of the first proposition of the Second Day Interlocutors, in fact, is an error. Somehow the levers and the fulcrum, with the diagram of the prism/cylinder on the wall, were represented poorly. And as a result, the relation only holds with the inverse relation of the items referred to, not the forward relation. So something was either wrong with the facienda preceding that, or something was not formulated correctly, or interpreted incorrectly. We know that many of Galileo's findings here were correct, because related through physics, however the way that he approached things, resulted sometimes in errors that are strewn here and there throughout this work. Still, in the attempt to find more errors, and having analyzed heavily some of these more recondite propositions in the book, I found Galileo to really be a man of encompassing intellect: someone far surpassing even Descartes in terms of mathematics. I had to spend an hour (at the most, though) on some of these seemingly simple propositions, because the relations that he made are more complex than at first appears. I feel like being taught by Galileo, who was a teacher, would have been a blessing, and would have cleared up some of the confusion, but I cannot lie that I have found multiple, aforementioned, errors in the work that do detract from the value of this book taken as a whole. This was an enjoyable read, however, and something I will always remember reading. Not only that, he fashioned it, mirroring a Platonic dialogue, which is absolutely incredible. I just wish more people did that, the last time I read something like that was Charles Dodgson's Euclid and his Modern Rivals. This was a good book, incredible work of art at that, and influential for years to come. The attempt to mathematize physics really was the beginning of one of the greatest sciences known to man, and physics owes its gratitude to this man, while being somewhat faulty, of opening the discussion for years to come.

[Petros · Rating 4 out of 5]

This book is a fascinating read.

This was the first time in human history that accelerated motion was described mathematically. Galileo used astoundingly penetrating reason, combined with a small amount of ingenious experiments (along with numerous thought experiments), to reach conclusions regarding accelerated free fall, the role of air resistance and the concept of terminal velocity, the combination of free fall and horizontal linear speed (and its application to projectiles), the strength of materials (and the effect of size vs weight vs shape in their strength), and even musings about musical pitches being vibrations of air (and why certain musical intervals are more pleasing to the ear) and the concept of infinity.

This book is by no means an easy read. In order to understand all the theorems and propositions, one would need a good grasp of all the books of Euclid. Regrettably, my knowledge of geometry is much more elementary than that, therefore I could only grasp the more basic theorems/oppositions, but at least it was sufficient (it think) to wrap my head around Galileo’s though process. It is really interesting, however, to see how the mathematical description and calculations of motion are done geometrically (rather than with algebra).

A momentous step in human thought, and the link between ancient philosophy and Newton’s physics. This book allows a small glimpse into that process.

[Jonathan Jerden · Rating 4 out of 5]

Very special to read the words this legend and genius wrote - explaining gravity, geometry, the Pythagorean theorem, velocity and force in a most readable fashion. Finished and published while he was under the Pope's house arrest, and where he died.

Galileo is regularly referencing work by Euclid, Plato and Aristotle and none of his contemporaries, and thereby acknowledging the 2,000-year gap in the serious study of mathematics, physics, and the scientific approach to the world's wonders. In this respect the Dark Ages lasted much longer than we give it credit.

[Christopher Byram · Rating 3 out of 5]

I first discovered this book when it was referenced on Khan Academy, in the article 'READ: Galileo Galilei', in Unit 5, in the course 'World History Project - Origins to the Present'. The article states that the author rallied and in his last years wrote a book summarizing all his ideas, published in 1637 in Holland in Italian. This book was translated into English in 1661, and Isaac Newton read it in 1666.

[Michal Paszkiewicz · Rating 4 out of 5]

A most interesting book, especially due to the section on parabolic curves. In all honesty, I find the dialogue annoying and wish Galileo had clearer structure in the book, but it was a worthwhile read

[Cam Huynh · Rating 4 out of 5]

If you are into physics or science in general, this is a must-read. Galileo covered a lot of interesting concepts of physics, and the thought experiments are both plenty and very well explained.

[Ramona Fisher · Rating 4 out of 5]

Read portions of this book for the ten year reading program on the Great Books of the Western World. I do write ups of all the readings at the end of each quarter.

[Alba · Rating 5 out of 5]

pepinardo

[M. Filozofs - Lauvassirds · Rating 2 out of 5]

not for a general audience!

[Jackson Snyder · Rating 4 out of 5]

Really cool and interesting, I’d love to read more of his stuff about projectile motion.

[Robert Smith · Rating 5 out of 5]

I found great joy and satisfaction in reading this edition of Two New Sciences. As I proceeded toward the work without definite aim, there were so many moments that emerged worthy of memory. One of my many favourite parts of the dialogues was Galileo’s account of the speed of light using flickering lanterns. But the dialogues are filled with many incredible moments. Take, for instance, some of the geometrical demonstrations, such as the theorem of how 'the volumes of right cylinders having equal curved surfaces are inversely proportional to their altitudes'. Or the theorem presented by Galileo on the area of a circle as 'a mean proportional between any two regular and similar polygons of which one circumscribes it and the other is isoperimetric with it'. [As an aside, isoperimetric inequalities and ratios are very interesting. So, too, is the isoperimetric problem].

The dialogues are fascinating in that they weave together and connect so many concepts and theories, like any great book – from geometry, ballistics, and acoustics to astronomy, the dialogues flow in a way that seems so rare today. Galileo’s presence, or voice, also emerges through the pages, with the work offering a rare opportunity to spend time with one of the great masters. Perhaps it is the clarity of the edition, but it is easy to follow Galileo from thought to thought, as though sitting beside him pondering some of the pressing physical questions of the 17th century. I like it, too, because of momentary engagements with his compatriots, even the philosopher Simplicio, a fictitious straw man, created to perform the perfect mediate that keeps the discussion between Sagredo and Galileo (Salviati) unfolding. One of Simplicio’s great passages is as follows:

'What a sea we are gradually slipping into without knowing it! With vacua and infinities and
indivisibles and instantaneous motions, shall we ever be able, even by means of a
thousand discussions, to reach dry land?'

