Mishnat ha-Middot sahifasining manbasini koʻrish

'''Mishnat ha-Middot''' (h{{Lang-he|מִשְׁנַת הַמִּדּוֹת}} — „Oʻlchovlar risolasi“) — [[Ivrit tili|ibroniycha]] [[Geometriya|geometriyaga]] oid eng qadimgi risola boʻlib, olti bobdan iborat 49 ta ''mishnayotdan'' iborat. Olimlar asarni Mishnaik davriga yoki [[Islom oltin davri|ilk islom davriga]] tegishli deb ham hisoblashadi.

== Tarixi ==

=== Tarkib sanalari ===
Moritz ''Shtaynshnayder Mishnat ha-Middotni'' milodiy 800-1200-yillar oraligʻida deb hisoblashgan<ref name="steinschneider">{{Kitob manbasi|editor=Steinschneider|title=Mischnat ha-Middot, die erste Geometrische Schrift in Hebräischer Sprache, nest Epilog der Geometrie des Abr. ben Chija|location=Berlin|date=1864|language=Hebrew, German}}</ref>. Sarfatti va Langermann Shtaynshnayderning asar terminologiyasiga [[arab tili]] taʼsiri haqidagi daʼvosini ilgari surdilar va matn IX asr boshlariga toʻgʻri kelishini aniqlanadi<ref>{{Kitob manbasi|first=Gad B.|last=Sarfatti|language=he|chapter=Mishnat ha-Middot|editor=Ben-Shammai|title=Ḥiqrei Ever ve-Arav [Festschrift Joshua Blau]|location=Tel Aviv and Jerusalem|date=1993|page=463}}</ref><ref>{{Cite journal|title=On the Beginnings of Hebrew Scientific Literature and on Studying History through "Maqbiloṯ" (Parallels)|first1=Y. Tzvi|last=Langermann|journal=Aleph|volume=2|issue=2|year=2002|pages=169–189|publisher=Indiana University Press|jstor=40385478|doi=10.2979/ALE.2002.-.2.169}}</ref>.

Boshqa tomondan, Hermann Shapiraning taʼkidlashicha, risola oldingi davrga, ehtimol Mishnaik davriga tegishli, chunki uning matematik terminologiyasi [[Islom oltin davri|arab davri]] ibroniy matematiklaridan katta farq qiladi{{R|schapira}}.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<ref name="gandz1936">{{Cite journal|title=The Sources of Al-Khowārizmī's Algebra|first1=Solomon|last=Gandz|author-link=Solomon Gandz|journal=Osiris|volume=1|date=January 1936|pages=263–277|publisher=University of Chicago Press|jstor=301610|doi=10.1086/368426}}</ref>.Tarkib [[Geron|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''<ref>{{Cite journal|title=Studies in Hebrew Mathematics and Astronomy|author-link=Solomon Gandz|first1=Solomon|last=Gandz|journal=Proceedings of the American Academy for Jewish Research|volume=9|date=1938–1939|pages=5–50|publisher=American Academy for Jewish Research|jstor=3622087|doi=10.2307/3622087}}</ref>.

=== Zamonaviy tarix ===
''Mishnat ha-Middot'' Myunxen kutubxonasining MS 36 da 1862-yilda Moritz Shtaynshnayder tomonidan topilgan{{R|steinschneider}}. 1480-yilda [[Konstantinopol|Konstantinopolda]] ko‘chirilgan qo‘lyozma V bobning oxirigacha boradi. Kolofonga ko‘ra, nusxa ko‘chiruvchi ishongach matn toʻliq boʻlishi kerak edi<ref name="scheiber">{{Cite journal|last=Scheiber|first1=Sándor|author-link=Sándor Scheiber|issn=0360-9049|journal=Hebrew Union College Annual|pages=191–196|title=Prague manuscript of ''Mishnat ha-Middot''|volume=45|jstor=23506854|year=1974}}</ref>. Shtaynshnayder asarni 1864-yilda Leopold Zunzning yetmish yilligi sharafiga nashr etilgandi{{R|thomson}}. Matn 1880-yilda matematik Hermann Schapira tomonidan tahrirlangan va qayta nashr etilgan<ref name="schapira">{{Cite journal|editor-first=Hermann|editor-last=Schapira|editor-link=Hermann Schapira|title=Mischnath Ha-Middoth|place=Leipzig|year=1880|language=Hebrew, German|journal=Zeitschrift für Mathematik und Physik}}</ref>.

Otto Noygebauer Bodleian kutubxonasida VI bobni oʻz ichiga olgan genizah parchasini topgach, Solomon Gandz 1932-yilda chuqur [[Filologiya|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{{R|scheiber}}.

