Customer Reviews


13 Reviews
5 star:
 (6)
4 star:
 (1)
3 star:
 (1)
2 star:
 (1)
1 star:
 (4)
 
 
 
 
 
Average Customer Review
Share your thoughts with other customers
Create your own review
 
 

The most helpful favorable review
The most helpful critical review


98 of 105 people found the following review helpful
5.0 out of 5 stars Brilliant (but mostly not so _newly_ known)
Again I feel I must post a review to counter misleading

information in an earlier review. The author of the

previous review seems to think these works were _not_

available to scholars during the Renaisance. In fact,

the famous "Archimedes Palimpsest" that resurfaced in

the 1990s is only a small part of the works of...
Published on February 9, 2007 by Michael Hardy

versus
12 of 16 people found the following review helpful
1.0 out of 5 stars NOT the Works of Archimedes!
This review is for the 46-page CreateSpace edition, NOT the 326-page Dover publication.

The CreateSpace book is NOT the works of Archimedes, but a brief commentary on them.

Unfortunately, because the titles are the same, Amazon lumps all the reviews together.

THEY ARE NOT THE SAME BOOK.

If you are looking for a translation of...
Published on September 8, 2011 by S. D. Weitzenhoffer


‹ Previous | 1 2 | Next ›
Most Helpful First | Newest First

98 of 105 people found the following review helpful
5.0 out of 5 stars Brilliant (but mostly not so _newly_ known), February 9, 2007
By 
Michael Hardy (Minneapolis, MN, USA, for the Time Being) - See all my reviews
(REAL NAME)   
This review is from: The Works of Archimedes (Dover Books on Mathematics) (Paperback)
Again I feel I must post a review to counter misleading

information in an earlier review. The author of the

previous review seems to think these works were _not_

available to scholars during the Renaisance. In fact,

the famous "Archimedes Palimpsest" that resurfaced in

the 1990s is only a small part of the works of Archimedes

found in this book. Moreover, this book is a reprint of

the translation published in 1897 by Thomas L. Heath.

Heath _did_ have access to the Palimpsest (or maybe to

a translation into German or to a copy--of this I am

unsure) and did include a translation in this book in

1897. It is true that after the Palimpsest resurfaced

in the 1990s and began to be examined by modern methods,

some lacunae were filled in. But that's not even most

of the Palimpsest, let alone most of the contents of

this book. Moreover, the newly discovered material is

not in this book (but Heath's translation of the Palimpsest

is). The previous reviewer is _extremely_ confused about

the history.

Now to the contents of the book. The famous Palimpsest

actually is my favorite part. Prepare to be dazzled.

Many 20th-century calculus texts, saying that integral

calculus was anticipated by Archimedes in the 3rd century

BC, are so phrased that they may give their readers

the impression that Archimedes worked with something similar

to Riemann sums, or similar nonsense. The truth is far more

interesting. Archimedes used infinitesimals explicitly.

His proofs were amazingly efficient. If you think that a

brilliant proof by an ancient mathematician having only

relatively primitive methods at his disposal must be longer

and more complicated than a proof by modern methods, think

again. Modern methods are indeed more efficient, but not

because one writes _shorter_ proofs; rather it is because

(at least in the present case) one writes _fewer_ proofs.

Archimedes introduced the concept of center of gravity.

In the Palimpsest, he finds not only areas and volumes,

but centers of gravity (that of a solid hemisphere of

uniform volume is 5/8 of the way from the "north pole" to

the center of the sphere, Archimdes shows in one of his

startlingly efficient proofs--just one example).

It was not only by the use of infinitesimals that Archimedes

solved problems that would now be treated by integral calculus.

For example, one of the methods (just one of them) by which

Archimedes found the area between a parabola and one of its

secant lines involved dividing that area into an infinite

sequence of triangles, the sum of the areas of which is a

geometric series. Many other examples are in these pages.
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


17 of 18 people found the following review helpful
5.0 out of 5 stars Archimedes, etc., March 22, 2011
Verified Purchase(What's this?)
This review is from: The Works of Archimedes (Dover Books on Mathematics) (Paperback)
This is an excellent book, and a great way to begin a study of mathematics that will never be outdated. It's been argued that such antiquated works are no longer pertinent, but I completely disagree. Yes, this is a fairly hard read, but that's because that's how Archimedes' mind worked, and the complicated thoughts out of a complicated mind are going to be complicated.

