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VERSE: Nu21-13b

============================ Nu21-13b =========================

SUCCINCT SUMMARY:
-----------------
One of Rashis 10 major goals is to illustrate complex
geometric designs or algebraic complications. This is
called the Rashi method of SPREADSHEETS, since
SPREADSHEETS are one method of clarifying a complex
relationship.  The SPREADSHEET method can refer to
any illustration of a verse that clarifies it.

EXAMPLE Nu21-13b
----------------
Nu21-13b states
------------------------------
From there they moved, and camped
on the other side of Arnon, which
is in the wilderness that comes out
of the borders of the Amorites; for
Arnon is the border of Moab, between
Moab and the Amorites.
------------------------------

Rashi clarifies the complex geometric design
-------------------------------------------------
EMORI LAND | MOAB LAND   |
           |             |
           |             |
----------------|        |
EMORI LAND   x2 |x1Arnon |
----------------|        |
--------------------------

Rashi clarifies that
- if we picture EMORI and MOAB as rectangles
- then EMORI has a PROTRUSION cutting into Moab
- this PROTRUSION end at ARNON
Hence
- ARNON is the BORDER between Moab and EMORI
- The Jews camped at spot X2

Now let us re-examine the verse
--------------------------------------------------
VERSE                     PICTURE
-----------------         ------------------------
They camped on            They camped at
OTHER SIDE OF ARNON       x2
arnon in wilderness       x2 in protrusion
comes past Emori borders  protrudes
ARnon is border           x1-x2 is border
of Moab and Emori         x2 to Emori;x1 to Arnon
-------------------------------------------------

This example nicely illustrates why I call this
the SPREADSHEET method---Rashi's main goal
is to clarify a complex relationship that is
hard to visualize.

LIST690L below summarizes this spreadsheet pattern.
LIST690a presents other Rashis where the SPREADSHEET rule
is used.
================================================================
ITEM                     DETAIL
======================== =======================================
RASHI RULE CLASS:        SPREADSHEETS
RASHI SUBRULE CLASS      ALGEBRA
RASHI WORKBOOK PRINCIPLE #30
SEE BELOW                LIST690L
List of                  Geometric features of Moab-Emori border
-----------------        --------------------------
SEE BELOW                LIST690a
List of Rashis using     Spreadsheets/Algebra
================================================================

========================== LIST690L ======================
List of       Geometric features of Moab-Emori border*10
==========================================================
VERSE TEXT (Nu21-13b)     GEOMETRIC*10 INTERPRETATION
========================= ================================
They camped on            They camped at
OTHER SIDE OF ARNON;      position x2;
------------------------  ----------------------------
arnon                     position x2
is in the wilderness that is in the rectangle that
comes past Emori borders  protrudes past Emori borders
------------------------  ----------------------------
ARnon is border           x1-x2 is border
of Moab and Emori         x2 belongs to Emori;x1 to Arnon
-------------------------------------------------

NOTES
-----

---------------- LONGER FOOTNOTES ----------------------
*10
Rashi clarifies the complex geometric design
-------------------------------------------------
EMORI LAND | MOAB LAND   |
           |             |
           |             |
----------------|        |
EMORI LAND   x2 |x1Arnon |
----------------|        |
--------------------------
==========================================================

==================== LIST690a ==================================
List of Rashis using     Spreadsheets/Algebra
================================================================
VERSE         Item Spreadsheet is used for
============  ==================================================
nu21-13b.htm  Illustrate complex geometric border design
nu13-22b.htm  Israel is superior of all lands
gn49-26d.htm  your fathers blessings greater than my fathers
dt21-17a.htm  How to give 1st-born double *1
ex38-24b.htm  Computation of relative value of Biblical currency
nu03-39b.htm  Accounting of Levite children
nu31-26a.htm  Division of booty in war
gn05-32b.htm  Computation of relative ages of Noachs children
gn25-20a.htm  Proof that Rivkah was 15 when she married Isaac

NOTES
-----
*1  Many people are familiar with the concept of the
    FORMULA PLUG IN. That is a problem is solved by a
    formula which you plug into.

    But some problems intrinsically cannot (initally)
    be solved by a formula. Instead you have to
    formulate the problem algebraically and solve;only
    then do you have the formula.

    In other words these problems are solved by
    the EQUATION vs the FORMULA

    Thus the statement that the eldest gets double
    suggests the following model.

    - Suppose the are B brothers
    - Suppose 1 of them is eldest
    - The Fathers total assets are T (Total)

    - Let A be the amount each brother inherits
    We have no formula for A

    - Then each of the B-1 brothers obtains A
    - The eldest obtains double, 2A.
    - Together this exhausts the Fathers estate, T

    Hence we have (B-1)A + 2A = (B+1)A = T

    This gives rise to the formula  A = T / (B+1)

    An example is a father with 100,000 and 4 children
    - T=100,000
    - B=4
    - So each child take T/(B+1) = 100000/5 = 20,000
    - Eldest takes 2*20000=40000
    - Other 3 take 20000
    - Total distribution =3*20000+40000=100000

    See Rambam Inheritance Chapter 2
================================================================
---------------------------------------------------
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Volume 26 Number 13


#*#*#*#  (C) 2000-2005, RashiYomi Inc. Dr Hendel President #*#*#*#
Volume 26 Number 13