Eccentricity heart * To go further in explaining the operation of the Cross of Lorraine, I am obliged to introduce the concept of eccentricity heart. You should know what an eccentric to understand how a cardioid that turns on itself. Here is the corresponding mathematical document alleging the Larousse Encyclopedia of Words and Things (1900):
Row:
Who passes that cut through: Ray section. Straight line which cuts several others. In geometry, this name was given to meeting the three straight sides of a triangle or their extensions. The theory of transverse, very old indeed, gave rise to applications of a remarkable simplicity. It is based on the following convention. Abc is the transverse (Fig. 1): we should give signs to each of the segments formed on each side, taking the origins of these segments a, b, c. Segments on the same side are of opposite signs or even sign, depending on whether the meeting point of the crossbar with this side is on itself or on its production.
Menelaus Theorem:
When a triangle ABC (Fig. 1) is cut by a transversal abc was determined between the segments on the sides, the relationship:
(1) (aB / aC) * (bc / bA) * (cA / cB) = + 1
agreeing to consider aB Ba as a positive and negative. Indeed, leading CD parallel to AB was in similar triangles acd, abc:
(aB / aC) = (cB / Dc)
and similar triangles BCD, BCA:
( bC / bA) = (DC / AC)
and multiplying the two proportions memberwise:
(aB / aC) * (bc / bA) = (cB / DC) * (DC / AC) = (cB / cA)
or absolute:
(aB / aC) * (bc / bA) * (AC) = 1
As for the sign, it suffices to note that it may take only two cases: either the cross-cutting both sides and the extension of the other, and then two reports are negative and third positive, or the cross-cut extensions on three sides and the three reports are positive anyway, the product is positive. Conversely
. - If the three sides of a triangle, considered as indefinite, we take three points a, b, c (Fig. 1), such as the relationship (1) is verified, a, b, c are online right. This theorem may seek whenever you want to prove that three points are in a straight line. It can be applied in particular to demonstrate ownership of the bisector of an angle of a triangle:
The bisector of an angle sharing the opposite side into segments proportional to the adjacent sides.
Indeed, if the cross-ABC (Fig. 1) is perpendicular to the bisector of angle C, the triangle is isosceles Cba, and the sides AC and BC are equal in absolute value, and indeed they have same sign, according to our conventions, the relationship (1) becomes:
(cA / cB) = (BA / AB) or (cA / cB) = (CA / CB)
assuming that the cross is the bisector itself.
reciprocal Row:
The notion of reciprocal cross is used to easily build and geometrically the tangent at a point of some algebraic curves. Consider in particular the strophoid:
this curve is generated as follows: By the end A (Fig. 3) the diameter AA 'with a circle O, we draw a radius vector AD on which we take every moment AI = CD. The curve described by the point I is the strophoid. To construct the tangent to this curve at point I, draw a radius vector AC'D infinitely close ': The point I' as AI '= C'D' is a point of strophoid. We can notice that the lines and II'K CC'K 'are reciprocal cross over to the triangle DDA', since the points C 'and I', C and I are mirror images of the midpoints of sides AD 'AD. Suppose the line AD 'approaches indefinitely AD, I' comes I, the secant II 'becomes the tangent to strophoid in the I and DD 'becomes the tangent to the circle at point D: the above property exists and point H (Fig. 4) is symmetrical to the point H' to the point D.
So, to lead the tangent at a point in the strophoid, we draw the radius vector of this meeting point D with the circle, we draw the tangent to the circle DH ': the symmetric H H-point 'determines the point I considered the curve tangent required.
The same construction applies similarly to most remarkable Coubes studied in geometry analytically.
