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Tabvla Festorvm – Table of important Catholic dates from Opera Mathematica
|| 8/13/2008 || 6:32 pm || Comments Off on Tabvla Festorvm – Table of important Catholic dates from Opera Mathematica || ||

Page 394 in the Fifth Volume of Chrisopher Clavius’s Opera Mathematica (1612)
Courtesy of the Mathematics Library at the University of Notre Dame

One of the chief architects of the Gregorian Calendar was Jesuit mathematician & astronomer Chrisopher Clavius. In his “Romani calendarii a Gregorio XIII restituti explicatio” (Rome, 1603) he explained the process behind the creation of the Gregorian Calendar. The table above shows the contemporary dates of the Pentecost, Septuagesima, the Paschal Full Moon as well as some other calculations that are hardly used today. Shortly after his death in 1612, this explanation was republished in volume five of Opera Mathematica.

This volume, known as the explanation of the Gregorian Calendar, literally features hundreds upon hundreds of charts like the one above that show the Roman Calendar going thousands of years into the future. Seriously, its truly amazing how far into the future his tables go! If I had some more time to dabble around with his calculations, it would be neat to see how far they are off after nearly 400 years.


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The Use of the Analemma – As explained around 1780
|| 8/1/2008 || 4:54 pm || Comments Off on The Use of the Analemma – As explained around 1780 || ||

A couple months ago I posted the astrophotography of Anthony Ayiomamitis and went into some cursory detail in explaining what an Analemma was. Last night I was perusing the on-line collection of maps in the Library of CongressGeography & Mapping Division and came across Bowles’s new and accurate map of the world, or Terrestrial globe : laid down from the best observations and newest discoveries particularly those lately made in the south seas by Anson, Byron, Wallis, Bouganville, Cook, and other celebrated circumnavigators, illustrated with a variety of useful projections and representations of the heavenly bodies the most approved astronomical and geographical definitions tables, and problems with an easy and familiar explanation of the most curious and interesting phoenomena in the universal system. (yeah thats the official name of the map!)

It was published around 1780 in London for the proprietor Carington Bowles and it features quite a few ancillary maps, including a map of the solar system- both northern & southern hemisphere, astronomical latitude and longitude analemma (below), a chart of the world drawn according to Mercator’s projection, a map of the moon (a selenograph), and a diagram of seasons (which I absolutely love). I expect to reuse portions of this map for upcoming entries because its so laden with unique information. For example, there are drawings on how the planets looked like through the telescope and even the oldest drawings of sunspots that I’ve ever seen.

As for this entry, on the right side of the map are two spheres that were designed to teach the viewer how to understand the Analemma and use it to estimate the location of the Sun, planet, or any fixed star anytime in the past, present, or future. While I still haven’t fully wrapped my mind around the instructions, I have transcribed the text from the map below. There are a few errors and typos but I tried my best to keep the text as close to the original as possible.

By clicking on either of the images you can view a larger version and investigate the text yourself. As a decorative element, I used a portion of the tessellation I used to construct Meridian Hill Park Quilt #4 as the background.

The Use of the Analemma
The Analemma is a very useful (tho’ not commonly used) Projection of the Sphere on a plane. In this Projection the Eye is supposed to view the Sphere or Globe with all its Lines both real and imaginary from a Place so far distant that Mathematicians usually term this Distance in definite, and sometimes infinite.

In this Projection the Meridians and Circles of Declination as they are farther removed from the Centre of the Projection, appear nearer to each other and therefore more confused and on this Account Maps of the Earth and Heavens are generally delineated according to other Principles. Nevertheless there are several Properties belonging to this orthographic Projection, which are superior to all other Projections namely. 1st. In this Projection, the Circles of Latitude on the Earth’s Globe, from the Equator to the Pole, are all of them strait Lines, as are also all those Circles of equal Distance from London or any other Place on the Earth’s Globe all around London or any other Place. 2nd. The Distances of Places in the same Latitude are also measured by strait Lines in this Projection 3rd. The Meridians are Ellipses in this Projection and the Degrees of terrestrial Latitude are here measured on those Ellipses.

