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10. Definitions

Astrology — the science linking the events occurring in the Universe with the motions of the massive heavenly bodies.

Aspect — on a given zodiac an aspect is defined for two arbitrary points of the zodiacal circle and accordingly, for their prototypes on the celestial sphere. Two points on a zodiacal circle are in an aspect of the Nth harmonic, if one point belongs to the Nth order family of the second point. An aspect is also the corresponding angular distance between images of two given points on a zodiacal circle.

Dynamic angle — the angle between the plane of the local equator and the axis of anisotropy.

Zodiacal circle — a circle of zodiacal longitudes with a reference point and sensitive points on it.

Conform progressed mapping (or conform progression) t = P(T) puts into correspondence to the interval T of (transit) time another interval t (t) of (progressed) time such that the displacement for the considered time interval T of the local ascending node of the second zodiac on the first one with respect to the fundamental reference point of the first zodiac is equal to the displacement for the time interval t of the local descending node of the first zodiac on the second one with respect to the fundamental reference point of the second zodiac.
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Conform directed mapping (or conform direction) is a composition of two identical conform progressions, i.e. the repetition of the conform progressed mapping: t = D (T) = P ( P (T)). The directed time is the progressed time of a progressed time.
Conform mapping of a profection (or Conform profection) is a composition of two different conform progressions, i.e. of 2 progressions of 2 different pairs of zodiacs of a born. For example, the conform solar-lunar solar-terrestrial profection= RSL–ST (T  PSL ( PST (T)) (SL means solar-lunar, ST — solar-terrestrial) is close to the usual definition of a profection (30 per year).
Fast conform profection — a composition of two different conform progressions, in which at first the fast mapping applies to transit time, and afterwards the slow. The Fast is identified with the mapping that "compresses" time by more times.
Slow conform profection — a composition of two different conform progressions, in which the slow mapping applies firstly to a transit time, and afterwards the fast. By its full name it can be distinguished from the fast conform profection. The solar, terrestrial and lunar zodiacs generate 3 pairs of profections. Examples:
Quick profection of the 1st kind (solar-lunar solar-terrestrial):
= RSL–ST (T  PSL ( PST (T)). “30 per year”
Slow profection of the 1st kind (solar-terrestrial solar-lunar):
= RST–SL (T  PST ( PSL (T)). “30 per year”
Fast profection of the 2nd kind (lunar-terrestrial solar-terrestrial):
= RLT–ST (T  PLT ( PST (T)). “12 per year”
Slow profection of the 2nd kind (solar-terrestrial lunar-terrestrial):
= RST–LT (T  PST ( PLT (T)). “12 per year”
Fast profection of the 3rd kind (lunar-terrestrial solar-lunar):
= RLT–SL (T  PLT ( PSL (T)). “day per year”
Slow profection of the 3rd kind (solar-lunar lunar-terrestrial):
= RSL–LT (T  PSL ( PLT (T)). “day per year”

Cusp of a station of a central body of Nth order — a point of the family of Nth order of the fundamental reference point (locating at 90 clockwise from the central body), i.e. a point on a zodiacal circle with longitude equal to the part of the full circle , where n — number of cusp, N —order of the fundamental reference point family. For N=12 — simply the cusp of station.
Cusps of the zodiacal signs of Nth order — points of the Nth order family of some reference point different from the fundamental reference point.
Cusp of a house — a projection of a station cusp onto another zodiac.
Cusp of a two-dimensional station — a great semicircle of points on the celestial sphere with the zodiacal longitude.

