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Astrolabes. An introduction to the theory and practice of constructing astrolabes, sundials, and other astronomical and navigational instruments based upon the works of Georg Hartmann. Astrolabes.

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Astrolabes

An introduction to the theory and practice of constructing astrolabes, sundials, and other astronomical and navigational instruments based upon the works of Georg Hartmann.

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Astrolabes

An astrolabe (Greek: ἁστρολάβον astrolabon 'star-taker') is a historical astronomical instrument used by classical astronomers, navigators, and astrologers. Its many uses include locating and predicting the positions of the Sun, Moon, planets, and stars; determining local time (given local latitude) and vice-versa; surveying; and triangulation.

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Astrolabes

Astrolabes were used primarily for astronomical studies, as well as in other areas as diverse as astrology, geography, navigation, surveying, and timekeeping.

There is often confusion between the astrolabe and the mariner's astrolabe. While the astrolabe could be useful for determining latitude on land, it was an awkward instrument for use on the heaving deck of a ship or in wind. The mariner's astrolabe was developed to address these issues.

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Table of Contents

  • History of the Astrolabe
  • Biography of Georg Hartmann
  • Hartmann's Seven Propositions
  • Hartmann's Dial Lines
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History of the Astrolabe

An early rudimentary astrolabe was invented in the Hellenistic world by around 200 BC and is often attributed to Hipparchus. The astrolabe was effectively an analog calculator capable of working out several different kinds of problems in spherical astronomy.

Astrolabes continued in use in the Greek-speaking world throughout the Byzantine period. About 540 AD the Christian philosopher John Philoponus wrote a treatise on the astrolabe in Greek, which is the earliest extant Greek treatise on the instrument. It was undoubtedly from such Eastern Christian scholars, either Greek or Syriac-speakers, that Muslim scholars were first introduced to the astrolabe.

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History of the Astrolabe

Astrolabes were also used in the medieval Islamic world, chiefly as an aid to navigation and as a way of finding the qibla, the direction of Mecca. The first person credited with building the astrolabe in the Islamic world is reportedly the eighth century mathematician, Muhammad al-Fazari.

The mathematical background was established by the Arab astronomer, Muhammad ibn Jābir al-Harrānī al-Battānī (Albatenius), in his treatise Kitab az-Zij (ca. 920 AD), which was translated into Latin by Plato Tiburtinus (De Motu Stellarum). The earliest surviving astrolabe is dated AH 315 (927/8 AD).

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History of the Astrolabe

The spherical astrolabe, a variation of both the astrolabe and the armillary sphere, was invented during the Middle Ages by astronomers and inventors in the Islamic world. The earliest description of the spherical astrolabe dates back to Al-Nayrizi (fl. 892-902). In the 12th century, Sharaf al-Dīn al-Tūsī invented the linear astrolabe, sometimes called the "staff of al-Tusi", which was "a simple wooden rod with graduated markings but without sights. It was furnished with a plumb line and a double chord for making angular measurements and bore a perforated pointer." The first geared mechanical astrolabe was later invented by Abi Bakr of Isfahan in 1235.

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History of the Astrolabe

The English author Geoffrey Chaucer (ca. 1343–1400) compiled a treatise on the astrolabe for his son. The first printed book on the astrolabe was Composition and Use of Astrolabe by Cristannus de Prachaticz.

The first known metal astrolabe known in Western Europe was developed in the fifteenth century by Rabbi Abraham Zacuto in Lisbon. Metal astrolabes improved on the accuracy of their wooden precursors.

In the 16th century, Johannes Stöffler published a manual of the construction and use of the astrolabe. Four identical 16th century astrolabes made by Georg Hartmann provide some of the earliest evidence for batch production by division of labor.

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Biography of Georg Hartmann

Georg Hartmann (sometimes spelled Hartman) was born in 1489 in Eggolsheim near Forchheim, Bavaria. He was a German engineer, instrument maker, author, printer, humanist, churchman, and astronomer.

At the age of 17, he began studying theology and mathematics at the University of Cologne. After finishing his studies, he traveled through Italy and finally settled in Nuremberg in 1518. There he constructed astrolabes, globes, sundials, quadrants and other instruments. Hartmann was possibly the first to discover the inclination of Earth's magnetic field.

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Biography of Georg Hartmann

Hartmann's two published works were Perspectiva Communis (Nuremberg, 1542), a reprint of John Peckham's 1292 book on optics and Directorium (Nuremberg, 1554), a book on astrology. He also left an unpublished work on sundials and astrolabes that was translated by John Lamprey and published under the title of Hartmann's Practika in 2002 (it is this work upon which this guide is based).

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Seven Propositions

  • First
  • Second
  • Third
  • Fourth
  • Fifth
  • Sixth
  • Seventh

“To draw the Equinoctial Sundial, it is necessary to know some propositions whose thorough understanding is needed to make the various dials.”

On June 12, 1526, Hartmann completed Book One of his Practika. In this book we are introduced to the seven propositions that are necessary to make sundials and astrolabes.

Find a copy of Hartmann's Practika at a library near you

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The First Proposition

Draw a perpendicular line above a point marked out upon a straight line.

AS is the line . C is the point marked out on the line. You should set the two points D and E upon both sides, which arc located equally from C. Set the immovable foot of the compass at

point D and swing the movable above C and make a faint arc.

Afterward, with unchanged compass, that is, that you do not make wider or narrower, set the foot of the compass at the E and once again swing the other movable foot above this E and make the second faint arc.

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The First Proposition

Then draw a straight line through the point where each of the arcs cut through each other and through the point C. Such line is then a right angle or perpendicular line at the point C upon the line AS as marked out on the preceding figure.

