Successive
steps in the Logic of Geometrical Propositions and Applied Mechanics in
Direct Demonstration. |
www.rolf-keppler.de | |

Impressum |

**(p.87)**
**THE FACTS of the observations and
experiments presented in the preceding chapters are quite sufficient to
demonstrate the earth's non-convexity, and to destroy the premise of the
modern system of astronomy. To the mind capable of comprehending a few
simple laws of vision, the observations on the water's surface as conclusively
demonstrate that the earth is concave, as the more direct processes involved
in the Koreshan Geodetic Survey.**
**Indeed, the fact that we have seen
the concave arc, and that it can be seen again under similar circumstances,
is a settlement of the question for those who desire ocular demonstrations.**
**>From these facts, we pass to the
consideration of the more direct processes in the demonstration of the
earth's contour.**
**p.88**
**The most accurate measurements
of the earth's surface are made by mechanical means. The employment of
apparatus for this purpose extends as far back as the history of astronomy.**
**Starting with the simplest factor
of linear measurement, the mind can at once conceive of the necessity of
mechanical appliances.**
**Space exists between any two points
on the earth's surface, embracing a number of units of measure-inches,
feet, yards, etc.**
**After a unit of measure has been
agreed upon as the standard, its length must be preserved, and the means
of preservation reduced to convenience of application or use; wood, iron
or other solid material must constitute the embodiment of space units,
as the rule, yard-measure, or the surveyor's chain. The process of measuring
by all such appliances, is simply that of marking their lengths upon a
surface, or by placing them end to end successively throughout the distance
to be measured. The measurement of meridian arcs in geodetic survey does
not differ in principle from these simple processes; all modern**
**measurements of the earth involve
the same factors.**

**Ancient and Modern Geodetic Apparatus.**
**The evolution of geodetic apparatus
from the days of Ptolemy to the present time, has resulted from the obvious
necessity of obtaining the greatest possible accuracy. Successive improvements
have simply increased precision of adjustment. The first apparatus consisted
of wooden rods placed end to end upon the**
**ground; degrees of latitude and
longitude have been thus measured, and miles of space determined. In modern
times, similar apparatus were used by Picard, the French astronomer.Improvements
were made by Osterwald, of Germany; by Mason and Dixon, of London, surveyors
of the famous Mason and Dixon line in America.**
**p.89**
**Beccara mounted the sections of
his wooden apparatus upon tripods; Cassini de Thury employed bars of iron
with adjusting devices; Bessel, iron and zinc; Helmert, platinum and iridium,
resting on iron trusses. U. S. geodetic measurements are made by compound
bars of iron and brass, adjusted so as to compensate**
**for contraction and expansion,
-an invention of Prof. A. D. Bache. The rods are enclosed in spar-shaped
cases made of wood, and mounted on tripods. The adjustments are made by
contact of fine points, determined by a delicate index. Similar apparatus
are in use by every government in the world, engaged in geodetic work.**

**All such apparatus are employed,
not for the purpose of determining a straight line, but to accurately measure
distances or meridian arcs; they involve adjustment of single points only.
There is no attempt at rectilineation; but the fact remains that their
use in modern times by the most skilful geodetic surveyors, proves that
accurate adjustments are not only possible, but are actually made by simple
contact of metal surfaces. The principles involved in the Koreshan Geodetic
Apparatus differ radically from those involved in any other apparatus.
It is susceptible of as great precision in linear measurement; and consideration
of the principles which distinguish it in its form, purpose, and use, will
make apparent its superiority over any other instrument of survey, as a
means of determining the actual contour of the earth.**
**Fundamental Principles of Geometry.**
**p.90**
**We purpose in this and the succeeding
chapters of this work, to make a direct demonstration of the concavity
of the earth's surface, involving principles and processes so simple and
so absolute as to be both easy of comprehension and conclusive. A direct
demonstration proceeds from a premise by regular deduction. First, the
premise must be known and absolutely proven, to the utter exclusion of
all assumptions; and second, all factors involved in the train of logic
must be direct and positive.**
**In the line of sequences, we must
take nothing for granted that would render our conclusion less certain
than the premise.**
**Our every step must be upon the
sure footing of fact. We purpose toshow that our premise, as well as resultant
conclusion, is so firmly established as to exclude all possibility of doubt
or denial.**
**We begin at the foundation of geometry,
and delineate for the mind, step by step, the inevitable conclusions. Geometry
is the science of earth-measurement, from (( [Gr. ge], earth, and ((((((
[metron], to measure. Modern geometry is a fragment of the true system
of the relations and properties of form that existed in the past, from**
**which its present name is derived.**
**Every form has its opposite form,
and every form has its coordinate form, possessing correlated functions.
There is no transmutation possible without segmentation; in the evolution
of a circle to its coordinated square, we have the intersection of secant
and arc, and relation and bisection of radius and chord, as in the**
**diagram, Fig. A, on following page.
The radius, which is perpendicular to the chord, bisects the chord, and
also the arc which it subtends.**
**The simplest angle to which relations
of form can be referred, is the right angle.**

**p.91**
**There can be no mergence of one
circle into another as in figure (diagram) B, without the relations of
the cross. If two circumferences intersect each other,the common chord
which joins the points of intersection, is bisected at right angles by
the straight line which joins their centers.**

**Our simplest premise, that the angles
relating perpendicular and horizontal are equal, is susceptible of being
known from a geometrical standpoint.**

**The principles upon which depend
right angles depend - by which they may be formed, also furnish a conclusive
test and demonstration of the perpendicular relations of straight lines.
To draw a line at right angles with another, independently of a square
as a guide, we may relate the points of intersection of arcs of merging
circles to the line connecting their centers, as before illustrated, and
as shown in diagrams Fig. D and E.**
**Having demonstrated the principles
of right angles, our premise is proven; and we are ready to take the next
step in the line of sequential propositions and arguments.**
**p.92**
**From the above geometrical facts
as a premise, we may construct**
**a square having four right angles,
four sides, two perpendicular and two horizontal parallels, because two
straight lines which are**
**at right angles with a given straight
line, are parallel with each other.**
**We can know as absolutely that
the sides of a rectangle are parallel to each other, as we can know that
two straight lines are at right angles, and by the same processes.**
**If we place two rectangles of equal
breadth together, we form a new rectangle which is equal in area to the
surn of the areas of the rectangles comprising it;**
**the sides joined being in unity,
the extremes are parallel, The other sides are as the extension of straight
lines.**
**If this is the result in the conjunction
of two rectangles, the same**
**results would obtain if ten thousand
rect angles were drawn end to end. There could be no possible deviation
from a straight rectilinear direction, and we defy any mathematician to
show that there could be!**