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Grimoire Quadrantis Telemetrum

398 pages, black & white. 129 graphics, 22 tables. Perfect bound. 8" x 5" (20.5 x 13.5 cm)


The degree to which the result of a measurement, calculation, or specification conforms to the correct value or a standard.
Either a distance measurement usually in the vertical direction between a reference datum and a point or object; or, the angle of elevation of a celestial object above the horizon.
Angular size
The angular measurement describing how large an object appears from a given point of view. In the vision sciences it is called the visual angle; in the optic sciences, it is the angular aperture of a lens. The angular diameter can alternatively be thought of as the angle through which an eye or camera must rotate to look from one side of an apparent circle to the opposite side. Angular radius equals half the angular diameter. Synonyms: Angular diameter, apparent diameter, apparent size.
The point on a planet's orbit around the Sun that is farthest from the Sun. See: perihelion
The most distant point (of the Moon) in its orbit around Earth. See: perigee
Origin: Greek. Literally: "Star-taker". Astrolabos comes from astron, or "star". Lambanein, or "to take." An elaborate inclinometer historically used by astronomers and navigators to measure the altitude above the horizon of a celestial body. It can be used to identify stars or planets, to determine local latitude given local time (and vice versa), to survey, or to triangulate. It was used in classical antiquity, the Islamic Golden Age, the European Middle Ages and the Age of Discovery for all these purposes.
Astrological houses
The division of the ecliptic into six parts above and six parts below the horizon.
The angle measured along the horizon, typically clockwise from north, and used to indicate direction of a celestial object from the observer in terms of compass bearing.
Celestial coordinates
The right ascension and declination of an object on the celestial sphere specify its position uniquely. The coordinate systems are implemented in either spherical or rectangular coordinates. Spherical coordinates, projected on the celestial sphere, are analogous to the geographic coordinate system used on the surface of Earth. These differ in their choice of fundamental plane, which divides the celestial sphere into two equal hemispheres along a great circle. Rectangular coordinates, in appropriate units, are simply the Cartesian equivalent of the spherical coordinates, with the same fundamental (x, y) plane and primary (x-axis) direction. Each coordinate system is named after its choice of fundamental plane.
Celestial equator
The projection of the Earth's equator onto the celestial sphere.
Celestial poles
The projection of the Earth's north and south poles onto the celestial sphere.
Celestial sphere
An abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, which may be centered on Earth or the observer.
The moment when two celestial bodies have the same ecliptic longitude, usually related to the position of the Moon or a planet to the Sun.
A region of the sky that is separated from other regions, comprising groups of visible, bright stars. At the beginning of the 20th century, the boundaries of 88 constellations were defined. This enabled researchers to easily assign celestial bodies to positions on the celestial sphere. See: signs of the zodiac
The instant of time that it takes a celestial object (the Sun, Moon, a star, constellation or other deep-sky object) to transit across the observer's local meridian.
The sliding marker on the index line, used to store a value or to project from one scale to another.
One of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. The declination angle is measured north or south of the celestial equator, along the hour circle passing through the point in question. Declination in astronomy is comparable to geographic latitude, but projected onto the celestial sphere. The hour angle is likewise comparable to longitude. Points north of the celestial equator have positive declinations, while those south have negative declinations. Polaris is 90° declination, equator is 0°. The declination of the Sun is the angle between the Sun's rays and the equatorial plane of the Earth. The declination angle is the same for anywhere on Earth on a given day.
The dimension across the largest extension of an object, measured in one straight line from edge to edge.
The numerical measurement of the distance between objects. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria. In most cases "distance from A to B" is interchangeable with "distance from B to A".
Diurnal arc
The part of the apparent solar path that lies above the theoretical horizon for a specific geographical location and a given date. Its length corresponds to the time span between the rising and setting of the Sun. (Opposite of diurnal: nocturnal.)
Ecliptic longitude
The distance of the first point of Aries to the perpendicular of a celestial body to the ecliptic, measured in degrees.
The mean plane of the apparent path in the sky that the Sun follows over the course of one year; it is the basis of the ecliptic coordinate system. This plane of reference is coplanar with Earth's orbit around the Sun. The ecliptic crosses the celestial equator on the equinoxes, and intersects the tropics on the solstices.
The positional vertical location along a vertical direction, above or below a given vertical datum. Vertical distance or vertical separation is the distance between two vertical positions. Many vertical coordinates exist for expressing vertical position: depth, height, altitude, elevation, etc.
In astronomy and celestial navigation, an ephemeris (plural: ephemerides) gives the the trajectory of astronomical objects (natural or man-made) over time, including position and possible velocity. The etymology is from Latin ephemeris, meaning 'diary'. Historically, positions were given as printed tables of values, given at regular intervals of date and time. The calculation of these tables was one of the first applications of mechanical computers. Modern ephemerides are often computed electronically, from mathematical models of the motion of astronomical objects and the Earth. However, printed ephemerides are still produced as they are useful when computational devices are not available.
