Volume appears to be created by volume dividing volume

Schwaller Came to believe that 

The entirety of Egyptian Mathematics

and philosophy was based on the notion that 

the primary 

expression of Being 

is

Volume

Specifically 

Three dimensional Form

Where Form is formed

from a Surface formed 

from a line formed

from a point

There fo/u/re

A n apex of a Volume is any point

A Vertex of a volume is any edge/line

A Surface of a Volume is any Face/area

Every volume then defines every other volume

by the identity of the points

lines and forms forming

the surfaces

defining

the 

interior

. : .

and

Exterior

volume/z identified

as the aether  . : .  and

Geometry   points  to the 

shapes the way the stars form 

ideas of form

from

light

. : .

The point,

 the first irreducible One, 

generates the line by addition,

 for any it (point) cannot manifest itself

- [line]-

 by multiplication since

 1 times 1 is always 1

 and likewise

 1 times a point always 

remains a point ... 

The point will  become a line 

 by being added to another point

 or 

 by separating one point into two .:

which amounts to the same thing : .

 Hence, in creation, addition and division

 have the same effect . : .

 multiplication

 is 

the inverse  of

 Division

 Hence by the definition of the words used

the irreducible One

if divisible

 must be assumed

 to be a multiplicity—

and we now know 

how this original conflict is resolved:

 by under standing the triple nature

 of the irreducible One,

 i.e., the quality

 which allows one to conceive

 the procreating function,

 during which 

addition being the consequence of division,

division simultaneously must be

no function other than addition—

 and division of  UNITY generates 

 multiplication as the inverse

of itself neither of which

can exist in the absence of the other

  I = the generative point 

 II = the point generated by division

 III = the point generated by addition

 The number III is the effect of I.

 The number II is generated by division,

 the cause not yet having an effect.

The point can only create by addition

 division is addition,

Addition or division create - line

  line can only pro~create —

and never create :.

 A line added to itself is, 

and always remains, 

a line, 

where

 as soon as a Line is multiplied by itself,

 a line becomes a face . : .

The numbers 1, 3, 5, 7 

 do not contain any procreated form

and so 

are the creative numbers

 They are the prime and un~composed numbers.

 they generate all figures and forms

and

with regard to the concrete/visible world

 play, 

 the same role that the irreducible One

 plays

 with regard to the abstract/in visible world.

these creative numbers

  By addition 

can produce

 other prime or un~composed numbers

 in the sense of pro~creation such as 11

 which is the first representation in the concrete world of the function of II in the abstract world.

 This is because 11 is intermediary, just as II is and

results from an addition of 1, 3, 5, and 7,

 and does not in~volve multiplication.

 The numbers 1, 3, 5, 7 are the generators

 in the phase of id~eat~ion . : .

 By multiplication with themselves they : .

 produce faces,

 are only engendered by addition,

 and

 provide the perfect transition from

 the abstract to the concrete 

through the phases of idea~t-ion .  :  .

We have said that the square is the first stable face

 By stable we mean  : :

 is the consequence of  : :

 a function: always equal 

 and 

produces no complex effect  : . : . :

as a second function

that diverges from 

the natural consequence 

of the generation of the first function. 

 the first face is not The face which has four sides

 for 

to establish a face

 three vertices are sufficient 

 so that the first face is therefore

 the 

triangle.

 The triangle,

 as it is multiplied by itself,

  produces a circle

 The triangle,

 as it is divided by itself,

  produces a square

the first stable face of the square, 

as we shall see in the next cycle

 differs in this facet

  As 

 The

 function

 presiding over

 the cycle of ideation

 is the multiplication aka 

 the inverse division 

of a

 simple or complex

 unity

 not itself 

a 

root 

en~gen~dered by

The

Function

of

 multiplication

 The natural consequence of this function is

 the creation of the face.

The triangle does not conform to this law.

 It is a face  engendered

 by 

 the first scission

Addition aka Division

Not

 by

multiplication aka subtraction

it 

aka the triangle

engenders a stable face

 as a result of multiplying itself

by itself by

removing the ambiguity 

for it 

As it 

is not really a definitively

 constituted

 AKA

 a stable face

The first perfect triangle would therefore be one that would fulfill the following conditions:

 first:    to be the first face;

 second:  to be constituted by three vertices;

 third:    to en~gender a stable face by multiplying itself;

 fourth: to be con~stitut/able/ed by a stable face

 

The apparently insurmountable difficulty that human reason encounters here is easily resolved by the knowledge

 that this short study of numbers

 has given us. 

