Talk:Astrolabe

References (for University of Edinburgh course Stars, Robots & Talismans)
'''Bibliography for National Museum of Scotland al-Saffar astrolabe ' Hernández Pérez, Azucena, Catalogo razonado de los astrolabios de la Espana medieval'', Madrid 2018, pp 43-49.

Hernández Pérez, Azucena, Astrolabios en al-Andalus y los reinos medievales hispanos, Madrid 2018, p 96.

Jones, Jean and Uhl, Mary (eds.), Under One Roof, Edinburgh, 1996.

King, D. A., ‘Some Medieval Astronomical Instruments and their Secrets’, in Mazzolini, R. G. (ed.), Non-Verbal Communication in Science prior to 1900, Florence 1993, pp.29–52.

King, David A. 'Medieval Astronomical Instruments: A Catalogue in Preparation' in Bulletin of the Scientific Instrument Society No 31 (1991), pp 3-7.

Macdonald, A. and Morrison-Low, A.D., A Heavenly Library: Treasures from the Royal Observatory's Crawford Collection, Edinburgh, Royal Observatory and NMS, 1994, p. 24.

Maddison, F., and Turner, A., Science and Technology in Islam, exhibition catalogue, London 1976, pp.104–6.

Plenderleith, R. W., ‘Discovery of an Old Astrolabe’ in The Scottish Geographical Magazine, Vol. 76, No. 1, 1960: 25.

Phillips, P., The Collectors’ Encyclopeadia of Antiques, London 1973, p.604, fig. a.

Glairedanderson (talk) 20:42, 8 October 2020 (UTC)

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Applications
It lists that there are around 1000 applications, what are some of the more common ones that were heavily used? How was the astrolabe able to do it? Krjwvq (talk) 18:00, 19 February 2021 (UTC)

Dubious claim an armillary sphere is an astrolabe
I was surprised that what is seemingly-obviously an armillary sphere, or at least obviously a sphere, was labeled as an astrolabe. It's a depiction of a sphere. It's not a flat disk. I don't see any pointers for stars like an astrolabe has. Don't see a rete or alidade. Not sure how it could be an astrolabe. I tried to look at the source for the claim, but it's a book I don't own in a language I don't read.

I did a quick search and grabbed the first 2 journal objects that discuss it, both call it an armillary sphere. One even includes it as a figure along with their tracing: https://www.mdpi.com/arts/arts-08-00062/article_deploy/html/images/arts-08-00062-g005-550.jpg

When I searched for sources that claim it's an astrolabe, I found one -- this wiki. Skintigh (talk) 23:19, 30 August 2023 (UTC)


