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The Works of Archimedes (Dover Books on Mathematics) Paperback – April 16, 2002

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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 326 pages
  • Publisher: Dover Publications (April 16, 2002)
  • Language: English
  • ISBN-10: 0486420841
  • ISBN-13: 978-0486420844
  • Product Dimensions: 8.4 x 5.3 x 1.1 inches
  • Shipping Weight: 1.3 pounds (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #222,234 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

101 of 109 people found the following review helpful By Michael Hardy on February 9, 2007
Format: 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.
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20 of 21 people found the following review helpful By Alex M. on March 22, 2011
Format: Paperback Verified Purchase
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.
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22 of 27 people found the following review helpful By mathwonk on May 24, 2008
Format: 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.
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2 of 3 people found the following review helpful By Mihai Olteanu on April 18, 2012
Format: Paperback Verified Purchase
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.
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