This week's WEMSK is supposed to be on geometry in the Middle Ages.

Actually, it is easy, since anyone can find a Euclid, and that is

what they used for the most part. I thought I would follow a

suggestion from a lurker, who wanted to learn by the royal road.

I. If you know nothing about mathematics, a good book to page

through is Lancelot Hogben, _Mathematics for the Million_ (London:

Allen & Unwin). Unfortunately, I own only my old German edition,

_Mathematik fuer Alle_, tr. Waldemar Bodmer (Cologne: Kiepenheuer

& Witsch, 1953).

2. For learning the math behind computers: John G. Kemeny (he

invented BASIC) et al., _Introduction to Finite Mathematics_, 2d

ed. (Englewood Cliffs, NJ: Prentice-Hall, 1966). Do the parts
on

truth tables, and you will have learned a lot about wiring and the

organization of the computer. You can also impress your computer-

jock friends by telling what a nor-gate really is and drawing them

a truth table. If you can still find one, there is a great game,

named WFF-n Proof. My kids learned to read the Journal of Symbolic

Logic and do the proofs from this, which teaches you Polish

notation, more cocktail party fare. This number is a TAN.

3. There are other good books one level up from Hogben: George

Polya, _How to Solve It_, 2d ed. (Garden City, NY: Doubleday Anchor

Books, 1957. George Polya, _Mathematical Discovery_, 2 vols. (NY:

John Wiley and Sons, 1962-65). Both delightful and not hard to

read; don't let them buffalo you. Another sort of elementary
book,

but forbidding: Evert W. Beth, _The Foundations of Mathematics_,

rev. ed. Harper Torchbooks, TB 581 X (NY: Harper & Row, 1964).

Again, these are just for reading through and getting a feeling for

how mathematicians work.

4. For looking at the mathematicians themselves, there are good

reading books:

a. The Treasury of Mathematics, ed. Henrietta O. Midonick (NY:

Philosophical Library, 1965). If you see this in some used

bookstore, pick it up. Lots of historical sources.

b. A grand set of books, usually boxed and available in paperback:

_The World of Mathematics_, ed. James R. Newman, 4 vols. (NY: Simon

& Schuster, 1956). This is great just to have around the
house and

page through. More cocktail party fare: "Have you heard of the

cocktail-party problem?" "They say that the four color problem has

been solved, but you cannot solve a math problem by iteration."

"Did you know that Goethe tried to solve the Seven Bridges to

Koenigsberg?"

c. Another good source book is David Eugene Smith, _A Source Book

in Mathematics_, 2 vols. (NY: Dover, 1959; repr. of a 1929 book).

It is probably still available, but it leans too much to the

present to be of much use to us.

d. Somewhat more forbidding and less historical: _Mathematics. Its

Content, Methods, and Meaning_, ed. A. D. Aleksandrov, A. N.

Kolmogorov, M. A. Lavrent'ev; transl. by S. H.Gould and T. Bartha,

3 vols. (Cambridge, MA: M.I.T Press, 1963). As a medievalist
you

may as well forget about this one, but it comes nicely boxed and it

can help.

5. For the history of mathematics:

a. David Eugene Smith, _History of Mathematics_, 2 vols. (Boston:

Ginn & Co., 1923-25). Your best first port of call. Well
written,

though it passes through our period rather rapidly. It has also

been reprinted by Dover; make sure and read the 2nd vol. also.

b. Moritz Cantor, Vorlesungen ueber Geschichte der Mathematik, 2d

ed., 4 vols. (Leipzig: Teubner, 1894-1908). The volumes which

interest us most are the first and second. Also available in

microcard (micro-opaque) (NY: Readex Microprint, 1968.

6. For the history of medieval geometry itself:

a. Wilbur Richard Knorr, Textual studies in ancient and medieval

geometry (Boston: Birkhauser, 1989). Fairly up to date, about 15

pages of bibliography. Look here first for geometry.

b. Archimedes in the Middle Ages, ed. Marshall Clagett. 4 vols.

Memoirs of the American Philosophical Society, 117, 125, 137

(Madison: University of Wisconsin Press, 1964-80). Vol. one not
in

Memoirs. Readable and thorough. We have a later section
on

mechanics and engineering, but this really belongs here.

c. Cornelius Lanczos, Space through the ages: The evolution of

geometrical ideas from Pythagoras to Hilbert and Einstein. (NY:

Academic Press, 1970). Just for paging through.

7. If you want to read some of the texts, first read Euclid, then

you can branch out:

a. Medieval Mensuration: Quadrans vetus and Geometrie due sunt

partes principales, ed. Nan L. Hahn. TAPS 72.8 (Philadelphia:

American Philosophical Society, 1982). Robertus anglicus and

Johannes anglicus, both of the 13th.

b. Lynn Thorndike, The Sphere of Sacrobosco and its commentators.

Corpus of Mediaeval Scientific Texts 2 (Chicago: UChicagoP, 1949).

An easy read and worthwhile.

c. Nicole Oresme and the Medieval Geometry of Qualities and

Motions; a treatise on the uniformity and difformity of intensities

known as Tractatus de configurationibus qualitatum et motuum, ed.

with an introd., English transl., and commentary by Marshall

Clagett (Madison: University of Wisconsin Press, 1968).
You can't

beat Clagett. Latin with facing English.