From ptrourke@methymna.com Sun Mar 3 19:14:51 2002 Received: from mailscan5.cac.washington.edu (mailscan5.cac.washington.edu [140.142.32.14]) by lists.u.washington.edu (8.12.1+UW01.12/8.12.1+UW02.01) with SMTP id g243EnnJ042634 for ; Sun, 3 Mar 2002 19:14:49 -0800 Received: FROM mxu1.u.washington.edu BY mailscan5.cac.washington.edu ; Sun Mar 03 19:14:48 2002 -0800 Received: from relay03.valueweb.net (relay03.valueweb.net [216.219.253.237]) by mxu1.u.washington.edu (8.12.1+UW01.12/8.12.1+UW02.01) with ESMTP id g243Elc6018148 for ; Sun, 3 Mar 2002 19:14:48 -0800 Received: from thor.valueweb.net ([216.219.254.23]:29451 "EHLO thor.valueweb.net") by relay03.valueweb.net with ESMTP id ; Sun, 3 Mar 2002 22:14:18 -0500 Received: from h00500480cb85.ne.mediaone.net ([24.147.80.203]:59147 "HELO caliban") by thor.valueweb.net with SMTP id ; Sun, 3 Mar 2002 22:14:06 -0500 Message-ID: <003001c1c32a$a3eff7a0$cb509318@caliban> From: "Patrick T. Rourke" To: Cc: Subject: [Unicode and HTML] Greek Numeral Systems Date: Sun, 3 Mar 2002 22:13:59 -0500 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_002D_01C1C300.B7BDA540" X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2600.0000 X-MIMEOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 This is a multi-part message in MIME format. ------=_NextPart_000_002D_01C1C300.B7BDA540 Content-Type: text/plain; charset="utf-8" Content-Transfer-Encoding: quoted-printable For FAQ purposes. [ Sorry that this is in Unicode and HTML, but that's = the only reasonable way to represent them. This will look best in = Outlook Express 6 in Windows 2000 or XP; it might be readable on Mozilla = mail agents (except on Macintosh) and in Macintosh OS X's Mail = application with e.g. James Kass's Code2000 or Ralph Hancock's Vusillus = fonts. ] Basically there are two systems: the Milesian and the acrophonic. = George Pesely has already provided a good description of the Milesian = system - this is the one that you will see in any literary, historical, = or mathematical texts. The acrophonic system, on the other hand, is found in a lot of = inscriptions. It follows about the same pattern as Roman numerals, and = as Chad Fauber has mentioned, is well discussed by Tod and described in = its bare outlines in Smyth. Arabic Roman Milesian Attic Acrophonic 1 I =CE=B1=CD=B4 alpha = | (a solid vertical stroke) 2 II =CE=B2=CD=B4 beta = || 3 III =CE=B3=CD=B4 gamma = ||| 4 IIII =CE=B4=CD=B4 delta = |||| 5 V =CE=B5=CD=B4 epsilon = =CE=A0 (Pi) (epichoric form, looks like a gamma with a descender) 6 VI =CF=9A=CD=B4 stigma = =CE=A0| (a pi and one vertical stroke) 7 VII =CE=B6=CD=B4 zeta = =CE=A0|| (pi and two vertical strokes) 8 VIII =CE=B7=CD=B4 eta = =CE=A0|||=20 9 VIIII =CE=B8=CD=B4 theta = =CE=A0|||| 10 X =CE=B9=CD=B4 iota = =CE=94 (Delta) 11 XI =CE=B9=CE=B1=CD=B4 iota