The first triangle fulfills 

the Second and Third conditions 

 the first and the fourth conditions

are not fulfilled

Indeed

 there cannot be a face which only includes

 one

unit of height to 

two

 units of length 

for 

One unit of height added to two units of length

constitutes a LINE and not a face. 

 The second triangle fulfills the first, second, and third conditions. The fourth condition will therefore be met, beginning with the third triangle: This constitutes the tetraktys or quaternary, 

See the cube in the hexagon
Vertex Middle bottom Line
Center Dot Hides its double
Apex is base of 
the origin

which, first:

 is the first possible face;

 second, is triangular/composed of three vertices;

 third, engenders

 by multiplication with itself

 a stable face

which is 9 

as was shown above; 

and fourth,  contains the first square 

which is 4

The speed of light is approximately 

 186,624 miles per second

 Given

 the first triangle

The anGle associated with any

Radius gives the opposite side length

This determines a triangle whose height

 is half as great as its base.

 This triangle 

frames absolute Unity 

the vital breath in the things of this world.

 There are therefore in the quaternary triangle

 actually two distinct triangles

 These are the triple creative nature in the One

 and this triple nature as generated

 by the thrice three unities of the first triangle.

 This figure, which is the first manifest triangle, 

fulfilling all the conditions laid down above, 

engenders the perfect square,

 which is 9, for it contains all the

numbers.

 In this way all squares become divisible 

into two triangles,

 since 4 is 1 and 3; 

9 is 3 and 6; etc.

 

The squares, beginning with 10, 

become compounds

 The uneven are positive, AKA masculine numbers

 form the squares of whose two triangles one is negative

 and the other positive (even and uneven). 

The even numbers, meanwhile, give the squares whose triangles are both negative or both positive. 

We cannot enter here into any explanation of the reason for this fact. 

It will be sufficient to indicate to the student that

 the even numbers are all compounds:

 2 equals 2 times 1

4 equals 2 times 2

 6 equals 2 times 3

 8 equals 2 times 4

 this function determines the intermediate

 AKA variant forms of the square,

 such as the

the parallelograms with two unequal sides.

 We have said that the essentially creative numbers are 1, 3, 5, 7 and that they establish the following principles which we find everywhere at the base of creation of the two natures.

 The multiplication of any quantity by itself (procreation) 

results from the addition of a positive, masculine, odd nature

 to a negative, feminine, even nature.

 The other figures—pentagons, hexagons, polygons—

are the effects of an addition of different

 triangular and square figures,

 just as the numbers above 10

 are the result of addition to this 10

 of the numbers 1 through 9. 

The square is the stable base of forms

First: Addition of the point to the point gives the line.

 Second: Multiplication of the line by the line 

creates the face

The first line form is the triangle 

multiplication of the Face by itself

Gives the Face  the first form 

this is the square

Multiplying the form by itself gives the first volume

this is the cube

 This constitutes the cycle of formation. 

the perfect face is THE SQUARE

 The perfect form, 

results from the multiplication of the square: 

the cube.

 As in the preceding cycles, 

the face, in order to become the cube, 

will pass through all the phases 

of polarization and ideation.

 The square again becomes the point—

the point of departure—

for the form. 

The first pole for the generation of the cube,

 is the face. 

The cycle of the polarization of the solid

 therefore

begins with the face, 

which 

possesses a spatial tendency in one - direction only,

and is called is one - dimensional

 Face/Form then proceeds to 

the second dimension

The second step of generation

 in order to become the third dimension

 three-dimensional 

Compounding the positive and negative 

This last phase is

 the cycle of formation

 in

 the cycle of formation

It is always important to recall

 that each of the three cycles

 is likewise subdivided into three cycles, 

and that: as the cause varies 

 the effect varies as the result 

The first cause is the point

 the second the line

 and the third the face

The cycle of polarization is 

the phase of addition

 where/by the non~dimensional 

becomes the first dimension: the line. 

the cycle of ideation gives the second dimension, 

By multiplication of the line into

the face, and thus the face 

gives the solid by multiplication 

of A first multiple.

A ROOT

 At the base of all creation is movement. 

Addition is the first, or linear, movement. 

The first multiplication is the second, 

or planar, movement, 

and multiplication of the latter 

gives the third, or solid, movement.

 In a solid, movement