Mishnat ha-Middot

Mishnat ha-Middot (hivritcha: מִשְׁנַת הַמִּדּוֹת — „Oʻlchovlar risolasi“) — ibroniycha geometriyaga oid eng qadimgi risola boʻlib, olti bobdan iborat 49 ta mishnayotdan iborat. Olimlar asarni Mishnaik davriga yoki ilk islom davriga tegishli deb ham hisoblashadi.

Tarixi tahrir

Tarkib sanalari tahrir

Moritz Shtaynshnayder Mishnat ha-Middotni milodiy 800-1200-yillar oraligʻida deb hisoblashgan^[1]. Sarfatti va Langermann Shtaynshnayderning asar terminologiyasiga arab tili taʼsiri haqidagi daʼvosini ilgari surdilar va matn IX asr boshlariga toʻgʻri kelishini aniqlanadi^[2]^[3].

Boshqa tomondan, Hermann Shapiraning taʼkidlashicha, risola oldingi davrga, ehtimol Mishnaik davriga tegishli, chunki uning matematik terminologiyasi arab davri ibroniy matematiklaridan katta farq qiladi^[4].Solomon Gandz matn 150 dan kechiktirmay tuzilgan deb taxmin qildi (ehtimol, ravvin Neximiyo tomonidan) va Mishnaning bir qismi boʻlishni maqsad qilgan, ammo uning oxirgi kanonik nashridan chiqarib tashlangan, chunki asar juda dunyoviy deb hisoblangan edi^[5].Tarkib Iskandariya Qahramonining (taxminan 100-yil) ishiga oʻxshaydi va al-Xorazmiy (taxminan 800 y.)va oldingi tanishuv tarafdorlari shuning uchun yunon va islom matematikasini bogʻlaydigan Mishnat ha-Middotni koʻrishgan^[6].

Zamonaviy tarix tahrir

Mishnat ha-Middot Myunxen kutubxonasining MS 36 da 1862-yilda Moritz Shtaynshnayder tomonidan topilgan^[1]. 1480-yilda Konstantinopolda ko‘chirilgan qo‘lyozma V bobning oxirigacha boradi. Kolofonga ko‘ra, nusxa ko‘chiruvchi ishongach matn toʻliq boʻlishi kerak edi^[7]. Shtaynshnayder asarni 1864-yilda Leopold Zunzning yetmish yilligi sharafiga nashr etilgandi^[8]. Matn 1880-yilda matematik Hermann Schapira tomonidan tahrirlangan va qayta nashr etilgan^[4].

Otto Noygebauer Bodleian kutubxonasida VI bobni oʻz ichiga olgan genizah parchasini topgach, Solomon Gandz 1932-yilda chuqur filologik tahlil bilan birga Mishnat ha-Middotning toʻliq versiyasini nashr etdi. Asarning uchinchi qoʻlyozmasi 1965-yilda Praga yahudiy muzeyi arxivida kataloglanmagan materiallar orasidan topilgan edi^[7].

Tarkibi tahrir

Garchi birinchi navbatda amaliy ish boʻlsa-da, Mishnat ha-Middot atamalarni aniqlashga va geometrik qoʻllanilishi va nazariyasini tushuntirishga harakat qiladi^[9].Kitob I bobda (§ 1-5) turli xil tekislik figuralari (toʻrtburchak, uchburchak, aylana va aylana segmenti) uchun „aspektlar“ni belgilaydigan munozara va maydonlarni oʻlchashning asosiy tamoyillari bilan boshlanadi. (§ 6-9). II bobda ish tekislik raqamlarini oʻlchashning qisqacha qoidalarini (§ 1-4), shuningdek hajmni hisoblashda bir nechta muammolarni (§ 5-12) taqdim etgandi. III-V boblarda Mishnat ha-Middot toʻrt turdagi tekislik figuralarini oʻlchashni raqamli misollarga asoslanib yana batafsil tushuntiradi^[10]. Matn VI bobdagi Chodirning nisbatlarini muhokama qilish bilan yakunlanadi^[11]^[12].

Risolat Tanax geometrik nisbatni π ni 3 ga toʻliq teng deb belgilaydi va uni 3 deb belgilaydi, degan keng tarqalgan eʼtiqodga qarshi bahs yuritadi va 3<span data-cx="[{"adapted":true,"partial":false,"targetExists":true,"mandatoryTargetParams":[],"optionalTargetParams":[]}]" data-mw="{"parts":[{"template":{"target":{"wt":"Fraction","href":"./Andoza:Fraction"},"params":{"1":{"wt":"7"}},"i":0}}]}" data-ve-no-generated-contents="true" id="mwZw" typeof="mw:Transclusion"> </span> ni uning oʻrniga kiritadi^[5]. Kitob formulalar boʻyicha aylananing maydonini hisoblash orqali bu taxminga keladi.

A=d^{2}-{\tfrac {d^{2}}{7}}-{\tfrac {d^{2}}{14}}

va

A={\tfrac {c}{2}}\cdot {\tfrac {d}{2}}

^[11].