 * My understanding is that the word "astrolabe" did not originally refer to the planar version, but to something more like an armillary sphere. This predictably causes some confusion. Cf. . Sometimes people specify that they mean a "planispheric astrolabe" or the like. –jacobolus (t) 23:27, 30 August 2023 (UTC)
 * Ha, I was just editing my comment to say almost the same and got a collision.
 * I wondered if it was a mistranslation from German from Greek?
 * I also note the image filename is "astrolabium" not "astrolabe." Ptolemy called the armillary sphere "astrolabon" and I swear I saw them called "astrolabium" somewhere... Skintigh (talk) 23:35, 30 August 2023 (UTC)
 * From what I can tell those are all synonyms caused by non-uniform translation/transliteration. –jacobolus (t) 23:43, 30 August 2023 (UTC)
 * I can't speak for the time of Ptolemy, but they are absolutely not synonyms anymore. Not for the last... I dunno, between 500 years and 1,800 years.
 * And "Astrolabium" may never have been a synonym. I did some searching and found: an astronomical compendium, a book named Astrolabium from 1575, some clocks named that, and a wristwatch, but no astrolabes nor spheres called that.
 * Closest I found was this mangled description: "Astronomical Compendium or Astrolabium (Astrolabe)"
 * https://www.toledomuseum.org/art/provenance-and-repatriation/astronomical-compendium-or-astrolabium-astrolabe
 * They have a picture of an object that seems to clearly be not an astrolabe, but is definitely an astronomical compendium. But perhaps it has astrolabe features as well that I can't see?
 * The only source that implies Astrolabium was the name of an astrolabe is this wiki, in 2 places:
 * 1) a mislabeled/confusingly labeled photo which displays an astrolabe but names the book instead of the image. I clarified it.
 * 2) This image (that may not belong in this wiki): File:Het gebruik van het astrolabium door Amerigo Vespucci, Jan Collaert II, Museum Plantin-Moretus, PK.OPB.0186.018.jpg
 * Is the orphaned word "Astrolabivm" related to the contents of the image? Or is it the title of the source book? Just an artistic name for the image? Does it mean "navigation" or "star gazing?"
 * Either way, it seems the image does NOT depict an astrolabe. There is what appears to be an armillary sphere on the table, and another armillary sphere in his hand. However, he's holding the armillary sphere the way one would hold an astrolabe... but looking over the top of the sphere rendering it completely useless. Maybe he's just doing arm workouts?
 * I wondered if it was this a spherical astrolabe, but the few photos I found of those showed a solid sphere, would be tough to look through that. But I guess if he's looking over the top it doesn't matter what he's holding. Could be a coconut or soccer ball.
 * I suspect this is just a confused artist drawing the wrong tool held the wrong way with the wrong label. It may even be based more on Dante's Purgatorio than reality.
 * Maybe this bizarre and (at best) misleading image shouldn't be in the wiki.
 * Same for the Mosaic.
 * They aren't even the right shape... Skintigh (talk) 04:53, 31 August 2023 (UTC)
 * Most of the sources containing "astrolabium" at the internet archive (~8500 sources in total) seem to be written in German or Dutch. A bunch are from the 20th century. From what I can tell they use it to mean "astrolabe". –jacobolus (t) 05:29, 31 August 2023 (UTC)
 * Actually, it does look to me like an (octagonal rather than circular) astrolabe. There is what looks like a gnomon standing upright in the center of the plate, and the darker-colored Rorschach blob spread over it could well be a rete denoting star positions. As for “compendium,” that might refer to the instrument hanging (pendere) from a chain or cord when in use. I’m pretty sure that object is an astrolabe.
 * Dodiad (talk) 06:59, 31 August 2023 (UTC)
 * Are we looking at the same picture? Where do you see an octagon? I see what appears, to my eye, an inkwell with a quill in it, sitting towards the rear of the table. Is that what you're looking at? I was referring to what looks to me like a sphere in his hand and another at the front left side of the table. [edit: wait, were we talking about the mosaic? Sorry, it's been a while...]
 * Anyway, I think I found an answer!!!!!!! From a note in a translation of the Almagest Book V On the construction of an 'astrolabe' instrument:
 * An adjective! How's that for a twist?
