ယောဇနာ

ယောဇနာ
သၞောတ်ယူနေတ်	အရထသာသ္တြမ် (Arthashastra)
ယူနေတ် မဆေင်ကု	ဇမၠိင်
သင်္ကေတ	ယောဇနာ
အပြံင်အလှာဲ ယူနေတ်
1 ယောဇနာ in ...	... ဂှ် တုပ်သၟဟ် ကု ...
SI units	m
Imperial/US units	8 mi;

မွဲ ယောဇနာ (သံသကြိုတ်: योजन; အၚ်္ဂလိက်: yojana; သေံ: โยชน์; ဗၟာ: ယူဇနာ) ဂှ် ဒှ် လၟိဟ်မၜတ် ဇမ္ၚောဲ ခေတ်တြေံ ပ္ဍဲအိန္ဒိယ၊ ရးနိဂီုမန်၊ ရးနိဂီုဗၟာ ကေုာံ ရးနိဂီုသေံ။ မွဲယောဇနာဂှ် နွံဒၟံင် ၜိုတ် ၁၂ - ၁၅ ကဳလဝ်မဳတာ။

လိက်တၟအ် သၟိင်အသောက (ဘဳသဳ ၃ ဗွဝ်ကၠံ)[ပလေဝ်ဒါန် | ပလေဝ်ဒါန် တမ်ကၞက်]

ပ္ဍဲကဵုလိက်တၟအ် သၟိင်အသောက မဂၞန် ၁၃ ဂှ် ဂွံဆဵုကေတ် ဗ္ၜတ်ဇမ္ၚောဲ အကြာ ဍုင်ပါတလိပုတ် ကဵု ဍုင်ဗေဗဳလောန် နွံ ၆၀၀ ယောဇနာ။^[၁] ဍုင်ပါတလိပုတ် ကဵု ဍုင်ဗေဗဳလောန်ဂှ် နွံဒၟံင် ၜိုတ် ၄၀၀၀ ကဳလဝ်မဳတာ (= ၂၄၈၅,၅ တိုင်)၊ ဟိုတ်ဂှ်ရ မွဲယောဇနာဂှ် နွံၜိုတ် ၇ ကဳလဝ်မဳတာ (= ၄,၃၅ တိုင်) ဟီုမာန်ရ။ ပ္ဍဲကဵု အဋ္ဌကထာ ဗြဟ္မဇာလသုတ်ဂှ် ဗၟံက်ထ္ၜးလဝ် ဍုင်နာလန္ဒာ ကဵု ဍုင်ရာဇာဂြိုဟ်ဂှ် နွံ မွဲယောဇနာ ဂးလဝ်ရ။ ခေတ်လၟုဟ် ဂၠံင်ကွဳပၟတ် အကြာဍုင်ၜါဂှ် နွံ ၈ တိုင် (= ၁၂,၈၇ ကဳလဝ်မဳတာ) ရ။ ပ္ဍဲကဵု ပြကိုဟ်ဝင်ပထဝဳ ဗုဒ္ဓသာသနိကဂှ်လေဝ် ဗၟံက်ထ္ၜးလဝ် မွဲယောဇနာ နွံ ၈ တိုင်ကီုရ။

ယောဇနာ အတိုင် မကၠုင် နူပြကိုဟ်ဗိသၞုပုရဏ[ပလေဝ်ဒါန် | ပလေဝ်ဒါန် တမ်ကၞက်]

ယောဇနာဂှ် ဗၟံက်ထ္ၜးလဝ် ပ္ဍဲပြကိုဟ်ဗိသၞုပုရဏ ကၞပ်ပထမ၊ ဆဋ္ဌမ ဝဂ် မဒှ်လိက် မလုပ်လၟိဟ် မဟာပုရဏ ၁၈ ကၞပ် အတိုင်ဗွဲသၟဝ်ရ။^[၂]

ဗၞတ်ဗ္ၜတ်ဂမၠိုင်[ပလေဝ်ဒါန် | ပလေဝ်ဒါန် တမ်ကၞက်]