If you want to pass a basic set of classes, then you don't need this; just stick to the textbooks and you'll do fine. However, if you really want to understand what's going on in that math, and why it's going on, this is a great place to start. There's no place like to source for good information.

As for this particular translation, this edition has a surprising amount of explanatory notes and introductory material relating the circumstances under which this writing was made, and the interaction between the author and the other well known thinkers of the time. The first ~150 pages were explanations by Heath, including terminology of Archimedes, which was useful at times.

All in all, the works of Archimedes are definitely worth reading for anyone interested in learning the process of mathematical discovery.
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


21 of 26 people found the following review helpful
5.0 out of 5 stars maybe more than one point of view is possible, May 24, 2008
This review is from: The Works of Archimedes (Dover Books on Mathematics) (Paperback)
I enjoyed the previous review, but do not wholly agree. It seemed to me the method of centers of gravity was the one by which Archimedes discovered, rather than proved, his results. His proofs do seem to me to involve limiting arguments which are at least reminiscent of riemann sums. Indeed even the method of centers of gravity involved slicing up solids in a way that to me suggests again riemann sums. Perhaps i have not read as carefully as the previous reviewer. I agree however that the works are startlingly wonderful and inspiring.

The key to Archimedes' geometry solutions was the principle of parallel slices, that two figures all of whose slices parallel to a given reference line or plane have equal areas, or lengths, themselves have equal volume, or area. This is of course the fundamental theorem of calculus for equating areas, and the cavalieri principle, for equating volumes. Note it does not suffice to calculate them, merely to equate two such areas. thus Archimedes had to bootstrap up from one known area or volume to another.

Thus starting from an actual decomposition of a cube into three pyramids, one sees that a right pyramid has volume 1/3 of cube. Then by parallel slices one sees the same for any pyramid or cone. then by taking complements one computes the volume of a sphere, by showing that horizontal slices of a cone and a sphere add up to the slice of a cylinder. Knowing cylinder and cone volume thus gives a sphere's volume.

Finally one of the hard problems we give students is finding the volume of a bicylinder, the intersection of two transverse cylinders. After seeing Archimedes' solution of the volume of a sphere, by the principle of parallel slices, equating the volume of a sphere, slice by slice, with that of the complement of a (double) cone in a cylinder, one easily intuits his (still lost) solution of the volume of a bicylinder, as that of the complement of a square based (double) pyramid in a block! (of course reading further one sees it was rediscovered by Zeuthen 100 years ago, but so what, it is fun to do it oneself.)
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


12 of 16 people found the following review helpful
1.0 out of 5 stars NOT the Works of Archimedes!, September 8, 2011
By 
S. D. Weitzenhoffer (Houston, TX United States) - See all my reviews
(REAL NAME)   
Verified Purchase(What's this?)
This review is for the 46-page CreateSpace edition, NOT the 326-page Dover publication.

The CreateSpace book is NOT the works of Archimedes, but a brief commentary on them.

Unfortunately, because the titles are the same, Amazon lumps all the reviews together.

THEY ARE NOT THE SAME BOOK.

If you are looking for a translation of Archimedes' works, get the Dover edition.

I admit, the mistake was partly mine, as I should have seen the page count and realised it was wrong, but it slipped my attention.

This is the collected works of Archimedes:
The Works of Archimedes

Unfortunately, this review also shows up for the correct Dover book.
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


2 of 2 people found the following review helpful
1.0 out of 5 stars Don't get Archimedes-Screwed! This is NOT what it looks like., December 25, 2012
The Works of Archimedes by T. L. Heath is NOT contained in these pages!