In like Manner for the Heavens 1st. The Parallels of the Sun’s and Stars Declination from the Equator, are in this Projection measured by strait Lines, which affords a very easy and elegant Construction of Properties of the celestial Sphere on a Plane. 2nd. The Parallels of Altitude for Sun or Stars at any Place on the Earth’s Globe are here also Strait Lines, Like the Parallels of Declination. 3rd. The Celestial Meridians, and the great Circles extending from the Zenith to the Nadir, in this Projection are Ellipses. 4th The Sun’s Declination North or South being but 23 1/2 degrees and the Degrees being in this Projection so near to an Equality from the Centre to the Tropic of Cancer and the Tropic of Capricorn, several of the most entertaining and useful Particulars relating to the Doctrine of the Sphere & Astronomy are more easily & elegantly solved by this Construction than any other.

From all which it follows that the Analemma or orthographical projection of the Sphere on a Plane is what everyone should understand who would not be at the expense of those expensive Instruments, Spheres, Globes etc., nor be at Pains and Attention enough to learn Mathematics and the necessary calculation.

On these Accounts we have given on the opposite side of this Map a Delineation which will be abundantly useful in the Application of the Analemma. And for a further Illustration of the Projection, Read what follows.

At the upper Part of this Map we have given a Table of the Sun’s Declination for the Beginning, Middle, and End of every Month throughout the Year, and which will be true till the Year 1808, by which Table and a single Proportion of Allowance for the Increase or Decrease of Declination, the true Declination for any Day may be easily found, also above we have given Geographical & Astronomical Definitions from which the Names of the several and respective Lines of the Earth and Heavens may be known.

Now supposing you would know the Hour of Sun Rising or Sun Setting or the Hours and Minutes of Time any Star, Planet, or the Moon is above the Horizon from the Rising to the Setting by the Analemma you first know the Latitude of that Place of the Earth where the Answer is required for. Secondly you must know the Declination of the Phenomenon whether it be Sun, Moon, or Star, and by these you may find the Time of Duration above the Horizon thus Count the Degrees of Latitude from the Equator of the Analemma downwards towards its Pole and a Strait piece of Paper of Line laid from thence to the Centre will cut the Line of Declination and the elliptical Meridians Equal to the Length of the Half Day more than Six Hours when the Place and Declination are both alike that is both North or both South but less than Six Hours, when the Place of Declination are both unlike that is one North and the Other South and this assensional Difference being either added to or subtracted from Six Hours gives the Length of the Half Day, and consequently the Time of Rising or Setting of the Sun.

The like is also to be understood of the Rising and setting of the Moon, Planets, or Fixed Stars, with this Difference, that in these you mist know if the Moon, Planet, or Stars rise sooner or Later than the Sun, which you may known whither such Star as you enquire about doth by the above Hemispheres, but for the Moon and Planets you may have Recourse to an Ephemeris Another very curious and useful Problem in the Doctrine of the Sphere is solveable after the most easy and elegant Manner by the Analemma relative to the Crepusculum or Twilight its Beginning & Ending in any Place of the Earth & at any Time of the Year it is as follows Viz.Count as before mentioned from the Equator of the Analemma to the Latitude & draw a real or imaginary Line thro’ the Centre to the opposite Side of the Analemma, then in the Circumference of y3 Analemma count 18 Degrees on each side downward & where the Parallel of the Sun or Stars Declination cuts this Strait Line the Number of elliptic Meridians from the Centre shews the Ascensional Difference.

N.B. The Equator of the Analemma is the Line 180 to 180 thro’ the Centre.

In this Analemma the Place in the Ecliptic or Distance from the next Equinoctial Point being known (which the adjacent Table will shew) the Declination and Right Ascension of the Sun are known by Inspection and for the Moon or Planets which have Latitude if such Latitude be reckoned from the Ecliptic towards the Ecliptic’s Pole the Declination & Right Ascension answering to such Latitude will be known by Inspection in the Analemma the Use of which will appear to such as know a little of the Sphere.