ဗၞတ်ဗ္ၜတ်	မတုပ်သၟဟ် ကု ... (ဗၞတ်ဗ္ၜတ် ဟိန္ဒူ)	တင်စၟတ်ဂမၠိုင်
10 paramanu	1 parasúkshma	Paramanu refers to atom.^[၃]
10 parasúkshmas	1 trasarenu	1.9 nanometers (atoms are 0.1-0.5 nm)
10 trasarenus	1 mahírajas (particle of dust)	19 nanometers
10 mahírajas	1 bálágra (hair's point)	0.19 microns, aka 190 nanometers
10 bálágra	1 likhsha	1.9 microns
10 likhsha	1 yuka	0.019 mm (19 microns)
10 yukas	1 yavodara (heart of barley)	0.19 mm
10 yavodaras	1 yava (barley grain of middle size)	1.9 mm
10 yava	1 aṅgula (finger-breadth)	1.89 to 1.91 cm or approx 3/4 inch – here angula does not mean 1 inch rather 3/4 inch
6 fingers	1 pada (the breadth of a foot)	other sources define this unit differently: see Pada (foot)
2 padas	1 vitasti (span)	22.86 cm
2 vitasti	1 hasta (cubit)	45.7 cm
4 hastas	1 dhanu
1 danda	2 nárikás equals 6 ပေs (1.8 m)	1 paurusa (a man's height)
2,000 dhanus	1 gavyuti (distance at which a cow's call or lowing can be heard)	12,000 ပေs (3.7 km)
4 gavyutis	1 yojana
1 yojana		About 12.8 kilometers

ယောဇနာ အတိုင်မကၠုင် နူအခိုက်မန်[ပလေဝ်ဒါန် | ပလေဝ်ဒါန် တမ်ကၞက်]

အတိုင်မဗၟံက်ထ္ၜးလဝ် ပ္ဍဲလိက် လျးညာဏ် ကောန်ဂကူမန်၊ ကျာ်ဇၞော်ဝေဒဂူ မပ္တိတ်လဝ်ဂှ် ဂွံဆဵုကေတ် အတိုင်ဗွဲသၟဝ်ဝွံရ။^[၄]


ဗ္ၜတ်	မတုပ်သၟဟ် ကု
၁၀ မုဟ်သောက်	၁ မလ္ၚဴ
၆ မလ္ၚဴ	၁ မယဴ
၄ မယဴ	၁ လပုဟ်
၈ လပုဟ်	၁ မိဟ်
၃ မိဟ်	၁ ဟတ်
၄ ဟတ်	၁ ဖိဟ်
၇ ဟတ်	၁ တာ
၂၀ တာ	၁ ဥသဘ
၂၀ ဥသဘ	၁ ကိုဟ်
၄ ကိုဟ်	၁ ဂါဝုတ်
၄ ဂါဝုတ်	၁ ယောဇနာ
၁၀၀၀ တာ	၁ တိုင်
၆ တိုင်၊ တာ ၄၀၀	၁ ယောဇနာ

ဗ္ၜတ် နာနာ[ပလေဝ်ဒါန် | ပလေဝ်ဒါန် တမ်ကၞက်]

ဇမ္ၚောဲ ယောဇနာဂှ် ပြကိုဟ်မွဲကုမွဲ ဟွံတုပ် ရေင်သကအ်ရ။ ပ္ဍဲပြကိုဟ်သုရိယသိဒ္ဓန္တ (ကၞောတ် အေဒဳ ၄ ဗွဝ်ကၠံ တမ် အေဒဳ ၅ ဗွဝ်ကၠံ) ဂှ် ဗၟံက်ထ္ၜးလဝ် မွဲယောဇနာဂှ် နွံ ၈ ကဳလဳမဳတာ (= ၅ တိုင်)။^[၅] တုဲပၠန် တုပ်ကဵု လညာတ် နူပြကိုဟ်အရိယဘတိယ (၄၉၉) ကီုရ။^[၆] ဆဂး ဗၞတ်ဗ္ၜတ် နူ ၁၄ ဗွဝ်ကၠံဂှ် ပံက်လဝ် သ္ၚောဲနူဂှ် ၜိုတ် ၁,၅ အလန် မဒှ်ဒၟံင် ၜိုတ် ၁၃ ကဳလဝ်မဳတာ (= ၈ တိုင်)။^[၅] လညာတ် အစာဂုရု အဘယ စရဏာရဝိန္ဒ ဘက္တိဝေဒါန္တ သွာမဳ (Abhaya Caraṇāravinda Bhakti-vedānta Svāmī) မ္ဂး မွဲယောဇနာဂှ် နွံဒၟံင် ၜိုတ် ၁၃ ကဳလဝ်မဳတာ (= ၈ တိုင်) ^[၇] အတိုင် ညးမပံက်လဝ် အဓိပ္ပါယ် နူကဵု ပြကိုဟ်ဘဂဝတပုရဏ ဂှ်ရ။ အာလေဿေန္ဒြာ စုန္နိန္ဃမ် (Alexander Cunningham) ဟီု ဗ္ၜတ်တိ အိန္ဒိယ ခေတ်တြေံဂှ် မွဲယောဇနာဂှ် နွံဒၟံင် အကြာ ၈ ကဵု ၉ တိုင်၊ ၜတ် ကုဗ္ၜတ် ကြုက်မ္ဂး နွံဇမ္ၚောဲ အကြာ ၆,၇ တိုင် (၁၀,၈ ကဳလဝ်မဳတာ) ကဵု ၈,၂ တိုင် (၁၃,၂ ကဳလဝ်မဳတာ)ရ။^[၈]