and alpha = =CE=94| (Delta and one vertical stroke) 20 XX =CE=BA=CD=B4 kappa = =CE=94=CE=94 (two Deltas) 30 XXX =CE=BB=CD=B4 lambda = =CE=94=CE=94=CE=94 40 XXXX =CE=BC=CD=B4 mu = =CE=94=CE=94=CE=94=CE=94 50 L =CE=BD=CD=B4 nu = [=CE=A0=CE=94] [single sign consisting of the epichoric pi with a = delta inside] =20 60 LX =CF=87=CD=B4 xi = [=CE=A0=CE=94]=CE=94 70 LXX =CE=BF=CD=B4 omicron = [=CE=A0=CE=94]=CE=94=CE=94 80 LXXX =CF=80=CD=B4 pi = [=CE=A0=CE=94]=CE=94=CE=94=CE=94 90 LXXXX =CF=9E=CD=B4 qoppa = [=CE=A0=CE=94]=CE=94=CE=94=CE=94=CE=94 100 C =CF=81=CD=B4 rho = =CE=97 (eta) 200 CC =CF=83=CD=B4 sigma = =CE=97=CE=97 300 CCC =CF=84=CD=B4 tau = =CE=97=CE=97=CE=97 400 CCCC =CF=85=CD=B4 upsilon = =CE=97=CE=97=CE=97=CE=97 500 D =CF=86=CD=B4 phi = [=CE=A0=CE=97] [single sign consisting of the epichoric pi with an eta = inside] 600 DC =CF=87=CD=B4 chi = [=CE=A0=CE=97]=CE=97 700 DCC =CF=88=CD=B4 psi = [=CE=A0=CE=97]=CE=97=CE=97 800 DCCC =CF=89=CD=B4 omega = [=CE=A0=CE=97]=CE=97=CE=97=CE=97 900 DCCCC =CF=A0=CD=B4 sampi = [=CE=A0=CE=97]=CE=97=CE=97=CE=97=CE=97 1000 M =CD=B5=CE=B1 alpha = =CE=A7 [Chi] 5000 repeats = [=CE=A0=CE=A7][single sign consisting of the epichoric pi with a chi = inside] 10,000 = =CE=9C [Mu] 50,000 = [=CE=A0=CE=9C][single sign consisting of the epichoric pi with a mu = inside] Note that the font I'm using, Palatino Linotype, does not provide the = lower case for the stigma, qoppa, sampi, or digamma. The Attic = acrophonic is not yet represented in Unicode, though it probably will be = soon; I've provided the best approximating Greek characters when = available, and provided the two characters used in a vertical ligature = separately in brackets with an explanation. The stigma in the Milesian system replaced an earlier digamma = (=CF=9C=CD=B4).=20 Of course the Roman numerals later used the system we're used to, IV for = 4, IX for 9, XL for 40, XC for 90, CD for 400, and CM for 900. =20 etc. In addition to the books mentioned by GP and CF, there's a Reading the = Past book on Mathematics and Measurements (O.A.W. Dilke) which provides = an introduction and tables for both Greek systems on pages 13-14, as = well as other systems on other pages. This it would seem to me would be = a perfect book for students. =20 Hope this helps. PTR ptrourke@methymna.com=20 ------=_NextPart_000_002D_01C1C300.B7BDA540 Content-Type: text/html; charset="utf-8" Content-Transfer-Encoding: quoted-printable =EF=BB=BF
For FAQ purposes. [ = Sorry that=20 this is in Unicode and HTML, but that's the only reasonable way to = represent=20 them.  This will look best in Outlook Express 6 in Windows 2000 or = XP; it=20 might be readable on Mozilla mail agents (except on Macintosh) and in = Macintosh=20 OS X's Mail application with e.g. James Kass's Code2000 or Ralph = Hancock's=20 Vusillus fonts.  ]