 * So the armillary sphere was never called an "astrolabe," (the noun) by Ptolemy. At least per this source.
 * And the adjective can be correctly applied to an armillary sphere, to an "astrolabe" (the noun), and many other instruments which could explain the term popping up elsewhere (and the later confusion). Including in the above picture, where he is certainly taking the position of stars. Skintigh (talk) 20:23, 14 October 2023 (UTC)
 * We were already previously discussing Toomer's note here. This doesn't really seem like a "twist" to me. The relevant section is called "Περὶ κατασκευῆς ἀστρολάβου ὀργάνου" [On the construction of a star-taking instrument]. Abbreviating "ἀστρολάβου ὀργάνου" as "ἀστρολάβος" is an entirely ordinary kind of linguistic transition. If Theon (2 centuries later) called the planispheric astrolabe the "little star-taker", it stands to reason that "little" was in comparison with some "bigger" instrument, which most plausibly would be the same "star-taking instrument" of Ptolemy. –jacobolus (t) 20:55, 14 October 2023 (UTC)
 * Okay, seeing your quotation of Toomer's note led me back to the shelf, to Neugebauer (HAMA II 866 ff.). Here's what Neugebauer says (p. 871):
 * The term "astrolabe" is used by Ptolemy in the Almagest for the armillary sphere, described in detail in Book V, 1. Probably the "horoscopic astrolabe," recommended in the Tetrabiblos for accurate observations, is a similar, if not the same, instrument. In the Geography (I, 2) "astrolabes" are mentioned as instruments for the determination of geographical coordinates, thus most likely again referring to the armillary sphere which would serve this purpose wlel. Thus we can be fairly sure that the term "astrolabe" in the time of Ptolemy only means instruments for the observation of positions of celestial bodies, but not the planisphaerium. ¶ [...] I think one can describe Ptolemy's "horoscopic instrument" as an anaphoric clock, but not of the Vitruvian type (preserved in Salzburg and Grand) but with the equator and horizon coordinates fixed and the stars with the ecliptic made movable. ¶ It is also clear that the term "astrolabe," meaning to take, to observe, the positions of a star, has originally nothing to do with the planisphaerium which only performs the functions of a celestial globe in a convenient planar projection. Only when the central pivot which is needed for the spider is utilized to carry on the other side of the disk a diagonal ruler equipped with sighting holes the instrument becomes and "astrolabe." Held in vertical position the circular rim can be graduated for the observation of altitudes of stars of of sun and moon. We have no reason to assume such a combination with a "diopter" for Ptolemy's "horoscopic instrument"; but we will see that this transformation to an "astrolabe" was known to Theon.
 * The following pages of HAMA are also well worth reading for anyone trying to figure out the early history of astrolabes. –jacobolus (t) 21:36, 14 October 2023 (UTC)
 * According to Neugebauer, the works on the Astrolabe by John Philoponus and Severus Sebokht are both derivative of a work by Theon of Alexandria. Later al-Yaʿqūbī credited Ptolemy for more or less the same work (al-Yaʿqūbī only gives a table of contents for the first 2 (of 4) parts, including the section about the plane astrolabe, but his table of contents is nearly identical to the organization used by Sebokht, suggesting both were working from a common source), but it seems likely that he was substituting the name of Ptolemy for Theon.
 * Apparently Ptolemy's Almagest and also Proclus's Hypothyposis consistently used the name "astrolabe" to mean armillary sphere, but Theon used the name "little astrolabe" to refer to the plane astrolabe. Medieval sources started using just "astrolabe" to mean the plane astrolabe. –jacobolus (t) 04:48, 31 August 2023 (UTC)
 * No sure if you get notified of my other reply, but I think I found the answer and posted it above.
 * Long story short: "astrolabe" was an adjective in Ptolemy's time, and he used it as such, he never called the armillary sphere that name as a noun.
 * It became a noun in Theon's time. Skintigh (talk) 20:43, 14 October 2023 (UTC)
 * Long story short: "astrolabe" was an adjective in Ptolemy's time, and he used it as such, he never called the armillary sphere that name as a noun.
 * It became a noun in Theon's time. Skintigh (talk) 20:43, 14 October 2023 (UTC)