နိဿဲ[ပလေဝ်ဒါန် | ပလေဝ်ဒါန် တမ်ကၞက်]

↑ Inscriptions of Asoka p.43
↑ Vishnu Purana, Translated to English: 45:6 In the other three Puráńas, in which this legend has been found, the different kinds of inhabited places are specified and p. 46 introduced by a series of land measures. Thus the Márkańd́eya states, that 10 Paramáńus = 1 Parasúkshma; 10 Parasúkshmas = 1 Trasareńu; 10 Trasareńus = 1 particle of dust, or Mahírajas; 10 Mahírajasas = 1 Bálágra, 'hair's point;' 10 Bálágras = 1 Likhyá; 10 Likhyás= 1 Yúka; to Yúkas = 1 heart of barley (Yavodara); 10 Yavodaras = 1 grain of barley of middle size; 10 barley grains = 1 finger, or [an] inch; 6 fingers = a Pada, or foot (the breadth of it); 2 Padas = 1 Vitasti, or span; 2 spans = 1 Hasta, or cubit; 4 Hastas = a Dhanu, a Danda, or staff, or 2 Nárikás; 2,000 Dhanus = a Gavyúti; 4 Gavyútis = a Yojana. The measurement of the Brahmanda Purana is less detailed. A span from the thumb to the first finger is a Pradeśa; to the middle finger, a Nála; to the third finger, a Gokerna; and to the little finger, a Vitasti, which is equal to twelve Angulas, or fingers; understanding thereby, according to the Váyu, a joint of the finger; according to other authorities, it is the breadth of the thumb at the tip. (A. R. 5. 104.) The Váyu, giving similar measurements upon the authority of Manu, although such a statement does not occur in the Manu Sanhitá, adds, that 21 fingers = 1 Ratni; 24 fingers = 1 Hasta, or cubit; 2 Ratnis = 1 Kishku; 4 Hastas = 1 Dhanu; 2,000 Dhanus = l Gavyúti; and 8,000 Dhanus = 1 Yojana. Durgas, or strongholds, are of four kinds; three of which are natural, from, their situation in mountains, amidst water, or in other inaccessible spots; the fourth is the artificial defences of a village (Gráma), a hamlet (Khet́aka), or a city (Pura or Nagara), which are severally half the size of the next in the series. The best kind of city is one which is about a mile long by half a mile broad, built in the form of a parallelogram, facing the northeast, and surrounded by a high wall and ditch. A hamlet should be a Yojana distant from a city: a village half a Yojana from a hamlet. The roads leading to the cardinal points from a city should be twenty Dhanus (above 100 feet) broad: a village road should be the same: a boundary road ten Dhanus: a royal or principal road or street should be ten Dhanus (above fifty feet) broad: a cross or branch road should be four Dhanus. Lanes and paths amongst the houses are two Dhanus in breadth: footpaths four cubits: the entrance of a house three cubits: the private entrances and paths about the mansion of still narrower dimensions. Such were the measurements adopted by the first builders of cities, according to the Puráńas specified.
↑ Legends of Science: Kanada – Discoverer of the Atom (18 February 2021).
↑ ဝေဒဂူ, ကျာ်ဇၞော် (၂၀၀၅). လျးညာဏ် ကောန်ဂကူမန်၊ လိက်ဗဟုသုတဂဏန်, ၄။
↑ ^၅.၀ ^၅.၁ Richard Thompson (1997). Planetary Diameters in the Surya-Siddhanta 11, 193–200 [196]။ ထာမ်ပလိက်:Rs?
↑ "Aryabhata I" Mac Tutor History of Mathematics aarchive. University of St Andrews။
↑ Srimad Bhagavatam 10.57.18 (translation) Archived ၂၀၁၈-၁၂-၀၇ at the Wayback Machine "one yojana measures about eight miles"
↑ Alexander Cunningham, Measures of Distance. Yojana, Li, Krosa. in The Ancient Geography of India: I. I. The Buddhist Period, Including the Campaigns of Alexander, and the Travels of Hwen-Thsang, Trübner and Company, 1871, pp. 571-574