* Thus, the Sun, turning around the Earth, not only trace a heart around the center of the earth but no sign inside a heart strophoid! To understand what a strophoid, we must know what a Row. We find the explanation of the cross in the Encyclopedia of Words and Things of Cambridge (1900): Eccentric
: Said of two circles, one of which is contained in the other and which does not have the same center, the opposite is concentric. - Sm. An eccentric. In the first case of Hipparchus, the circle a planet, the sun, the moon, would have described around the Earth without it should occupy in the center. - We know that the second hypothesis was that of Hipparchus deferent and epicycle. All chuck through which the workpiece can be placed on the tower in the air so that the center of this piece does not coincide with the axis of turn. Body
used in machines for converting a continuous circular motion into straight reciprocating. It consists of a solid disk or hollow, mounted perpendicular to the axis of a rotating shaft, spindle, which did not occupy the center of the figure. It follows from this position of the axis that, while the disc rotates, successive points of its contour are not equally distant from the center of rotation, and that acting like a cam at the end of part straight, they can move in the direction of the length.
By giving the disc a proper contour, is contacted by the piece or straight bar that is to move the reciprocating motion that is desired.
For example, point O (Fig. 2) is the projection of the axis of the shaft turning point, if you give the disc a contour as AMCM, and if the rotating shaft is driven by a uniform motion, this disc by pressing successively on rollers protruding G and G 'to print the vertical TT ', that doors and passing through the slides, a reciprocating uniform. An eccentric kind of has the property that all the strings such that MM 'conducted by the center O of rotation are of equal length. This kind of body has been called eccentric because of the position of point O in the disk surface. The eccentric he just mentioned is called eccentric heart or curve
heart and is one we usually employs to transform a uniform circular motion in a back and forth alternative.
Here's how we track: Let AB (Fig. 3), the race to be run the rod moved by the eccentric race that takes place in A and B of A to B , either at the same time the O axis projection of the rotating shaft: to construct spot the outline of the eccentric, AB is partitioned into a number of equal parts, eight for example. Then the point O, with radius OB, describes a circle as you share in each half eight equal parts, and we draw the lines O1, O2, O3, O4, etc.., we suffisammen extends outside the circumference. That is, the point O as center, with distance from this point in Section 1 of AB describes the arc MM 'meeting ended extensions ray O1 and O1'. The two points M and M 'so determined belong to the contour of the eccentric. Then the point O as center, with distance from this point to Division 2 of AB describes the arc NN 'completed to meet the rays O2 and O2' extended. It has two new points N and N 'of the curve. Was repeated this construction for each division of the line AB. By passing a continuous curve through the points B, M, N, etc.., And B, M, N ', etc.., We obtain the contour of the cam with more accuracy than we took a greater number of points of division. This outline is a spiral of Archimedes, which axis the straight line BD and the two halves are symmetrical about comics. Assuming that the cam rotates from right to left, when the radius OM comes to merge with a portion of AB, the end B of AB has been pushed back to point 1, when we have taken the position O2, this same end B will appear at the second division of AB, and so on. When the radius OD has taken the position OA, the movement continues, the bar whose axis AB FIG return from A to B. These two movements will run in a uniform manner as it is assumed that the movement of the rotating shaft is itself uniform.
To move a piston P (Fig. 4.) In the interior of a pump body, it can act HM rod of this piston eccentric circular rotating around the point O.
This is an eccentric circle of radius CA surrounded by a concentric ring CA ' in the interior where it may slip. In the ring are fixed two rods connected in T'm TM and M with the piston rod. Assuming that the disk begins to move, advancing from point A to the right, its center C 'describe the circumference CDEF and when it arrived at D, the diameter AB has taken the position ab; by Thus the point M of the piston rod comes to the M position.'' The rotation continues, the center of the disc will travel half the circumference BFC, and the point M of the piston rod will move from M 'in M. The distance MM' is therefore the piston stroke.
can give other eccentrics forms the heart shape and round shape. Often their contour is a curvilinear triangle which rotates in a frame and prints it to a rectilinear movement back and forth.
(eccentric), sf. In the language of ancient astronomers, the distance from Earth at the center of the circle, following an initial assumption of Hipparchus, they assumed a single movement described by a planet from the Sun, the Moon. Having found the change in apparent angular velocity of these stars to explain this variation, each star admitted that Hipparchus traced round the Earth a circle in which it occupied the center point, circle which he gave the name of eccentric . Therefore they called eccentricity distance from the center OT of the eccentric O E Sun S, for example, T at the center of the Earth.