That is self evident.

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The Second Proposition

Draw a right angle from a point marked outside of the given line.

AB is the given line and C is the outside point. Set the immovable foot of the compass at the point C and open the movable foot toward AB and describe an arc which intersects the line AB at two points. Letter these points D and E.

After that, set the immovable foot of the compass at the D and open the movable foot as weide as you please and make an arc. Then set the immovable foot of the unchanged compass at point E and again swing the compass and describe an arc.

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The Second Proposition

Then draw a straight line through the points where these circles intersect each other and through the point C. That then is the line that is drawn at a right angle to AB from the outside point C.

That is self evident.

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The Third Proposition

You now mark out a line over a point. This is how you should draw a parallel line from that same point.

BC is the line marked out, as long or short as you want, and A is the point through which you will draw a line parallel to BC. You should now draw a right angle line, which is AE, from the pint A to the line BC, as you have already learned in the

Second Proposition.

After that, make a center point D where convenient on the line BC and describe a cemicircls whose radius is equal to the length AE.

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The Third Proposition

After that, draw a line through the point A at the length of the line BC and which is drawn to contact the semicircle below. That then is the parallel line that you have sought.

That is self evident.

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The Fourth Proposition

Given a line, you should draw a right angle to the end of the same line.

You will now draw a right angle to the point B, above itself at the end point of the given line AB. Set the immovable foot of the compass at the point B and open the other foot to as wide as you want toward A and make a semicircle (arc). Mark the point C awhere the arc cuts the line AB. Thereafter, set the immovable foot of the unchanged compass at the C and once again make an arc through point B with the other foot. The two arcs will intersect together at D. After that, set the unchanged compass with one immovable foot at D and again make a small arc above the point B with the other foot. That arc is EF.

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The Fourth Proposition

After that, lay the rule upon the points C and D and draw a straight line through out. Then make a point G where this line cuts through the small arc EF. After that, connect B and G with a straight line. Thus you have a right angle that goes over itself at point B of the line AB.

That is self evident.

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The Fifth Proposition

Bring three points that do not stand on a straight line into one circle.

There are three points A, B, abd C. To bring into one circle, set the immovable foot of the compass at the point A and open the other foot as wide as you want toward the point B and make a faint semicircle (arc). Afterward, set the immovable foot of the unchanged compass at B and again make a faint arc toward the A. These two arcs intersect together at D and E. In the same way also make an arc with unchanged compass at the point C and also make a faint arc toward point B. These two circles intersect together at F and G.

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The Fifth Proposition

Afterward, lay the rule upon the two points D and E and draw a straight line further out. Next lay the rule upon the points F and G and also draw a straight line. These two lines intersect together at point H. Point H is at the center. Yo should set the immovablefoot of the compass into it and open the other foot far enough so that you reach each of the points A, B, and C.

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The Fifth Proposition

After that, go around with the compass and make a circle so that the three points are drawn up into it. In this way you may bring three points, that do not stand on a straight line, into once circle. As such, they shall be reproduced in this way.

That is self evident.

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The Sixth Proposition

Finding the midday line upon a flat plane at the land at which you reside.

Take a plane that stands flat, prepared by a water level, so that it hangs nowhere but stands flat. Draw a circle upon such plane, long or small,. Accordingly you have a plane, large or small, and E is the center.

Erect a style EP over E perpendicular to the plane at such a length that the shadow of the style that is at its shortest about the midday remains within the circle for approximately one or two hours the same day.

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The Sixth Proposition

After that, look for the midday line as follows. When the sun shines before midday, then diligently mark where the last point of the shadow of the style contacts the circle and enters into the circle. And where the last point of the shadow touches the circle, make a point A upon the circle. Afterward, after midday, when the shadow again will become long and once again desires to move out of the circle, to pass as it hence entered, then mark where the last point from the shadow once again contacts the circle. Mark the same point with C.

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The Sixth Proposition

Afterward divide that between A and C into two equal parts and mark out the middle point with B and then draw a straight line through the circle from the point B, through the center E. Such line is BEF and from which day thereafter, to time everlasting, the shadow touches the line BEF when it is all right and true South, from which line all sundials should be made, ordered, and regulated.

Thus that from E toward the point B is toward the North, and that from E toward F lies toward the South. You then draw a right angle line to this line, through the circle, which is GH. Then G is toward the East and H indicates the true West.

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The Sixth Proposition

Conclusion

This proposition is exquisite and good. If you wish to build a house, then it will have more sun when the residence is toward the South. The church should likewise be built according to such marked out line.

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The Seventh Proposition

Construct a fourth of a circle or quadrant by scribing the whole circle.

It is obvious that a circle circumscribes a right hexagon figure within itself so that the sides of the same are equal to the radius of the same circle. The hexagon figure is inscribed into it. Out of it follows that you will produce one fourth of a circle that you would like to have by forming a whole circle.

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The Seventh Proposition

Set the foot of the compass at a point which is A and make an arc to approximately a quarter of a circle or more. Then make a straight line from the center A to the end of the circumference or perimeter, which is AB, which line is one side of the quadrant. After that, do not change the compass and set the immovable foot of the compass at the point B and swing the movable foot onto the arc and make a symbol, which symbol you should mark by C on the arc wnd which holds 60 degrees. Then divide the arc between B and C into two equal parts.

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The Seventh Proposition

Therefore the one part set above the C holds 30 degrees and that will be to the end of the quadrant, which should be marked out with the D. Make a line from the end D until at the center A, which is the second side of this quadrant.

That is self evident.