As the Fixed Stars are carried forward according to the Order of the Signs 50 Seconds per Year this Analemma will readily shew the Place of any Fixed Star for any Time past present or to come if its present Place be known & Contra.




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Tabvla Temporis [Semidiurni in fignis Borealibus / Australibus]
|| 5/25/2008 || 12:17 am || Comments Off on Tabvla Temporis [Semidiurni in fignis Borealibus / Australibus] || ||

This is the reverse side of Willem Janszoon Blaeu’s Nova totius terrarum orbis geographica ac hydrographica tabula (Amsterdam 1606) which I used in my recent creation A New & Arabesque Map of the Hirshhorn Museum. If you look closely, you can see the reverse of original map that bled through the paper after couple hundred years and some image manipulation. The table shown is similar to an Ephemeris, which is table of values that gives the positions of astronomical objects in the sky at a given time. I would love for someone to sit and explain the way one goes about reading these types of antique charts. I understand a fair amount of what is being shown, but I do not fully grasp how to apply the calculations.



A New & Arabesque Map of the Hirshhorn Museum & Sculpture Garden
|| 5/23/2008 || 10:43 am || Comments Off on A New & Arabesque Map of the Hirshhorn Museum & Sculpture Garden || ||


:: saved at 6,480 x 5,040 ::

To celebrate the new procedure I decided to get around to editing the Library of Congress‘ copy of Willem Janszoon Blaeu‘s Nova totius terrarum orbis geographica ac hydrographica tabula, which was published in Amsterdam in 1606. I removed the original map from the center and kept the decorative border similar to Nova et Accvratissima Totivs Terrarvm Orbis Tabvla, A New Map of the Terraqueous Globe : according to the the Ancient discoveries and most general Divisions of Geospatial Art, America as a Cloverleaf, and A New And Accurate Map of the World by John Speed. However, unlike the previous antique map mash-ups, which usually feature the earth laid out in two hemispheres, this map uses a rectangular space (Mercator?). The beauty of this open layout is that I can place any of my previously made maps inside of this 402-year-old template.

A common naming practice I’ve noticed in old map is the use of “New & Accurate” and since I like to play around with words, I changed Accurate to Arabesque to create a visual pun. The source map was about 6,500 pixels wide, I underlaid a rotated 9,000 x 6,000 copy of Hirshhorn Quilt to fit perfectly in the center of the new map. I think it would be fun to actually hand-color the engravings on this map to match other copies of this map which have the various figures colored in. The LOC’s copy is uncolored which means that its actually easier to add color to it than if it were already colored because pigment matching is not needed.



: detail of the planet Goddess Venus :

Across the top (left to right) you have the planet gods:

Drawn within each of these engravings are the signs of the Zodiac that the planets rule:

Below I dissect the rest of the border of the map:

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Then & Now Birds-Eye Views of the Westminster Neighborhood in Washington, DC [1884 & 2005]
|| 4/14/2008 || 12:42 pm || Comments Off on Then & Now Birds-Eye Views of the Westminster Neighborhood in Washington, DC [1884 & 2005] || ||

Detail the bicycle track before Westminster Street was created
from Adolph Sachse’s birds-eye view of the nation’s capital, 1884

Due to file format issues, only recently have I been able to open most of the maps available in the Library of Congress’ American Memory Collection. Last night I found an interesting birds-eye view map of Washington, DC by Adolph Sachse that was published in 1884. Its a massive map that appears to be composed of six separate sheets and contains a listing of many of the businesses in Washington City as well as locations of various public & government buildings. In many ways the map acts like a geovisual address book (the phone had not been invented yet) because, at a glance, one can easily find services offered by local merchants. Judging by the branding in the upper right hand corner of the original map, it appears that the map was sponsored by the Baltimore & Ohio Railroad Company, a major railroad company of the day.