In geometry, called the eccentricity ratio of the focal distance FF 'to the major axis AB. (V. Ellipse) In terms of modern astronomy, the eccentricity of the orbit of a planet, the ratio of the eccentricity of the elliptical orbit of the planet semi-major axis of that orbit, or what equivalently, the distance from the center of the orbit with one focus, expressed by taking the unit semi-major axis. Eccentricity planetary orbits is usually very low, that of the Earth's orbit is 0.01679. The planet whose orbit has the largest eccentricity is Juno, for which the eccentricity to a value of 0.25608. Variation in the width of one or several layers of wood surrounding the pith of a tree dicot and the effect which the marrow is not placed in the ideal axis of the rod, but on the side of it. State a point somewhere far away from the workplace or the community of the object to which it belongs: The large eccentricity of the suburbs of a city. Singularity, the oddity of the character, manners, speech of a person: Go to ridicule by his eccentricity. (Néol.) - Gr Eccentricity, in the sense of strangeness, is a loan recently made to the English language.
All this allows us to conclude that for an observer positioned at a center that is the exact point where the sun rises, it describes an eccentric movement and the movement draws a curve which is a cardioid and not an ellipse.
can give eccentric forms other than the heart shape and round shape.
Often their contour is a curvilinear triangle which rotates in a frame and prints this rectilinear movement back and forth.
By reading the explanations of the math section and an eccentric
we learn that with this combination of curves, converting a rotary motion into back-and-down ! Piston engines are based on this principle!
There is a movement back and forth between the invisible vertical earth and sky in the center of the heart that is the omphalos . That allows this exchange? It is our good old sun! So he initiates. The heart seems to allow more to determine the equinoxes and the changing seasons.
strophoid This gives the design of the famous Drop! One can find his presence in lieudits as:
Gout, wood gout, Algoutte, Omégout you, etc. (which may be small streams). The sun is the tangent to the strophoid. Here is the final explanation of the principle of the Cross of Lorraine:
* We thus find the swastika, which is defined by the four cardinal points. There are rotated around the axis of Zion which is a center of the world, an emptiness. The explanation of this central point is given by the Indo-European civilization with the word bindu.
* For the phenomenon of raising three suns, we get the explanation of triscèle megalithic civilizations.
* As I explained in the general introduction, we do not define the symbolism of the drop. We know that we find in the Bible: Song
5: 2. I was asleep, but my heart was watching ... It is the voice of my beloved, who strikes: Open to me, my sister, my love, my dove, my perfect! Because my head is filled with dew, my locks with the drops of the night.
Deuteronomy 32: 2 May my teaching drop like rain, my speech fell like dew, Like showers on the grass, Like drops of water on the grass!
Isaiah 40: 15 Behold, the nations are like a drop of a bucket, they are like the dust of the balance: behold, the islands are like a fine dust.
Job 36: 27 It attracts the water drops, it reduces the vapor to form rain;
Job 38: 28 The rain have a father? Which raises the drops of dew?
Micah 5: 7. (5:6) The remnant of Jacob shall be among the many peoples as a dew from the LORD, Like drops water on the grass: They do not count on man, they are not dependent children of men.
* The explanation lies in the symbolism of the pearl because the beads are cardinal gates. See where in the Bible is the word pearl
Apocalypse 17: 4 The woman was arrayed in purple and scarlet, and decked with gold, gemstones and pearls. She held in her hand a golden cup full of abominations and filthiness of her fornication.
Apocalypse 18: 12 cargo of gold, silver, gemstones, pearls, fine linen, purple, silk and scarlet, all kind of scented wood, all kinds of objects of ivory, every kind of valuable wooden objects, bronze, iron and marble
16 and say: Woe! woe! The great city which was clothed in fine linen, purple and scarlet, and decked with gold, precious stones and pearls! In one hour so great riches have been destroyed!
Apocalypse 21:
21 The twelve gates were twelve pearls, each gate was of one pearl. Instead of the city was pure gold, like transparent glass.
Song 1: 10 Your cheeks are beautiful in the middle of necklaces, Your neck is beautiful the middle rows of pearls.
Job 28: 18 The Coral and crystal are nothing to her: Wisdom is worth more than rubies.
