Kushyar ibn labbans introduction to astrology

The two fragmentary texts are: ff.


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The pages in the present manuscript cover II. This book was popular among the Jews of Yemen, and there are three other copies transcribed into Hebrew characters, all of them Yemeni identified by Langermann, , p. Arabic-speaking Jews copied out many, many Arabic books on science, philosophy, and other subjects into the Hebrew alphabet. The present manuscript is not complete; it lacks the definitions of astronomical terms that are found at the beginning of some copies, and it is also missing the third of the four sections into which the treatise is divided.

On the other hand, this copy has the full set of astronomical tables Brummelen cites only 4 Arabic-letter manuscripts that possess the complete tables, , p. It is by far the most complete of the Hebrew-letter copies, and, in fact, it appears to be one of the most interesting of all known copies of this early and as yet little-studied zij. Attention should be drawn in particular to the notes on ff. Moreover, the front and back matter, as well some of the marginalia, contain valuable technical comments.

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Five zijes mostly from around A. Please create a new list with a new name; move some items to a new or existing list; or delete some items. Kusyar ibn Labban's Introduction to astrology. Kusyar ibn Labban's introduction to astrology. Kusyar Ibn Labban's Introduction to astrology. Tokyo : Institute for the study of languages and cultures of Asia and Africa.

All rights reserved. Remember me on this computer. Cancel Forgot your password? The Ptolemaic value is 1,' [26,p. The Ptolemaic values for the minimum and maximum distances of the sun are 1," and 1,' [25, p. Kfishyr's values are 1,r and 1,'. Later in our text, Kushyr also uses 1,r and 1,' or I,' for the minimal and maximal solar distance. The fact that Ptolemy's and KDshyr's values for the distance of the sun are approximately 20 times less than the true value, is only.

Another reason. The magnitude of the body of the earth in terms of the body of the sun. Kflshyr assumes that the maximal distance of the moon to the earth is 64; 15', and that the mean distance of the sun to the earth is. Since the apparent diameters of the sun at its mean distance and of the moon at its maximum distance are equal, the ratio of the lengths of their diameters is equal to the ratio of their distances from the earth. This is true irrespective of the unit of length in which the lunar and solar diameters are expressed. Kushyr now introduces a new unit of length, which we will call 1", in such a way that the diameter of the moon is 64;15".

This is what K[shyr means when he says "we take : the distance of the moon as its diameter". Because 64; 15" " " 64;75' : ', the diameter of the sun, expressed in the new unit is 1. In general, if a celestial body has an apparent diameter equal to that of the moon at maximum distance, and its distance to the earth is A" for some number A, then the length of its diameter is 4".

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This principle will be used below for the determination of the volumes of the planets. Klshyr's method is an elaboration of a method mentioned by Ptolemy tnthe Planetary Hypotheses. Therefore the ratio of the diameter of the sun to that of the earth is I,20BB : 5. Thus the ratio of theirvolumes can be found as 5. The length of the shadow of the moon. This paragraph presents several problems which we have not been able to solve. They may have been caused by imperfect transmission of K[shyr's text. K[shyr actually computes the minimum length of the shadow of the moon, because he takes the moon at maximum distance 15" from the earth.

In the corresponding figure, the calculation of? KDshyr does not provide computations but states the result as ' , that is to say, equal to his own maximum distance of the moon. The equality of the minimum length of the shadow of the moon and the maximum distance of the moon from the earth implies that the apparent solar disc can be completely eclipsed by the lunar disc even in solar eclipses that occur at maximum distance of the moon' The same assumption was made by Ptolemy in the Almagest.

The distance and volume of Mercury. Klshyr adopts Ptolemy's onion-like model of the spheres of the celestial bodies for the minimum and maximum distances of the moon, Mercury, Venus, the sun, Mars, Jupiter and Saturn [11, pp. This model is presented in Ptolemy's Planetary Hypotheses, which has been preserved in an Arabic translation Kitdb al-manshurat or Kftab al-iqtisas and in a Hebrew translation as well [11, p. In this model, the maximum distance of each celestial body is equal to the minimum distance of the next body in the above-mentioned order.