Basically there are two systems: the = Milesian and=20 the acrophonic.  George Pesely has already provided a good = description of=20 the Milesian system - this is the one that you will see in any literary, = historical, or mathematical texts.

The acrophonic system, on the = other=20 hand, is found in a lot of inscriptions.  It follows about the same = pattern=20 as Roman numerals, and as Chad Fauber has mentioned, is well discussed = by Tod=20 and described in its bare outlines in=20 Smyth.

Arabic       =20 Roman       =20 Milesian       =20         Attic=20 Acrophonic
1         &nbs= p;     =20 I            =     =20 =CE=B1=CD=B4=20 alpha           =20           |  (a solid = vertical=20 stroke)
2          &= nbsp;    =20 II            = ;   =20 =CE=B2=CD=B4=20 beta           &nb= sp;           &nbs= p; ||
3         &nbs= p;     =20 III           &nbs= p;  =20 =CE=B3=CD=B4=20 gamma           &n= bsp;      |||
4    &= nbsp;          =20 IIII           &nb= sp; =20 =CE=B4=CD=B4=20 delta           &n= bsp;     =20      ||||
5          &nb= sp;    =20 V            =    =20 =CE=B5=CD=B4=20 epsilon         =20          =CE=A0   (Pi) = (epichoric form,=20 looks like a gamma with a=20 descender)
6         &nbs= p;     =20 VI            = ;  =20 =CF=9A=CD=B4=20 stigma           &= nbsp;      =CE=A0|=20 (a pi and one vertical=20 stroke)
7          &= nbsp;    =20 VII           &nbs= p; =20 =CE=B6=CD=B4=20 zeta           &nb= sp;      =20     =CE=A0|| (pi and two vertical=20 strokes)
8          =      =20 VIII           &nb= sp;=20 =CE=B7=CD=B4=20 eta           &nbs= p;       =20     =CE=A0|||
9   =20            =20 VIIII            = =CE=B8=CD=B4=20 theta           &n= bsp;       =CE=A0||||
10          &n= bsp;   X   =20              = =CE=B9=CD=B4=20 iota           &nb= sp;           =CE=94= =20 (Delta)
11   =20          =20 XI            = ;   =20 =CE=B9=CE=B1=CD=B4 iota and = alpha  =CE=94| (Delta and one vertical=20 stroke)
20   =20           XX  =    =20         =CE=BA=CD=B4 = kappa           &n= bsp;      =CE=94=CE=94=20 (two Deltas)
30          &n= bsp;   XXX   =20         =CE=BB=CD=B4 = lambda           &= nbsp;  =CE=94=CE=94=CE=94
40   =20          =20 XXXX         =CE=BC=CD=B4=20 mu            = ;           =CE=94= =CE=94=CE=94=CE=94
50          &n= bsp;   L        &n= bsp;         =CE=BD=CD=B4=20 nu            = ;            = =20 [=CE=A0=CE=94]  [single sign consisting of the epichoric pi with a = delta=20 inside]  
60          &n= bsp;   LX        &= nbsp;      =CF=87=CD=B4=20 xi            = ;            =   =20 [=CE=A0=CE=94]=CE=94
70          &n= bsp;   LXX   =20         =CE=BF=CD=B4 = omicron           =    [=CE=A0=CE=94]=CE=94=CE=94
80   =20           LXXX    =      =CF=80=CD=B4=20 pi            = ;            =   [=CE=A0=CE=94]=CE=94=CE=94=CE=94
90   =20          =20 LXXXX      =CF=9E=CD=B4=20 qoppa           &n= bsp;      [=CE=A0=CE=94]=CE=94=CE=94=CE=94=CE= =94
100   =20         C    =    =20          =CF=81=CD=B4=20 rho           &nbs= p;           =20 =CE=97 (eta)
200   =20        =20 CC            = ;  =CF=83=CD=B4=20 sigma           &n= bsp;       =CE=97=CE=97
300   =20         CCC    =    =20     =CF=84=CD=B4=20 tau           &nbs= p;           =20 =CE=97=CE=97=CE=97
400   =20        =20 CCCC         =CF=85=CD=B4=20 upsilon           =     =CE=97=CE=97=CE=97=CE=97
500   =20         D    =    =20          =CF=86=CD=B4=20 phi           &nbs= p;           [=CE=A0= =CE=97]=20 [single sign consisting of the epichoric pi with an eta = inside]
600   =20         DC    =    =20       =CF=87=CD=B4=20 chi           &nbs= p;            = ;=20 [=CE=A0=CE=97]=CE=97
700   =20        =20 DCC           = =CF=88=CD=B4=20 psi           &nbs= p;           =20 [=CE=A0=CE=97]=CE=97=CE=97
800   =20        =20 DCCC        =CF=89=CD=B4=20 omega           &n= bsp;    =20 [=CE=A0=CE=97]=CE=97=CE=97=CE=97
900   =20         DCCCC     = =CF=A0=CD=B4=20 sampi           &n= bsp;    [=CE=A0=CE=97]=CE=97=CE=97=CE=97=CE=97=
1000         =20 M            =    =CD=B5=CE=B1 alpha        =    =20         =CE=A7 [Chi]
5000          =             &= nbsp;       repeats   &= nbsp;           &n= bsp;   =20 [=CE=A0=CE=A7][single sign consisting of the epichoric pi with = a chi=20 inside]
10,000     =20             =    =20             =    =20             =    =20         =CE=9C [Mu]
50,000         &nbs= p;            = ;            =             &= nbsp;           &n= bsp;   [=CE=A0=CE=9C][single=20 sign consisting of the epichoric pi with a mu inside]
 
Note that the font I'm = using,=20 Palatino Linotype, does not provide the lower case for the stigma, = qoppa, sampi,=20 or digamma.  The Attic acrophonic is not yet represented in = Unicode, though=20 it probably will be soon; I've provided the best approximating Greek = characters=20 when available, and provided the two characters used in a vertical = ligature=20 separately in brackets with an explanation.
 
The stigma in the = Milesian system=20 replaced an earlier digamma (=CF=9C=CD=B4). =
 
Of course the Roman = numerals later=20 used the system we're used to, IV for 4, IX for 9, XL for 40, XC for 90, = CD for=20 400, and CM for 900. 
 
etc.
 
In addition to the books = mentioned by=20 GP and CF, there's a Reading the Past book on Mathematics and = Measurements=20 (O.A.W. Dilke) which provides an introduction and tables for both Greek = systems=20 on pages 13-14, as well as other systems on other pages.  This it = would=20 seem to me would be a perfect book for students. 
 
Hope this = helps.
 
PTR
ptrourke@methymna.com =
 
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