Matthew 07: 6 Do not give holy things to dogs, neither cast ye your pearls before swine, lest they trample them under their feet, and turn again and rend you.
Matthew 13: 45 The
kingdom of heaven is like a merchant looking for fine pearls. 46 It found a pearl of great price, and he went and sold everything he had and bought it.
Proverbs 03: 15 She is more precious than rubies, she has more value than all the valuables.
Proverbs 08: 11 For wisdom is better than rubies, she has more value than all the valuables.
Proverbs 20: 15. There are a lot of gold and pearls, but the lips of knowledge are a precious object.
Proverbs 23: 31 Do not look at wine when it is red, when it sparkles in the cup, which flows easily.
Proverbs 31: 10. Who can find a virtuous woman? It was much more valuable than pearls.
Thimothee 1 2: 9. I also want women to dress modestly, with decency and propriety, not to parent or braids, or gold or pearls or expensive clothes,
* There are so much the presence of the drop in the symbolism of the pearl through the Bible verses that are the Apocalypse 21, 21 and Matthew 13, 45,46. This presence is a key used to retrieve the coded explanation of how the tangent to the strophoid.
Here are definitions relating to strophoid from the dictionary Grammatical Napoleon Landais:
Stanza : plant of the family apocynées.
Strophéens : Name that gave the former Mercury
Stanzas : party at the old
Strophe: I mean running! At the feast of the stanza the chorus turned right around the altar, singing the verse and left singing the antistrophe.
antistrophe : marking an opposition alternative.
Conclusions: * The strophoid means "turn around", that is a heavenly circumambulation. * The symbol
strophoid Mercury is to say, Hermes,
so it was she who initiates !
The god Mercury is a curve that described the sun around an axis along any one year. We will find the former presence of a statue dedicated to Mercury in the center of Butte Sainte Genevieve Malzéville. On this hill stood a opidum Leuke. The reliefs coast of Butte Sainte Genevieve describe exactly strophoid! And at the foot of the hill of Sainte Genevieve is the town of Tomblaine TOMBLAINE word that comes from the tomb of Blaine, ie the place where the sun is out of the grave! A medal with a sun drawn on it has also been found in Tomblaine.
The great geographical location of monuments Lorraine has a religious reason for being far more important than you can imagine. Ormis the huge excess of the work he had undertaken, the complexity to achieve this alignment that entails, we must go further to understand the real value of this building.
In the text of the symbolism of the cross, we learn that the cross, facing the four cardinal points is the basis of all symbols of guidance to different levels of exitence rights. The total orientation of the triad requires a man ...: on the orientation of the animal relative to itself; spatial orientation relative to the cardinal points terrestrial celestial orientation finally compared to the cardinal points of heaven. Spatial orientation is based on the East-West, marked by sunrises and sunsets. Temporal orientation is based on the rotational axis of the world both North and South Holland High. The intersection of these two major carries the cross of total orientation. The concordance of both human and animal spatial orientation puts him in tune with the immanent world, three orientations of the animal, spatial and temporal world with the supra-temporal transcendental, by and through the Earth's environment. This leads us to conclude that the design and implementation of Churches in the same villages is the projection of the Heavenly Jerusalem on earth's surface. The first concern of Christians arrived in the territory to Christianize this pagan people were properly orient the housing so that the man who would live either in line with the kingdom of God. A central point was to indicate the correct position relative to the east of the tower, for this reason that all or nearly all churches are oriented in this way. Those who are not like the church of Pompey, and are oriented in the opposite direction, toward the west can be used to perfect alignment of the churches against each other. A steeple of a church they did match a "bug" on the map of the territory. To avoid mistakes, they started the quadrille. What is the mission had hermits, beggars and various saints of the early Christian era. We see the record of the Tomb of the Sun method they used to patrol the area. So they do not talk, then have them killed by cutting off their heads and later beatified in St. Céphalophore! Given the complexity of the work carried out and the short time that was put to perfect, it is reasonable to wonder if, before there was not already mapped pagan the territory that would have allowed the Christians to greatly simplify life by replacing the cross.
