By Peter Orlowski © 2012 no color no sound no odor no taste no texture no mass no weight no charge...
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SYNTHESIZING MAGNITUDES FROM A PRECISE UNDERSTANDING OF POINT by Peter Orlowski © 2012 no color no sound no odor no taste no texture no mass no weight no charge no magneticism no thickness no width no length no position no shape
Transcript of By Peter Orlowski © 2012 no color no sound no odor no taste no texture no mass no weight no charge...
SYNTHESIZING MAGNITUDES FROM A PRECISE
UNDERSTANDING OF POINTby Peter Orlowski © 2012
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ANALYSIS
SYN
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PHYSICAL BODY: Known with certitude, but in a confused way, i.e. all the features mixed together
PHYSICAL SURFACE: Known thru body, i.e. as the divider and boundary of a body
PHYSICAL LINE: Known thru surface i.e. as the divider and boundary of a surface
MATHEMATICAL LINE: Conceived through a moving point, as having length without width.
MATHEMATICAL POINT: Conceived precisely in itself, as having position without having parts
MATHEMATICAL BODY: Conceived through a moving surface, as having length, width, and thickness.
PHYSICAL ANDCONFUSED KNOWLEDGE
MATHEMATICAL ANDDISTINCT KNOWLEDGE
MATHEMATICAL SURFACE: Conceived through a moving line, as having length and width only.
PHYSICAL POINT: Known thru line, i.e. as the divider and boundary of a line.
SYN
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A mathematical body has depth, in addition to shape, length, and width. But it has no mass, charge, magnetism, color, odor, etc.
A mathematical surface has only length, width, and shape. It has no depth, and also not mass, charge, magnetism, color, odor, etc.
The mathematical line has only length and shape. It has no width, or depth, and also no mass, charge, magnetism, color, odor, etc.
The mathematical point has nearly nothing, no mass, no charge, no magnetism, no color, no odor, no shape, no parts . All it has is position.
MATHEMATICAL LINE: Conceived through a moving point.
MATHEMATICAL POINT: Conceived precisely in itself, what has position without parts
MATHEMATICAL BODY: Conceived through a moving surface
HOW ARE THESE FEATURES GENERATED?
MATHEMATICAL ANDDISTINCT KNOWLEDGE
MATHEMATICAL SURFACE: Conceived through a moving line
=
A precise understanding of line, surface, and solid can be had by the generation of these from a point. Such a precise understanding adds the complexity of a multitude of features without confusing the various features together.
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And the geometer said, “Let there be a point.”
I n t h e b e g i n n i n g
t h e i m a g i n a t i o n
w a s e m p t y a n d v o i d
And the geometer saw that the point had position and nothing
more, and knowing it precisely, he said that it was good.
POINT
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position
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MOTION
length
shapePOINT
position
length
shape
position
+
LINE
And the geometer said, “Let there be motion of the point.”
The motion added length with shape to the point’s position, and a line was made, the first magnitude.
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MOTION
width
shape
MOTION
length
shapePOINT
position
+
SURFACE
length
shape
position
+
LINE
shape
spread
position
Then the geometer said, “Let the line move in any way, so that it does not move along its length.
The motion of the line added width and contour to the line, and a surface was made, the second magnitude.
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MOTIONshape
thickness
MOTION
width
shape
MOTION
length
shape
BODY
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POINT
position
+
SURFACE
length
shape
position
+
LINE
shape
spread
position
shape
bulk
position
Then the geometer said, “Let there be motion in the surface so that it does not move along itself. And it was so.
The motion of the surface added thickness and form to the surface and a body was made, the third magnitude.
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no thickness
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no thickness
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MOTIONshape
thickness
MOTION
width
shape
MOTION
length
shape
BODY
+
POINT
position
+
SURFACE
length
shape
position
+
LINE
shape
spread
position
shape
bulk
position
And seeing distinctly all that he had made, and how all the
features of magnitude came to be, the geometer said that it was very
good.
no thickness
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or length
no position
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no thickness
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no thickness
or width
or length
no position
no shape
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no thickness
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or length
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THIS IS THE GENEOLOGY OF MATHEMATICAL MAGNITUDE AND HOW IT WAS MADE IN THE BEGINNING AND HOW ITS FEATURES WHERE
INHERITED.
MOTIONshape
thickness
MOTION
width
shape
MOTION
length
shape
BODY
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POINT
position
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SURFACE
length
shape
position
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LINE
shape
spread
position
shape
bulk
position