@,, : So what is the conclusion here? I’m having a bit of trouble following the argument. The point at issue seems to be the claim that the Casa Leda mosaic is the earliest known depiction of an astrolabe. As the claim is unverifiable to me (the nearest copy of the source book being over 200 miles away and in a foreign language; does anybody know what it actually says?) and as the sources in the image caption are unequivocal that it is in fact an armillary sphere, I can’t really see any justification in keeping either the statement or the image here. Is anybody here arguing that they should stay? If there are no objections I propose to remove them from the article. Thoughts? Moonraker12 (talk) 22:32, 24 September 2023 (UTC)


 * I think the article's Etymology/History sections need to do a better job describing the early meanings of the word "astrolabe", but I don't feel like I know the subject well enough to write it. I've been slowly working my way through sources about Ancient Greek astronomy/mathematics, but am by no means any kind of expert. –jacobolus (t) 23:17, 24 September 2023 (UTC)
 * @ : Well, I don't disagree about the etymology; but do you think the statement and image in question should stay, or are you OK with me deleting them? Moonraker12 (talk) 16:38, 29 September 2023 (UTC)
 * I think it's worth discussing and linking some kind of picture of an armillary sphere at the beginning of the history section. This mosaic happens to be one of the older extant depictions of an armillary sphere, but we could also use a photograph of a later 3d artifact. –jacobolus (t) 16:40, 29 September 2023 (UTC)
 * I don't believe our current text is supportable as a simple statement of fact: An early astrolabe was invented in the Hellenistic civilization by Apollonius of Perga between 220 and 150 BC, often attributed to Hipparchus. The astrolabe was a marriage of the planisphere and dioptra, effectively an analog calculator capable of working out several different kinds of problems in astronomy. But I want to do a bit more research in the literature to figure out what the best modern scholarship has to say about this question. We should sort out and clearly label which parts have direct evidence vs. which parts are speculative.
 * credits Eratosthenes with the armillary sphere (originally called an "astrolabe") but there were surely earlier examples of solid globes used for explaining astronomical phenomena, if not armillary spheres per se. –jacobolus (t) 16:49, 29 September 2023 (UTC)
 * @ : OK, but this page is about the astrolabe, specifically the planar astrolabe, so having an image of an armillary on it just confusing... Whatever the history of the word might be. And I don't disagree with you about the 'current text as a simple statement of fact' but I don't see what bearing it has on the question at hand. Pictures here should be of astrolabes (ie. what we currently understand to be astrolabes); pictures of armillaries belong on the armillary sphere page. Moonraker12 (talk) 17:03, 29 September 2023 (UTC)
 * My point is that the planar astrolabe didn't emerge in a vacuum: it was an evolutionary step in a tradition of Greek representations of the celestial sphere on a solid/armillary sphere, and related spherical-geometry/-astronomy problem solving methods like the analemma (which we don't currently have an article describing). There are a bunch of extant examples of pictures showing astronomers/geometers/philosophers standing around pointing at spheres which indicate that this was a standard method of astronomical education/research.
 * Theon of Alexandria's (4th century AD) term "little astrolabe" meaning planar astrolabe evolved out of the word "astrolabe" meaning armillary sphere in Ptolemy's day. It's not clear to me what the planispheric astrolabe was called in the 2nd century, but according to Neugebauer Ptolemy mentions it in his book Planisphere as a "horoscopic instrument". So far as I know we don't have any earlier direct evidence, but some scholars speculatively give credit for the stereographic projection or even the planispheric astrolabe as a device to Hipparchus, Apollonius (on the basis that Conics contains a theorem relevant to the stereographic projection), Archimedes, or even Eudoxus.