What you get is a 20 page magazine-sized "book", that's made to LOOK like the real thing. All that's in it are the brief chapter overviews written by Heath, ALL ACTUAL CONTENT FROM ARCHIMEDES HAS BEEN LEFT OUT. No publisher listed, no explanation on why everything was left out... flipping through it now I still can't comprehend what I'm looking at. As a fan of Greek mathematics I can definitely say that you DON'T want to get this for yourself or others. If you'd like to try the real deal, I suggest the Dover Edition The Works of Archimedes (Dover Books on Mathematics)

Sorry for the caps but I feel like I needed to warn people here.
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


1 of 1 people found the following review helpful
2.0 out of 5 stars Show more pictures, diagrams, & equations, Less text., July 30, 2014
Verified Purchase(What's this?)
This review is from: The Works of Archimedes (Dover Books on Mathematics) (Paperback)
I liked this book and Archimedes' Works in general but the toughest part is a lot of this book is in Latin. I feel as if it's hard to read but maybe that's just the way it translated or maybe it just can't really be translated. I am a Math Geek and all I really do care about are the equations anyways.
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


5.0 out of 5 stars I only read certain chapters of Archimedes (each chapter on a different topic essentially) and greatly enjoyed reading -how he t, August 25, 2014
This review is from: The Works of Archimedes (Dover Books on Mathematics) (Paperback)
The entire introduction - by Heath - is alone, worth the price of the book! I only read certain chapters of Archimedes (each chapter on a different topic essentially) and greatly enjoyed reading -how he thought -or, as Heath notes, what he actually put down. Some things, as noted, later mathematicians tried to figure out just how Archimedes came to such knowledge - often with great success - sometimes not - a great book for thinking about mathematics.
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


2 of 3 people found the following review helpful
3.0 out of 5 stars Archimedes weeps for a new editor, April 18, 2012
Verified Purchase(What's this?)
This review is from: The Works of Archimedes (Dover Books on Mathematics) (Paperback)
Dover and Heath makes for a bad edition. This is so not like the Greeks would have read it. The text is full of algebra, the steps of the demonstrations are oftentimes skipped and the arguments are not always presented in a geometrical form. There are also some errors and typos to the text. And why do they still keep that Greek text when trying to explain something ?!

Don't get me wrong, the math is there, and it's good. The other edition from the CreateSpace (2011) even puts it in the title: "The Works of Archimedes: Edited in Modern Notation With Introductory Chapters". So, there you have it, classic math in modern notation. Having read Euclid and Apollonius before Archimedes, this is a disappointment. I want to know how the Greeks wrote it, not how we interpreted it. I don't know if this is the case in the original text, but almost in every proposition there are skipped steps to the demonstration. Sometimes this is good, for if you have read Euclid, the gaps can be filled quite nicely with a little effort and with the added benefit of deepening one's understanding of the matter. But in other cases, even after reading Euclid and Apollonius I still don't have a clue of how he got from step A to step B. Heath always seems to keep some Greek in his text, which doesn't help much either. Can't believe this hasn't been edited in more than 100 years.

All in all, the content is great but the presentation is unsatisfactory in my opinion.

Later edit: This is a facsimile edition of The Works Of Archimedes (Heath, 1897). If you want to have a look over the content before you buy, you can download a free legal copy from Archive_dot_org.
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


2 of 3 people found the following review helpful
5.0 out of 5 stars Great book, December 6, 2012
By 
Michele (Oro Valley, AZ, United States) - See all my reviews
(REAL NAME)   
Verified Purchase(What's this?)
This review is from: The Works of Archimedes (Dover Books on Mathematics) (Paperback)
A masterpiece of scholarship, on par with Heath's edition of Euclid's elements. Truly a great read for anyone with a strong background in Ancient Greek also interested in the history of mathematics.
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


1 of 2 people found the following review helpful
1.0 out of 5 stars Misleading Title- NOT the works of archimedes, November 6, 2012
Verified Purchase(What's this?)
This is not the works of Archimedes. It is an introduction/summary. I bought this thinking it was an actual translation of Archimedes works, like every other book titled "The Works of Archimedes." This "pamphlet" should be retitled.
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


‹ Previous | 1 2 | Next ›
Most Helpful First | Newest First

Details

The Works of Archimedes (Dover Books on Mathematics)
The Works of Archimedes (Dover Books on Mathematics) by Archimedes (Paperback - April 16, 2002)
$24.95 $15.90
In Stock
Add to cart Add to wishlist
Search these reviews only
Send us feedback How can we make Amazon Customer Reviews better for you? Let us know here.