Local equator (plane) is determined by two vectors: the force vector F acting on a born on the part of the central body as a whole, and the velocity vector V of the central body without taking account of aberration in the non-rotating proper reference system of a born.
North pole of the local equatorial coordinate system is given by the unit vector in the direction of the vector product  V.
Fundamental reference point on the local equator (zodiacal circle) or the east point of the central body is given by the crossing point of the local equator and the plane of the local anisotropy horizon, the direction to which from the centre of the celestial sphere forms an obtuse angle with the velocity vector V of the central body in the proper non-rotating reference system of a born.
East point of the central body (fundamental reference point) is also given by the unit vector in the direction of the vector A=   P, where e is the anisotropy vector of the central body.
West point — the point on the celestial sphere opposite the east point.
Anisotropy vector e — phenomenological vector characterizing the space anisotropy caused by a massive body at the point of a born. For distant massive bodies this is the direction to its centre ignoring aberration, i.e. the tangent vector to the purely spatial geodesic connecting the born and the distant massive body. For the Earth this is the vector toward the gravitational attraction on the born from the Earth.
Local meridian plane — the plane perpendicular to the plane of the local horizon and the plane of the local equator.
Plane of the local horizon (of space anisotropy) — the plane perpendicular to the vector of space anisotropy caused by the central body.
Point of conjunction — crossing point of the straight line of intersection of the local meridian plane and the plane of the local equator with the celestial sphere, in the direction that forms an acute angle with the anisotropy vector e.
Point of opposition — the point opposite the point of conjunction.

World line of a born — the sequence of events in the life of a born expressed as combinations of coordinates and moments of time.

Moment of creation — the moment of birth of a born as a wholeness. We introduce this term in order to avoid futile debates as to what constitutes the exact moment of birth, as each astrologer has his own particular opinion in this matter. Let us emphasize that this is an exact moment, rather than a time interval, chosen by following events of a born’s life in the context of the techniques of the exact aspect and of the fundamental triad.

Orb of aspect — the maximum deflection of the zodiacal longitudinal difference between 2 points from the exact angular value characterizing an aspect, for which it is possible to consider the aspect as holding between the points for a given purpose.

Parameterization — the procedure of assigning the zodiacal longitudinal coordinate to points on the celestial sphere.

Planet as a zodiacal element — the point on a zodiacal circle having the same zodiacal longitude as a point on the celestial sphere representing a planet. A point representing a planet on the celestial sphere is defined by the direction of the anisotropy vector caused by this planet in the location of a born.

Projection (image) of a point on a first equator onto a second equator has the same zodiacal longitude in the coordinate system of the first zodiac, as its prototype (the source point on the first equator).

Born — a wholeness, whose world line (fate as an ensemble of events) is of interest to us.

Nth order family of points generated by the first point on a zodiacal circle — N points, symmetrically located in the corners of a regular N-agon inscribed within a zodiacal circle. More strictly: the points of the Nth order family of a given point can be generated from the first point by the action of a regular representation of the cyclic subgroup of the Nth order of the one-parametric group of rotations.
First point of a family — the point generating the family.

Event — the death of one wholeness and the birth of another. Any event occurs at a specific time and place, i.e. in this sense the term complies with the notion of an event as a collection of spatial and temporal coordinates, as used in the theory of general relativity.

Station (house, sign) — an interval on a zodiacal circle from the cusp of a station (house, sign) up to the cusp of the following station (house, sign).
One-dimensional station (house, sign) — an arc on a zodiacal circle identified with the equator of the local zodiac.
Two-dimensional station (sign) —ensemble of points on the celestial sphere, having the same zodiacal longitudes on the considered zodiac, as the points of the one-dimensional station (house, sign) on the local equator (zodiacal circle) of the considered zodiac.

Exact aspect — in the present work by an exact aspect we mean an aspect with an orb of 30". It is possible that this is not a fundamental orb, but an error in astronomical and astrological calculations. When we increase the precision of calculations we expect a decrease in the orb of an exact aspect to at least 1" without modifying the conception presented here.

Triad (fundamental) of an event: a planet, aspect, and the cusp of station (house). The planet and cusp are in exact aspect. The moment this aspect becomes exact fixes the occurrence of the event.

Local nodes — the crossing points of two local equators of a born and of their images on both zodiacal circles.
Ascending local node (of the equator of a second zodiac on the equator of a first zodiac) — the local node, for which after a small displacement from the considered crossing point in the positive direction along the second zodiacal circle, the obtained point is closer to the north pole of the equatorial coordinate system of first zodiac, than the crossing point.
Descending local node — the second crossing point, opposite to the ascending local node.
For example, it is possible to consider the vernal point as the ascending solar node on the terrestrial equator or as the descending terrestrial node on the solar equator (ecliptic).

Central body: a massive body generating the zodiac under consideration.

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