 * I think this article should describe (briefly) that the spherical astronomy model on which the planispheric astrolabe is based developed in Greece in the 5th–4th century BC, that astronomers/geometers used solid spheres and later armillary spheres as a physical representation, that the stereographic projection was probably known sometime before Ptolemy but we don't have precise evidence about it, that at Ptolemy's time the word astrolabe was used to mean armillary sphere but that the planispheric astrolabe existed in some form as a physical device by then, that Theon of Alexandria called the planispheric astrolabe the "little astrolabe", and that eventually the name "astrolabe" came to refer predominantly to the planispheric astrolabe with the armillary sphere getting called something else. I think it's worth including a (clearly labeled) picture of an armillary sphere in that discussion. –jacobolus (t) 17:33, 29 September 2023 (UTC)
 * OK, thanks for explaining:
 * I can appreciate that the term astrolobos could well cover a whole family of scientific /astronomical instruments (armillaries, planar astrolabes; Celestial globes? Orreries? ) But if so that would be better dealt with in a dedicated article on the astrolobos, covering the early development of it (or them), and their diversification into the instruments we know today.
 * As this article is focussed on the planar astrolabe (which is currently what the word refers to), tacking on the sort of broad description you seem to be suggesting would be confusing (IMO): It should be enough here to say that the planar astrolabe (as currently known) is descended from the astrolobolos (whatever that might be).
 * The history of the instrument isn’t something I know a lot about; I mainly came here to find out what an astrolabe actually did (having found a book saying it was an early timepiece! I thought it was a navigation aid!) Moonraker12 (talk) 19:50, 30 September 2023 (UTC)
 * This article does not need to go into an extensive history, but only put the planar astrolabe in 1–2 paragraphs of context and explain that the name astrolabe formerly meant armillary sphere. –jacobolus (t) 20:21, 30 September 2023 (UTC)
 * Agree with jacobolus. Dodiad (talk) 21:09, 30 September 2023 (UTC)
 * Hang on: a minute: It’s one thing to say that the astrolobos (whatever that might have been) was the precursor of the planar astrolabe and the armilla; it’s quite another to say that 'astrolabe' is an old word for an armillary sphere. Where is the evidence for that ?
 * For one thing the astrobolos was an instrument for making observations through, while an armillary is a device for making calculations (viz. here)
 * For another this assumption ignores the spherical astrolabe (which confusingly refers to two quite different articles; the later is this thing, which has a spherical rete and a ball-shaped tympanum) the earlier might well have looked something like one of these things.
 * So no, I don’t think you can say that… Moonraker12 (talk) 23:04, 1 October 2023 (UTC)
 * Ptolemy only ever uses the name "astrolabe" to refer to an armillary sphere (described in Almagest 5.1). Apparently Proclus also uses the same name in his commentary.
 * From what I understand, we don't have mention of other meanings for "astrolabe" until the time of Theon of Alexandria. Disclaimer: I am not an expert on this topic. –jacobolus (t) 23:32, 1 October 2023 (UTC)
 * The description of this armillary sphere can be found on page 217ff. in Toomer's translation here. Ptolemy's Planisphere mentions the planispherical astrolabe as a device, but just calls it a "horological instrument" and doesn't give it any specific name. For more about this instrument, Toomer recommends Rome (1927) (in French). –jacobolus (t) 23:39, 1 October 2023 (UTC)
 * Ptolemy never used it as a name for the armillary sphere. It seems the word wasn't a noun then, it was an adjective, and described any tool or component used for "star taking."
 * 2 centuries later it was used as a noun for what we still call an astrolabe. I posted a little more detail above with a source. Skintigh (talk) 20:49, 14 October 2023 (UTC)
 * PS: I've been wondering if some of the confusion this has engendered is because the word still means different things to different people (The source for the statement in question is a book in German; does the word in German cover armillaries as well as planar astrolabes?). Just a thought... Moonraker12 (talk) 19:52, 30 September 2023 (UTC)
 * @, : So, are there any objections to my removing the offending statement and image? If not I will go ahead over the weekend. Moonraker12 (talk) 16:40, 29 September 2023 (UTC)
 * I have no objections, seems no one else does either. Skintigh (talk) 00:51, 18 February 2024 (UTC)