Equal and unequal hours
In antiquity, the daily arc of the Sun, or the time from sunrise until sunset, including the night arc, which was divided into twelve equally long parts. Since the time from sunrise to sunset was longer in summer than in winter, the "hours" of summer were also longer than the "hours" of winter. These unequal hours or temporary hours were used over much of the Earth, for many centuries until the middle ages. The "hours" of any one day were equal, but the "hours" of the winter were short and the "hours" of summer long. It is for this latter reason that we refer to them as unequal hours. Around the 14th century, the method for counting the hours changed. The irregular unequal hours were replaced by hours of equal length. The time beginning with the passing of the low meridian, about midnight, until the passing of the next low meridian, was divided into 24 hours of equal length.
Equal hour
The hours dividing the day into 24 equal hours. See: equal and unequal hours
Equation of time
The difference between mean time and true solar time.
A great circle on the globe, the plane of which is perpendicular to the axis of rotation. See: celestial equator
The moment at which the Sun crosses the equator on its (apparent) orbit around the Earth. The beginning of spring or autumn. See: solstice
First Point of Aries
The singular point in the sky where the celestial meridian, the celestial equator, and the ecliptic meet. When the Sun annually reaches the First Point of Aries, the vernal equinox occurs in the northern hemisphere. The First Point of Aries is used as a reference point in celestial coordinate systems; it is often indicated with the symbol ♈ and defines the zero-point for right ascension, with its own coordinates being 0 h right ascension and 0° declination. Named for the constellation of Aries, it is one of the two points on the celestial sphere at which the celestial equator crosses the ecliptic, the other being the First Point of Libra, located exactly 180° from it. Due to precession of the equinoxes, the position of the Sun on the March equinox is currently in Pisces, while on the September equinox it is in Virgo.
From Greek: "one that knows or examines"; the part of a sundial that casts a shadow. Typically a vertical pole used in Sun observations and shadow calculations.
The abstract circle centered on the observer that marks the farthest extent of the visible surface of the Earth and defines the horizontal plane.
Hour angle
Angular distance on the celestial sphere measured westward along the celestial equator from the meridian to the hour circle passing through a point. It may be given in degrees, time, or rotations depending on the application.
Hour circle
In astronomy, one component together with declination and distance (from the planet's center of mass) required to locate any celestial object. It is the great circle through the object and the two celestial poles.
Index line
The virtual or drawn line created by the straightedge or a string across a nomogram (isopleth).
Julian date
The starting point of the Julian calendar is Monday, January 1st, 4713 BC, at noon for a Julian date of 0.00. The days are counted from noon to noon, the fractions of the day are displayed as decimal fractions.
A navigational aid consisting of a rectangular piece of wood (or similar) and a graduated string to measure distance and altitude.
A geographic coordinate that specifies the N-S position of a point on the Earth's surface. It is an angle which ranges from 0° at the equator to 90° (N or S) at the poles. Celestial latitude describes the angular distance north or south of the ecliptic on a celestial sphere.
A geographic coordinate that corresponds to the angle between the meridian passing through that location and the prime meridian. A distinction is made between eastern and western longitude. Celestial longitude describes the angular distance east or west of the vernal equinox, measured in the plane of the ecliptic. See: ecliptic longitude
A great circle passing through the celestial poles, as well as the zenith and nadir of an observer's location. Consequently, it contains also the north and south points on the horizon, and it is perpendicular to the celestial equator and horizon. See: prime meridian
A naturally occurring optical phenomenon in which light rays bend to produce a displaced image of distant objects or the sky.
The point of the celestial sphere exactly opposite the zenith. See: zenith
A two-dimensional diagram designed to allow the approximate graphical computation of a mathematical function.
A graphical calculating device that contains a nomogram.
Obliquity of the ecliptic
The angle between ecliptic and celestial equator.
The tilt in the axis of the Earth.
The closest point (of the Moon) in its orbit around Earth. See: apogee
The point on a planet's orbit around the Sun that is closest to the Sun. See: aphelion
Plumb line
A line with a weight attached to it, used as a vertical reference line or determining the vertical on an upright surface. It is essentially the vertical equivalent of a water level.
Commonly known as the North Star or the Pole Star, it is the brightest start in the constellation of Ursa Minor. It is designated Alpha Ursae Minoris (Latinized to Alpha Ursae Minoris, abbreviated Alpha UMi. It is very close to the north celestial pole, making it the current northern pole star. The revised Hipparcos parallax gives a distance to Polaris of about 433 light-years (133 parsecs), while calculations by other methods derive distances around 30% closer. The modern name Polaris is shortened from New Latin stella polaris "polar star", first coined in the Renaissance era. Then, the star had approached the celestial pole to within a few degrees. Gemma Frisius, writing in 1547, referred to it as stella illa quae polaris dicitur "that star which is called polar", placing it 3,7° from the celestial pole.