For Ptolemy, this equality between maximum and minimum distance of successive planets is the result of a philosophical principle to the effect that there cannot be useless space. Kiishyr deduces the equality from alleged parallax observations, which show that the parallax of a planet at maximum distance is equal to the parallax of the next planet at minimum distance. Such parallaxes were impossible to observe for the sun and the planets. According to modern astronomical data, the planet which comes closest to the earth is Venus, at a minimum distance of approximately 40 million km.

Thus the maximum parallax of any planet is less than o;1o.

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Kflshyr comectly states the mathematical principle that the ratio of the maximum distance of a planet to its minimum distance is very closely equal to the inverse of the ratio of its apparent diameters at these distances. We note that the maximum apparent diameters of.

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Venus and Jupiter are 0; 1,6o and 0; 0,50o according to modem astronomical data, so the apparent diameter of any of the five planets Mercury, Venus, Mars, Jupiter and Satum as well as the fixed stars could not have been observed in ancient Greek and medieval Islamic astronomy. So again Kushyr's account is misleading. Ptolemy derived the ratio between maximum and minimum distance from the geometical model eccenter with epicycle of the planet. Kushyr's values for the ratio between maximum and minimum distance are close to those of Ptolemy.

In the geometrical figure, Kflshyr then attempts to determine the diameter of Mercury in the new unit of length " which he defined above for the computation of the volume of. In the corresponding figure, BG is the diameter of a body at the mean distance AG : r of Mercury but with an appaent diameter equal to that of the moon at maximal distance and the sun at mean distance.

Therefore BG : ". Thus the ratio of the volume of the earth to that of Mercury is : 21, x 22, For the Ptolemaic value see the table at the end of the next section of the commentary. Note that the geometrical figure is confusing because D. E does not represent a celestial body at distance AE.

Mercury was a very small body in the Ptolemaic system because it is always seen as a point although it is close to the earth: its minimal distance was supposed equal to the maximum distance of the moon. The distances and volumes of Venus, Mars, Jupiter, Saturn. We write d for the minimum distance between any planet and the earth and D for its maximum distance. For each of the four planets Venus, Mars, Jupiteq and Saturn, Kushyr uses as his fundamental data the ratio d : D between minimal and maximal distance of the planet, and the ratio between apparent diameter of the planet and the apparent diameter of the sun when the planet is at its mean distance.

A is always supposed to be a nice fraction' For Mercury' ', D : I : 2! Here d and D are the volume earth-radii and u is the the volume of the planet divided by of the earth. Jupiter lll2 8, 14, 9O. This is consistent with K[shyr's account of the planetary spheres nested inside one another'. PtolemyhadfoundthemaximumdistanceofVenusl,0T9,andthe minimum solar distance 1,". In order to overcome the contradicuseless tion with the philosophical principle about the impossibility of distance of the sun Space, he discusses the possibility of decreasing the to the maximum equal in such a way that its minimum value becomes distanceofVenus[11,pp'4,7].

Klshyravoidedsuchdifficulties' Klshyr,scomputationsinvolveacertainamountofrounding'We we use illustrate his rounding procedure by a few examples in which the decimal fractions, which were not used by K[shyr' Sometimes. InthecaseofJupiter,thediameterofthebodyisgsS'I8: 4. Inthetext,thisnumberis given as 4. We have no explanation for Kushyr's accurate volume determination. Kiishyr's maximum distance 8,,' corresponds to a maximum solar distance of. Kushyr's results may be compared to those of Ptolemy inthe Planetary Hypotheses, which we have listed in the following table: Name.

The distances and volumes of the fixed stars. Just like Ptolemy, Kshyr assumes that the distance between the fixed stars and the earth is the maximal distance of Saturn to the earth, and that the apparent diameter of a star of the first magnitude is equal to uzath of the apparent diameter of the sun. Kshyr computes the volume of a star of the first magnitude as 9a] times the volume of the earth.

Ptolemy's value is. K[shyr states that the volume of stars of the sixth magnitude is 16 times that of the earth. This corresponds to a diameter of about 2. The ratio of their apparent diameter to that of the sun must have been supposed equal to 2. In modern astronomy, the system has become. Kiishyr's computations below' Distances in miles' We reconstruct ry of the moon: 33rt x 3, B1B - ,' ' ' '. MaximumdistanceofMars:8,x3'''' x 3' ''' Maximum distance of J"pit"tt 14' : 75' ' ' distance of Saturn: 19' x 3' Maximum.