Dubious claim: break

 * So, I've had a look at the sources you provided (finally!), though I feel they raise more questions than they answer.
 * For the Almagest, it seems that the diagram isn’t something that’s original to Ptolemy’s text, but was added from the other book you mentioned by Rome. So we are taking his word for it that the instrument described (which I cannot fathom) is an armilla; what word did Ptolemy use for this thing? Did he (as the footnote seems to suggest) just use the word astrolobos to  describe what it did (ie. take the stars)? An instrument for 'astrolabing'?
 * For the book by Rome, I can’t read French, so it’s pretty lost on me, but the bits I could translate suggest the story is a bit more complicated than astrolabe being an old word for an armillary sphere. What exactly was a meteoroscope? What is a prism astrolabe (were they familiar with spectroscopy even then)? How many different instruments for astrolabing were there?
 * As for Neugebaur, he seems mainly interested in proving the establishing the antiquity of the plane astrolabe, but I’m guessing he’s German, (as, I presume, is Wolf) which brings me back to my previous question: Is this just a difference in language? Do Germans refer to both (or all) of these instruments as 'astrolabes'?
 * However, none of this resolves the question posed here, which is should we have an image of an armilla and a statement claiming it is the oldest depiction of an astrolabe on a page about what is now an altogether different instrument?
 * Also, there’s still no information on what this Wolf actually says, or whether this is an just an interpretation by whoever put it here; but as it is contradicted by two sources we can see, I’m inclined to dismiss it as unreliable. If he offers some explanation of the claim then that could be added to resolve the contradiction, but otherwise it needs to go. Do you have access to this work? Moonraker12 (talk) 23:29, 31 October 2023 (UTC)
 * I don't know who Wolf is.
 * From what I can tell that's right, calling this a ἀστρολάβου ὀργάνου (astrolávou orgánou, "star-taking instrument") refers to its purpose. The image is a "modern" reconstruction but the description is pretty explicit: "We took two rings of an appropriate size... ".
 * The resolution of the question posed here is that in my opinion we should explicitly say that the "planispheric astrolabe" or "planar astrolabe" is a combination of a dioptra and a planisphere (by which, in my impression, modern scholars mean a stereographic projection of the celestial sphere, as described by Ptolemy in his book Planisphere [not the original title] and probably dating from 2–3 centuries earlier), and we should also explicitly say that the model of celestial mechanics on which the planispheric astrolabe is based is speculated to have originated with Eudoxus (4th century BC), but that at any rate by the 2nd century BC people were using armillary spheres (e.g. the mosaic under discussion) as a physical model, and that by the time of Ptolemy but possibly 2–3 centuries before, "astrolabe" (or if you like "astrolabe instrument") meant an armillary sphere capable of measuring star positions. We don't have any evidence of a planispheric astrolabe per se until ~400 AD.
 * It's worth mentioning other kinds of "astrolabes" before the planispheric astrolabe in the history section for context, and maybe including an image of one (though I'd pick a different one than the mosaic photo), because this instrument didn't just arise in a vacuum. It can be seen as a convenient portable variant of a "star taker" of which there were perhaps a variety of designs at the time but at least we know about the armillary version described by Ptolemy. –jacobolus (t) 00:03, 1 November 2023 (UTC)
 * For more on Ptolemy and the armillary astrolabe see Thurston (2002) :
 * Ptolemy’s description of how he used the astrolabon is confused, lending credence to the suspicion that he did not actually use it.12 He said that when the sun and moon were both visible he set the longitude ring to the graduation on the ecliptic ring that marked the longitude of the sun. Next he turned the two rings together until they both overshadowed themselves. Then the astrolabon is properly set. He cannot have done this. His tables for the longitude of the sun were out by over a degree, so if one ring overshadowed itself the other would not. And it is not a sensible procedure: he needed only to turn the ecliptic ring until it overshadowed itself. There is no need for any calculation. It is in the second and third steps, in which the astrolabon is used to measure the coordinates of stars, that it is oriented by setting the longitude ring to a predetermined longitude. FN 12: Ptolemy’s description of the astrolabon is in Syntaxis 3.1. A reconstruction is shown in Figure 3. The astrolabon consists essentially of a graduated ring, which I call the ecliptic ring, that can be swung into the plane of the ecliptic. Two other rings can be rotated about an axis perpendicular to the ecliptic ring. The inner one is fitted with sights; I call this the sighting ring, the other the longitude ring. Ptolemy explained that at a time when the sun and the moon were both visible he set the longitude ring to the graduation on the ecliptic ring corre- sponding to the longitude of the sun and rotated the astrolabon until the intersection of the two rings was in the direction of the sun and the rings overshadowed themselves. He then rotated the sighting ring to sight on the moon and read off the longitude of the moon from the position of the sighting ring on the ecliptic ring. Ptolemy described the next step in Syntaxis 7.2. He found the coordinates of several bright stars as follows. He calculated the position of the moon just after sunset from an observation just before sunset, allowing for the changes in longitude and parallax between the two times of observation. He set the longitude ring to this calculated longitude and sighted the moon with it. He then sighted the star with the sighting ring and read off its longitude from the position of the ring on the ecliptic ring and its latitude from the sights on the ring. In Chapter 4 he explained that he observed as many stars as he could by setting the longitude ring to the longitude of one of these bright stars and sighting on the star being measured with the sighting ring.
 * –jacobolus (t) 00:39, 1 November 2023 (UTC)
 * Apparently Synesius' (c. 400 AD and somewhat vague) letter about an astrolabe-like instrument is the source for the attribution of the stereographic projection to Hipparchus. There's good discussion in Dicks, The Geographical Fragments of Hipparchus pp. 194–207. –jacobolus (t) 14:57, 3 November 2023 (UTC)

About the Latin West
In the article it is stated: ''in the mid-7th century. Sebokht refers to the astrolabe as being made of brass in the introduction of his treatise, indicating that metal astrolabes were known in the Christian East well before they were developed in the Islamic world or in the Latin West''

During this period there was no clear boundary between the Latin West and Orthodox East. Actually huge territories (fe. in Italy) still belonged to the Byzantine Empire. And the The East–West Schism, also known as the Great Schism only happened as late as 1054. Also for centuries high level marriages were arranged between dynasties in the Latin West and the Byzantine nobility and a constant diplomatic exchange took place. It should also be noted that Sebokht is an important historic figure, but he basically lived on the fringes of the Byzantine Empire. Being a Orthodox Syrian scholar and monk and hence more interest and informed about what was happening in Persia and Arabia. So the little that he wrote about this topic has to be taken with a grain of salt. 213.142.96.201 (talk) 17:16, 4 December 2023 (UTC)


 * I looked it up, and actually Sebokht didn't wrote a single word about where the Astrolabe was in use or where people may had knowledge about it.

https://www.tertullian.org/fathers/severus_sebokht_astrolabe_01_trans.htm