METRICAL SOLUTIONSDERIVED FROMMECHANICSTREATISE BV ARCHIMEDESRECENTLY DISCOVERED AND TRANSLATED FROM THE GREEK BYDR. L. HEIBERGJ.CHICAGOE OPEN COURT PUBLISHING COMPANYLONDON AGENTSKEGAN PAUL, TRENCH, TRUBNER & LTD.CO.,GEOMETRICAL SOLUTIONSDERIVED FROMMECHANICSA TREATISE OF ARCHIMEDESRECENTLY DISCOVERED AND TRANSLATED FROM THE GREEK BYDR. L. HEIBERGJ.PROFESSOR OF CLASSICAL PHILOLOGY AT THE UNIVERSITY OF COPENHAGENWITH AN INTRODUCTION BYDAVID EUGENE SMITHPRESIDENT OF TEACHER S COLUMBIACOLLEGE, UNIVERSITY, NEW YORKENGLISH VERSION TRANSLATED FROM THE GERMAN BY LYDIA G. ROBINSONAND REPRINTED FROM "THE MONIST," APRIL, 1909.CHICAGOTHE OPEN COURT PUBLISHING COMPANYLONDON AGENTSKEGAN TRUBNER & LTD.PAUL, TRENCH, CO.,1909VCOPYRIGHT BYTHE OPEN COURT PUBLISHING Co.1909INTRODUCTION.there ever was a case of inappropriateness discovery,IFthe of this in the summer ofmanuscriptfinding 1906was one. In the first it thatwas the displace appropriateshould be made in itsince was herecovery Constantinople,that theWest received its first of the other exmanuscriptstant innine of the It wasworks, number, great Syracusan.furthermore that the should be madeappropriate discoveryProfessor all workersby facilis princepsHeiberg, amongin the field of the classics of Greek mathematics,editingand an searcher of the libraries ofindefatigable Europefor to aid him in his labors. Andmanuscripts perfectingit was most thisthat work shouldfinally ...
METRICAL SOLUTIONS
DERIVED FROM
MECHANICS
TREATISE BV ARCHIMEDES
RECENTLY DISCOVERED AND TRANSLATED FROM THE GREEK BY
DR. L. HEIBERGJ.
CHICAGO
E OPEN COURT PUBLISHING COMPANY
LONDON AGENTS
KEGAN PAUL, TRENCH, TRUBNER & LTD.CO.,GEOMETRICAL SOLUTIONS
DERIVED FROM
MECHANICS
A TREATISE OF ARCHIMEDES
RECENTLY DISCOVERED AND TRANSLATED FROM THE GREEK BY
DR. L. HEIBERGJ.
PROFESSOR OF CLASSICAL PHILOLOGY AT THE UNIVERSITY OF COPENHAGEN
WITH AN INTRODUCTION BY
DAVID EUGENE SMITH
PRESIDENT OF TEACHER S COLUMBIACOLLEGE, UNIVERSITY, NEW YORK
ENGLISH VERSION TRANSLATED FROM THE GERMAN BY LYDIA G. ROBINSON
AND REPRINTED FROM "THE MONIST," APRIL, 1909.
CHICAGO
THE OPEN COURT PUBLISHING COMPANY
LONDON AGENTS
KEGAN TRUBNER & LTD.PAUL, TRENCH, CO.,
1909V
COPYRIGHT BY
THE OPEN COURT PUBLISHING Co.
1909INTRODUCTION.
there ever was a case of inappropriateness discovery,
IFthe of this in the summer ofmanuscriptfinding 1906
was one. In the first it thatwas the displace appropriate
should be made in itsince was herecovery Constantinople,
that theWest received its first of the other exmanuscripts
tant innine of the It wasworks, number, great Syracusan.
furthermore that the should be madeappropriate discovery
Professor all workersby facilis princepsHeiberg, among
in the field of the classics of Greek mathematics,editing
and an searcher of the libraries ofindefatigable Europe
for to aid him in his labors. Andmanuscripts perfecting
it was most thisthat work shouldfinally appropriate ap
at a time affiliation ofwhen the andpear pure applied
mathematics is so all overbecoming generally recognized
the inworld. We are sometimes led to feel, considering
isolated that the contributors of the havecases, great past
inworked the field of mathematics and thealone,pure
of Plutarch that Archimedes felt that kindsaying "every
1
of art connected with needs was anddaily ignoble vulgar"
have this It therefore assistsmay strengthened feeling.
us in ourselves to read another treatproperly orientating
ise from the mathematician of that setsantiquitygreatest
before us his indebtedness to the mechanicalclearly appli
cations of his subject.
inNot the least of the the manu-interesting passages
1
Marcellus, 17.
009*76f
2 GEOMETRICAL SOLUTIONS DERIVED FROM MECHANICS.
is the first the to Eratosthenes. It isline,script greeting
well on the of Diodoros hisknown, testimony countryman,
that Archimedes studied in the latter freandAlexandria,
makes mention of Konon of Samos whom he knewquently
as a and to whom he indebtedwasthere, teacher,probably
for the of the that hisbears name. It issuggestion spiral
also this time that Eratosthenes was arelated, Proclos,by
of and if the of soArchimedes,contemporary testimony
alate writer as who lived in the twelfthTzetzes, century,
be taken as the former was eleven themay valid, years
of the Sicilian. Until we havenow, however,junior great
had definite to show that the two were ever acnothing
The Alexandrian savant,quainted. great poet, geog
called the stuarithmetician,rapher, affectionately by
2
dents the in five selectedPentathlos, champion sports, by
histo succeed Kallimachos themaster,Ptolemy Euergetes
as head of the this the mostpoet, great Library, man,
renowned of his time in could haveAlexandria, hardly
been a teacher of nor the fellow student ofArchimedes, yet
one who was so much his senior. It is more thatprobable
were friends in the later when Archimedes wasthey days
received as a savant rather than as a and this islearner,
borne out the statement at the close of Iby proposition
which refers to one of his earlier that thisworks, showing
treatise was a late one. This referenceparticular being
3
to one of the two works dedicated to Dositheos of Kolonos,
and one of these lineis anto(De spiralibus) referring
4
earlier treatise sent to we are led to believe thatKonon,
this was one of the latest of thatworks Archimedes and
a friend of hisEratosthenes was mature years, although
8
nickname of hisHis Beta is well because lecture roomknown, possibly
2.was number
8We little of his of which are extant. Geminos andknow noneworks,
refer to certain observations made him in 200 B. twelvePtolemy by C, years
after the death of Archimedes. also mentions him.Pliny