It is a marvellous moment in the context of the first day of the dialogues, in which Galileo ponders the role of infinite numbers and issues pertaining to the Aristotelian school of mechanics, among other things. It makes me think of some of the theoretical issues currently facing us in contemporary physics, as though, in some way, we’re continuously having to search for and reach dry land, and then, once we find it, the tide comes in a little bit more and pushes us a little bit further.

As a whole, it is obviously one of the great works ever produced by a human being, and certainly a work that anyone interested in physics or in studying to become a professional physicist ought to read. Galileo is one of those masterful scientists and philosophers that we hear about as kids, along with Newton, Franklin, and others. But encouragement to actually read his and other’s work would seem rare, and that is unfortunate.

[JP · Rating 4 out of 5]

A review of all of the learning of his youth, he writes this as a dialogue between three scientific explorers playing the role of teacher, experimenter, and student. He covers a lot of content in relatively few pages. More than anything else here, we see the process of the curious mind discovering physical truth incrementally through experimentation. Consider the humorous example of he and his friend convincing themselves that light probably is instantaneous as a result of their distant lantern echo from but a mile away. Nonetheless, there is truth here about acceleration (at least a third of the work dedicated to the path and time of the parabola of motion, geometry of mean proportionals to calculate time and distance), mechanics (especially discovering different tensile and hanging strengths, also about pressure of rope and friction), and geometry (the area of a circle relative to an infinitely-sided regular polygon; infinites and finites).

[Hangci Du · Rating 3 out of 5]

总评：

原书成书于1638年。（牛顿作品之前五十年）
读这本书的缘起，是想要寻找牛顿“力”“惯性”观念的源头，但略失望，伽利略并没有明晰地指出这些概念。伽利略最大的功绩，是首次研究了运动学的规律，然而对于“力”在运动中的应用则很少，也没有明确指明。因此还需要读更多资料研究牛顿“力的加速度表述”的观念源头。
在山西科学技术出版社的《科学名著赏析 物理卷》中我明白，这里的“两种信科学”指的是材料力学和动力学。“伽利略是用力的观念研究运动的第一人，是动力学的奠基人”（拉格朗日《分析力学》）。本书写于伽利略去世前，是伽利略一生研究的集大成。体裁是三人四天的对话（与其之前的作品《托勒密哥白尼对话》是相同体裁）。这种体裁的缺点就是不够明朗啊~
伽利略科学观受到三大思想影响：亚里士多德的思辨，欧几里得的几何，阿基米德的静力学。
按照《赏析》，本书四天的内容分为：
第一日，固体对断裂抵抗的讨论；（这是工程上的静力学嘛）
第二日：内聚力的原因
第三日：运动的讨论、均匀运动、自然加速运动
第四日：强迫运动和抛体
（第三第四日所讨论是我所感兴趣的（分别是运动学和动力学r），一二日所讨论的均是来自工程学的静力的内容，而这和时空的本性不相干，也不是我所感兴趣的）

第三天、第四天 （讲的是运动的变化）

分为三大部分：匀速运动；匀加速运动（前第三天）；抛射运动（第四天）。
在伽利略时代，关于运动的数学性质的研究还是一个新科学，并没有前人研究，因此伽利略最突出的贡献是运动学上的，主要是匀加速运动的数学性质。并且本书是按照欧几里得式的公理化体系进行演绎的。然而伽利略没有确定地给出力与运动的关系，在伽利略，力基本还是处于静力学的范畴：用于分析平衡以及不平衡。
另外，惊人地发现当时数学工具的简陋，代数的发展极其滞后，无论是牛顿还是伽利略，所运用的数学工具都是几何证明：大段的欧几里得几何的应用，可见在当时，几乎欧几里得的几何就是数学的全部，也可见欧几里得对于西方科学灵魂重大的塑造。
同时，书的第四日的最后，给了我重大的启发：将“力”与“运动”挂钩，杠杆原理是一个非常好的原理。通过虚位移的思想，很容易从杠杆原理出发，但这样似乎得到的也仅是动量守恒的结果。而牛顿的运动定律，是否可以从动量守恒导出呢？我还是没有理解牛顿的加速度定律的来源。得读一些这方面的书。

[Becky · Rating 3 out of 5]

I’m working my way through The Great Books of Western Literature and I must say this is my favorite math book so far. I appreciated the story-form and ‘breaks’ that the dialogue provided.

And let’s just say it. I am Simplicio.

Lots of gems in here.

“In digressions we reach new truths.”
“There is no better tool than geometry to sharpen the wit and strengthen the mind.”
“Infinity and indivisibility are incomprehensible. Now imagine combining the two.”

The man was a genius, modest, and FUNNY.

[Tassos · Rating 5 out of 5]

High recommendation to those that are curious to how science and mostly mechanics and engineering came to be what they are today.

A profound insight in Galileo's thoughts and the general way of thinking of that era, where science was still highly connected with philosophy.

[Tristan]

Interesting, but pretty hard to read as the whole thing is in (translated) dialogue of the times.

[Trey Kennedy · Rating 5 out of 5]

One of the most enjoyable books I have ever read on mathematics and science. Or ever. It’s like a Platonic dialogue, but with science.

[Sosinadesu]

i want read