Inasimilarvein,Ptolemyprovidesthecelestialsizesanddistances corresponds to 7'5 stades' in stades [11, pp. Dr' Hamid-Reza Giahi Yazdi Acknowledgement' We are grateful verston of this article' and to all for his comments on a preliminary available manuscript copies friends and librarian.

Kushyar ibn labbans introduction to astrology books

Glossary of Astronomy' Bagheri, M. Ramsay Wright, London ; reprinted in [32], vol. Arabic of. Taltdrd Nihayil.

III, Leiden, -. Too Many Cooks. QuellenundstudienzurGeschichtederMathematik'Astronomie pp' und Physik, B 3 ' reprinted in ' 83' , Hyderabad-Deccan, Osmania oriental Publication Bureau, 1 ;. A [20] Langermann, Y. Y Roma' Jones, Princeton: Princeton Uni-. Gillispie, ed.

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Search inside document. This chapter complements the earlier short Chapter 22 wherc only the results are stated without computation. The extra chapter can also be read and studied separately, as a more or less self-contained treatise on sizes and distances of the ce- lestial bodies. Kushyr's treatise on the celestial distances and sizes is historically impofiant for two reasons.

In the text, translation and commentary, the figures are not drawn to scale; i. No Measurement of the earth. If 5] parts is added to twice the distance between the two centers of the earth and of the eccentric orb which is equal to 20;38 parts, and the result is subtracted from 60 parts, the remainder is ,7 parts. A Let triangle ABG be half the triangle of the section of the shadow cone in longitude, AG the altitude of the shadow, DE the radius of the shadow at maximum distance of the moon , Z H its radius at the perigee of the epicycle, and BG the radius of the shadow's base i.

B the radius of the base of ttre equal to C'so it is known' BtttTB and AGBare similar' i nf is cone G' the altitude of the shadow and GB are also il;;-so is earth the of It is approximately parts' if the radius is known. So we multiply the maximum distance of the moon, which is 64], by 18f , the mean distance of the sun turns out to be approximately 1, pa-s, where the radius of the earth is one part.

If we multiply it for length, width and depth, the body of the sun is found to be plus plus times the body of the earth. Then T Z is the length of the shadow of the moon, and it is desired. Z Mercury.


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If we multiply it for length, width and depth, the body of Saturn turns our to be 81 plus plus times the body of the earth. The stars below the first magnitude decrease in size grad- finally at the sixth magnitude, their body is approximately 16 times the body of the earth. K[shytu on Distances and Sizes 91 The maximum distance of Mars, which is the minimum distance of Jupiter, is 33,, miles.

The center of this pare- cliptic orb coincides with the center of the earth. The two eclipses are mentioned in [25, pp. Secondly, Klshyr determines the radius of the earth's shadow at maximal lunar distance R6 in digits, using an incorrect method. This can dr lRa be explained as follows. Thus, the conect Because and result of Kflshyr's computation can be explained by the correct formula d2 - dt lRa : ry - qz lrlz.

We note that the Ptolemaic value for the solar distance is only of the value according to modem measurements, and that the maximum parallax of the sun is slightly less than 0;0,9o. Another reason is the assumption made by Ptolemy and Kfishyr that the planetary spheres are adjacent in a geocentrc model of the universe' We have terefore refrained from comparing Klshyr's values for the sizes and distances of the planets with modern values.

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Kflshyr assumes that the maximal distance of the moon to the earth is 64; 15', and that the mean distance of the sun to the earth is t2I0,. In the geometrical figure, Kflshyr then attempts to determine the diameter of Mercury in the new unit of length " which he defined above for the computation of the volume of the sun. This is consistent with K[shyr's account of the planetary spheres nested inside one another' PtolemyhadfoundthemaximumdistanceofVenusl,0T9,andthe minimum solar distance 1,".

Kiishyr's maximum distance 8,,' corresponds to a maximum solar distance of 7,r. The classification of the visible stars into six magnitudes according to their brightness was introduced by Hipparchus 2nd c. In modern astronomy, the system has become more precise and more extended. III, Leiden, - Jones, Princeton: Princeton Uni- versity Press, Sagar Sharma. Satinder Singh. Kuo Jixian. Columbia Gomez. Ira Fariha. Annie N. Muslim Majlis Uoj. Haley Mooney.