According to my neighborhood’s official history, Westminster Street did not exist in 1884 and the birds-eye view above supports this claim. While not labeled in the image above, Parcel 362, as it was known on the original DC maps, was called also called “the old circus ground” and Athletic Park. It had a 150-foot long grand stand along T Street, which was built in 1883 (building permit number 1047) in preparation for the fifth national convention of the League of American Wheelmen, a national organization of bicyclists. The first American bicyclist to ever ride 100 miles on an outdoor track did it on that track in 1884. As someone who uses a bicycle as their primary means of urban transportation, I can only smile knowing that 121 years ago my residence was an outdoor bicycle race track. However, I laugh because I traveled with an exgirlfriend’s family circus when I was younger!

Below is a birds-eye view of the Westminster Neighborhood published by Microsoft, with imagery of Pictometry International. It features imagery that was taken in 2005 and when compared, you can see how much the area has changed in the last 121 years. The Athetic Park is gone and in it’s place are dozens of rowhouses that were built shortly after the map above was published. A unique and historically aware addition to the neighborhood is something you can see below in the playground on Westminster Street. No, it’s not because that is where I had my exhibit “North, South, East, Westminster“. Rather, if you look closely, you can see a small race track! A scaled reminder of what once was.

Detail of the Westminster Neighborhood by Microsoft, with imagery of Pictometry International



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The Yu Ji Tu map [1137] and a map of the distribution of Moslems in China [1922] via Rev. Claude L. Pickens, Jr.’s trip to northwest China [1936]
|| 4/11/2008 || 6:42 pm || Comments Off on The Yu Ji Tu map [1137] and a map of the distribution of Moslems in China [1922] via Rev. Claude L. Pickens, Jr.’s trip to northwest China [1936] || ||

Page 6 of Rev. Claude L. Pickens, Jr. photo album featuring the photograph of the Yu Ji Tu
Image from the Harvard University Library

Last night I came across Harvard Library’s digitized photo album of Rev. Claude L. Pickens, Jr.’s trip to northwest China. Of all things to have on the inside of the album cover, there was a small map showing “Moslems in China”. After flipping through a few pages I spotted a photograph of one of China’s most famous maps: the Yu Ji Tu.

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Globe Graffiti – Continued
|| 4/8/2008 || 2:01 pm || Comments Off on Globe Graffiti – Continued || ||

Las month I posted photographs of the aftermath of DEBT tagging my friend’s antique globe that I had once used in an art installation. Today, via DECOY’s blog, I find censored pictures of DEBT in action.

Also, for the visually astute, the painting in the background by DECOY (I believe it’s called “Two Headed Monster”) was used as the cover of the popular book The Beautiful Things That Heaven Bears by Dinaw Mengestu.



The National Archives Experience: Digital Vaults, and a correction request
|| 4/2/2008 || 12:25 pm || Comments Off on The National Archives Experience: Digital Vaults, and a correction request || ||

I was recently directed to the the National Archives’ Digital Vaults webpage. After the flash animation was loaded up, I was greeted by a nice visual interface (above) that shows various items that are digitally scattered within the vault.

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Antique Stained Glass Sundials
|| 3/27/2008 || 3:27 pm || 2 Comments Rendered || ||

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ordered last week: New Blaeu
|| 3/10/2008 || 9:25 pm || Comments Off on ordered last week: New Blaeu || ||

New Blaeu by Nikolas Schiller

Originally created last summer as “NOVA ET ACCVRATISSIMA TOTIVS TERRARVM ORBIS TABVLA [2007 Remix],” when this map was published in the December 14th issue of the Christian Science Monitor, the editors truncated the name and simply called it “New Blaeu.”

Last week I decided to update the map slightly by trimming the edges and doing some color correction. It’s being printed at 20″x16″ and preserved behind glass in in an ornate gold frame. I am also planning on framing some of the other antique maps I purchased recently to compliment this map. I think they’ll look really cool all hung together; the real old with the fake new.

View the other detail:

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