Yana qarang tahrir

Qirq toʻqqizta qoidalarning Baraitasi

Manbalar tahrir

↑ ^1,0 ^1,1 Mischnat ha-Middot, die erste Geometrische Schrift in Hebräischer Sprache, nest Epilog der Geometrie des Abr. ben Chija (Hebrew, German) Steinschneider: , Berlin, 1864.
↑ Sarfatti, Gad B. „Mishnat ha-Middot“,. Ḥiqrei Ever ve-Arav [Festschrift Joshua Blau] (he) Ben-Shammai: , Tel Aviv and Jerusalem, 1993 — 463 bet.
↑ Langermann, Y. Tzvi (2002). "On the Beginnings of Hebrew Scientific Literature and on Studying History through "Maqbiloṯ" (Parallels)". Aleph (Indiana University Press) 2 (2): 169–189. doi:10.2979/ALE.2002.-.2.169.
↑ ^4,0 ^4,1 Schapira, Hermann, ed (1880). "Mischnath Ha-Middoth" (Hebrew, German). Zeitschrift für Mathematik und Physik (Leipzig).
↑ ^5,0 ^5,1 Gandz, Solomon (January 1936). "The Sources of Al-Khowārizmī's Algebra". Osiris (University of Chicago Press) 1: 263–277. doi:10.1086/368426. Manba xatosi: Invalid <ref> tag; name "gandz1936" defined multiple times with different content
↑ Gandz, Solomon (1938–1939). "Studies in Hebrew Mathematics and Astronomy". Proceedings of the American Academy for Jewish Research (American Academy for Jewish Research) 9: 5–50. doi:10.2307/3622087.
↑ ^7,0 ^7,1 Scheiber, Sándor (1974). "Prague manuscript of Mishnat ha-Middot". Hebrew Union College Annual 45: 191–196. ISSN 0360-9049.
↑ Thomson, William (November 1933). "Review: The Mishnat ha-Middot by Solomon Gandz". Isis (University of Chicago Press) 20 (1): 274–280. doi:10.1086/346775.
↑ Levey, Martin (June 1955). "Solomon Gandz, 1884–1954". Isis (University of Chicago Press) 46 (2): 107–110. doi:10.1086/348405.
↑ Neuenschwander, Erwin (1988). "Reflections on the Sources of Arabic Geometry". Sudhoffs Archiv (Franz Steiner Verlag) 72 (2): 160–169.
↑ ^11,0 ^11,1 The Mishnat ha-Middot, the First Hebrew Geometry of about 150 C. E., and the Geometry of Muhammad Ibn Musa Al-Khowarizmi, the first Arabic Geometry (c. 820), Representing the Arabic Version of the Mishnat ha-Middot, Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik A. Berlin: Springer, 1932.
↑ Sarfatti, Gad B. (1974). "Some remarks about the Prague manuscript of Mishnat ha-Middot". Hebrew Union College Annual 45: 197–204. ISSN 0360-9049.

Havolalar tahrir

MS Heb. c. 18, Bodleian kutubxonalaridagi Geniza parchalari katalogi.

[steinschneider-1] 1,0 ^1,1 Mischnat ha-Middot, die erste Geometrische Schrift in Hebräischer Sprache, nest Epilog der Geometrie des Abr. ben Chija (Hebrew, German) Steinschneider: , Berlin, 1864.

[2] Sarfatti, Gad B. „Mishnat ha-Middot“,. Ḥiqrei Ever ve-Arav [Festschrift Joshua Blau] (he) Ben-Shammai: , Tel Aviv and Jerusalem, 1993 — 463 bet.

[3] Langermann, Y. Tzvi (2002). "On the Beginnings of Hebrew Scientific Literature and on Studying History through "Maqbiloṯ" (Parallels)". Aleph (Indiana University Press) 2 (2): 169–189. doi:10.2979/ALE.2002.-.2.169.

[schapira-4] 4,0 ^4,1 Schapira, Hermann, ed (1880). "Mischnath Ha-Middoth" (Hebrew, German). Zeitschrift für Mathematik und Physik (Leipzig).

[gandz1936-5] 5,0 ^5,1 Gandz, Solomon (January 1936). "The Sources of Al-Khowārizmī's Algebra". Osiris (University of Chicago Press) 1: 263–277. doi:10.1086/368426. Manba xatosi: Invalid <ref> tag; name "gandz1936" defined multiple times with different content

[6] Gandz, Solomon (1938–1939). "Studies in Hebrew Mathematics and Astronomy". Proceedings of the American Academy for Jewish Research (American Academy for Jewish Research) 9: 5–50. doi:10.2307/3622087.

[scheiber-7] 7,0 ^7,1 Scheiber, Sándor (1974). "Prague manuscript of Mishnat ha-Middot". Hebrew Union College Annual 45: 191–196. ISSN 0360-9049.

[thomson-8] Thomson, William (November 1933). "Review: The Mishnat ha-Middot by Solomon Gandz". Isis (University of Chicago Press) 20 (1): 274–280. doi:10.1086/346775.

[9] Levey, Martin (June 1955). "Solomon Gandz, 1884–1954". Isis (University of Chicago Press) 46 (2): 107–110. doi:10.1086/348405.

[neuenschwander-10] Neuenschwander, Erwin (1988). "Reflections on the Sources of Arabic Geometry". Sudhoffs Archiv (Franz Steiner Verlag) 72 (2): 160–169.

[mishnathamiddot-11] 11,0 ^11,1 The Mishnat ha-Middot, the First Hebrew Geometry of about 150 C. E., and the Geometry of Muhammad Ibn Musa Al-Khowarizmi, the first Arabic Geometry (c. 820), Representing the Arabic Version of the Mishnat ha-Middot, Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik A. Berlin: Springer, 1932.

[12] Sarfatti, Gad B. (1974). "Some remarks about the Prague manuscript of Mishnat ha-Middot". Hebrew Union College Annual 45: 197–204. ISSN 0360-9049.

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