== Tarkibi ==
Garchi birinchi navbatda amaliy ish boʻlsa-da, ''Mishnat ha-Middot'' atamalarni aniqlashga va geometrik qoʻllanishi va nazariyasini tushuntirishga harakat qiladi<ref>{{Cite journal|title=Solomon Gandz, 1884–1954|first1=Martin|last=Levey|journal=Isis|volume=46|number=2|date=June 1955|pages=107–110|publisher=University of Chicago Press|jstor=227124|doi=10.1086/348405}}</ref>.Kitob I bobda (§ 1-5) turli xil tekislik figuralari ([[Toʻrtburchak|toʻrtburchak]], [[uchburchak]], [[aylana]] va aylana segmenti) uchun „aspektlar“ni belgilaydigan munozara va [[Yuza|maydonlarni]] oʻlchashning asosiy tamoyillari bilan boshlanadi. (§ 6-9). II bobda ish tekislik raqamlarini oʻlchashning qisqacha qoidalarini (§ 1-4), shuningdek [[Hajm|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<ref name="neuenschwander">{{Cite journal|title=Reflections on the Sources of Arabic Geometry|first1=Erwin|last=Neuenschwander|journal=Sudhoffs Archiv|volume=72|issue=2|year=1988|pages=160–169|publisher=Franz Steiner Verlag|jstor=20777187}}</ref>. Matn VI bobdagi Chodirning nisbatlarini muhokama qilish bilan yakunlanadi{{R|mishnathamiddot}}<ref>{{Cite journal|last=Sarfatti|first1=Gad B.|issn=0360-9049|journal=Hebrew Union College Annual|pages=197–204|title=Some remarks about the Prague manuscript of ''Mishnat ha-Middot''|volume=45|year=1974|jstor=23506855}}</ref>.

Risolat Tanax [[Geometriya|geometrik]] nisbatni [[:en:Pi|π]] ni 3 ga toʻliq teng deb belgilaydi va uni 3 deb belgilaydi, degan keng tarqalgan eʼtiqodga qarshi bahs yuritadi va 3<nowiki><span data-cx="[{&amp;quot;adapted&amp;quot;:true,&amp;quot;partial&amp;quot;:false,&amp;quot;targetExists&amp;quot;:true,&amp;quot;mandatoryTargetParams&amp;quot;:[],&amp;quot;optionalTargetParams&amp;quot;:[]}]" data-mw="{&amp;quot;parts&amp;quot;:[{&amp;quot;template&amp;quot;:{&amp;quot;target&amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;Fraction&amp;quot;,&amp;quot;href&amp;quot;:&amp;quot;./Andoza:Fraction&amp;quot;},&amp;quot;params&amp;quot;:{&amp;quot;1&amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;7&amp;quot;}},&amp;quot;i&amp;quot;:0}}]}" data-ve-no-generated-contents="true" id="mwZw" typeof="mw:Transclusion">&</nowiki>nbsp;<nowiki></span></nowiki> ni uning oʻrniga kiritadi<ref name="gandz1936">{{Cite journal|title=The Sources of Al-Khowārizmī's Algebra|first1=Solomon|last=Gandz|author-link=Solomon Gandz|journal=Osiris|volume=1|date=January 1936|pages=263–277|publisher=University of Chicago Press|jstor=301610|doi=10.1086/368426}}<cite class="citation journal cs1" data-ve-ignore="true" id="CITEREFGandz1936">[[Solomon Gandz|Gandz, Solomon]] (January 1936). „The Sources of Al-Khowārizmī's Algebra“. ''Osiris''. University of Chicago Press. '''1''': 263-277. [[Raqamli obyekt identifikatori|doi]]:[[doi:10.1086/368426|10.1086/368426]]. [[JSTOR (identifikator)|JSTOR]]&nbsp;[//www.jstor.org/stable/301610 301610]. [[S2CID (identifikator)|S2CID]]&nbsp;[https://api.semanticscholar.org/CorpusID:60770737 60770737].</cite></ref>. Kitob formulalar boʻyicha aylananing maydonini hisoblash orqali bu taxminga keladi.

: <math>A=d^2-\tfrac{d^2}{7}-\tfrac{d^2}{14}</math> va <math>A=\tfrac{c}{2}\cdot\tfrac{d}{2}</math>{{R|mishnathamiddot}}.

== Yana qarang ==

* Qirq toʻqqizta qoidalarning Baraitasi

== Manbalar ==
{{Manbalar|refs=<ref name=mishnathamiddot>{{cite book|year=1932|editor-link=Solomon Gandz|editor-last=Gandz|editor-first=Solomon|translator-last=Gandz|translator-first=Solomon|title=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|series=Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik A|volume=2|location=Berlin|publisher=Springer|url=https://books.google.com/books?id=m1BwPgAACAAJ}}</ref>
<ref name=thomson>{{cite journal|title=Review: The Mishnat ha-Middot by Solomon Gandz|first=William|last=Thomson|journal=Isis|volume=20|number=1|date=November 1933|pages=274–280|publisher=University of Chicago Press|jstor=224893|doi=10.1086/346775}}</ref>}}

== Havolalar ==

* [https://genizah.bodleian.ox.ac.uk/catalog/volume_29#MS_Heb_c_18-part10-item1 MS Heb. c. 18], Bodleian kutubxonalaridagi Geniza parchalari katalogi.
[[Turkum:Matematika tarixi]]