The displacement of the intersection of the ecliptic and the celestial equator compared to the fixed stars.
Prime meridian
The meridian that forms the reference line for the longitude on Earth. Today, the prime meridian runs through the former Greenwich observatory.
The direction used by Muslims in various religious contexts, including the ritual prayer. It is the direction of the Ka'bah in the Sacred Mosque in Mecca, Saudi Arabia.
An instrument that is used to measure angles up to 90 degrees. Quadrant means one fourth, of a circle in this case.
The SI unit (Système Internationale) for measuring angles that is the standard unit for angular measure used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is 180/π degrees.
Incoming light rays are "bent" due to the Earth's atmosphere, which leads to an apparent elevation of the position of the stars above the horizon. The exact value depends on temperature and air pressure. At +10° temperature and an air pressure of 760 mm (1013.25 hPa) the refraction is ~0.6°. It increases with higher air pressure and falling temperature and vice versa.
Right ascension
The position of a star around the celestial sphere, starting point is vernal equinox and measured in the plane of the celestial equator (generally expressed in terms of 0 to 24 hours).
Scientific notation
A method of expressing numbers that are too big or too small to be conveniently written in decimal form.
A numeral system with sixty as its base. It is used to measure time, angles, and geographic coordinates.
Shadow Square
Also known as an altitude scale, it is a set of scales used to determine the linear height of an object, in conjunction with a means of sighting. Used in angular observations, it represents the tangent and cotangent trigonometric functions.
"Of the stars"; a timekeeping system used to locate celestial objects based on the apparent movement of the stars as a result of the rotation of the Earth.
The procedure of aligning the sighting vanes of an instrument or the view through a tubular feature installed on an instrument with the target.
Signs of the zodiac
The 12 equal-sized parts of the ecliptic, also commonly referred to as the zodiac signs which were named after the corresponding constellations, that are traversed by the Sun, Moon, and planets on their orbit around Earth. Due to the precession that causes the first point of Aries to shift in relation to the fixed stars, constellations and signs of the zodiac are far apart today. At the beginning of spring, around March 21st, the Sun enters the Aries zodiac sign, and around April 19th, the Aries constellation. See: constellation
Slide rule
Two logarithmic scales in rule form that allow rapid multiplication and division of numbers. These common operations can be time-consuming and error-prone when done on paper. More elaborate slide rules allow other calculations, such as square roots, exponentials, logarithms, and trigonometric functions.
The deviation from the horizontal. Ratio of "vertical change" to the "horizontal change."
Solar altitude
The angle of the Sun relative to the Earth's horizon, measured in degrees.
Solar zenith angle
The angle between the zenith and the center of the Sun's disc.
The time of greatest (positive or negative) declination of the Sun. See: equinox
String theory
Wndsn string theory posits that the more perpendicular (or obtuse) the string is to the center scale, the more accurate are the results. This means that one can switch to a different unit (or power of 10) for increased readability.
Device used to remotely measure any quantity. It consists of a sensor, a transmission path, and requires either a display, recording, or controlling device. Telemeters are the physical devices used in telemetry.
"Measuring triangles"; the study of relationships involving lengths and angles of triangles. The 3rd-century astronomers first noted that the lengths of the sides of a right-angle triangle and the angles between those sides have fixed relationships: that is, if at least the length of one side and the value of one angle is known, then all other angles and lengths can be determined algorithmically. Note the distinction between defining trigonometric functions as ratios of sides of right angled triangles vs. the unit circle method.
The Tropic of Cancer and Tropic of Capricorn mark the northernmost and southernmost latitudes at which the Sun may be seen directly overhead (at the June solstice and December solstice respectively). The latitude of the tropical circles is equal to the Earth's axial tilt.
Unequal hour
The hours dividing the day and night into 12 unequal hours each. See: equal and unequal hours
Unit circle
A circle with a radius of one centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. It ties together Euclidean geometry (circles, points, lines, triangles, etc.), coordinate geometry (the x-y plane, coordinates on the plane, etc), and trigonometry (the sine, cosine and tangent ratios).
Universal time
World time UT, successor to GMT (Greenwich Mean Time), mean time, is based on the zero meridian. Defined as the Greenwich hour angle of the fictitious mean Sun plus 12 hours (the addition of 12 hours is necessary because the meridian passage of the fictitious mean Sun should take place at 12 o'clock UT, but its hour angle at this moment is 0 h).
The highest point of the celestial sphere located vertically above the observation point. See: nadir
The circular band on the celestial sphere, centered on the ecliptic, against which the Sun, Moon, and planets appear to move. It is divided into twelve 30° segments, each corresponding with a constellation.

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