[1] Inscriptions of Asoka p.43

[2] Vishnu Purana, Translated to English: 45:6 In the other three Puráńas, in which this legend has been found, the different kinds of inhabited places are specified and p. 46 introduced by a series of land measures. Thus the Márkańd́eya states, that 10 Paramáńus = 1 Parasúkshma; 10 Parasúkshmas = 1 Trasareńu; 10 Trasareńus = 1 particle of dust, or Mahírajas; 10 Mahírajasas = 1 Bálágra, 'hair's point;' 10 Bálágras = 1 Likhyá; 10 Likhyás= 1 Yúka; to Yúkas = 1 heart of barley (Yavodara); 10 Yavodaras = 1 grain of barley of middle size; 10 barley grains = 1 finger, or [an] inch; 6 fingers = a Pada, or foot (the breadth of it); 2 Padas = 1 Vitasti, or span; 2 spans = 1 Hasta, or cubit; 4 Hastas = a Dhanu, a Danda, or staff, or 2 Nárikás; 2,000 Dhanus = a Gavyúti; 4 Gavyútis = a Yojana. The measurement of the Brahmanda Purana is less detailed. A span from the thumb to the first finger is a Pradeśa; to the middle finger, a Nála; to the third finger, a Gokerna; and to the little finger, a Vitasti, which is equal to twelve Angulas, or fingers; understanding thereby, according to the Váyu, a joint of the finger; according to other authorities, it is the breadth of the thumb at the tip. (A. R. 5. 104.) The Váyu, giving similar measurements upon the authority of Manu, although such a statement does not occur in the Manu Sanhitá, adds, that 21 fingers = 1 Ratni; 24 fingers = 1 Hasta, or cubit; 2 Ratnis = 1 Kishku; 4 Hastas = 1 Dhanu; 2,000 Dhanus = l Gavyúti; and 8,000 Dhanus = 1 Yojana. Durgas, or strongholds, are of four kinds; three of which are natural, from, their situation in mountains, amidst water, or in other inaccessible spots; the fourth is the artificial defences of a village (Gráma), a hamlet (Khet́aka), or a city (Pura or Nagara), which are severally half the size of the next in the series. The best kind of city is one which is about a mile long by half a mile broad, built in the form of a parallelogram, facing the northeast, and surrounded by a high wall and ditch. A hamlet should be a Yojana distant from a city: a village half a Yojana from a hamlet. The roads leading to the cardinal points from a city should be twenty Dhanus (above 100 feet) broad: a village road should be the same: a boundary road ten Dhanus: a royal or principal road or street should be ten Dhanus (above fifty feet) broad: a cross or branch road should be four Dhanus. Lanes and paths amongst the houses are two Dhanus in breadth: footpaths four cubits: the entrance of a house three cubits: the private entrances and paths about the mansion of still narrower dimensions. Such were the measurements adopted by the first builders of cities, according to the Puráńas specified.

[3] Legends of Science: Kanada – Discoverer of the Atom (18 February 2021).

[4] ဝေဒဂူ, ကျာ်ဇၞော် (၂၀၀၅). လျးညာဏ် ကောန်ဂကူမန်၊ လိက်ဗဟုသုတဂဏန်, ၄။

[Thompson-5] ၅.၀ ^၅.၁ Richard Thompson (1997). Planetary Diameters in the Surya-Siddhanta 11, 193–200 [196]။ ထာမ်ပလိက်:Rs?

[6] "Aryabhata I" Mac Tutor History of Mathematics aarchive. University of St Andrews။

[7] Srimad Bhagavatam 10.57.18 (translation) Archived ၂၀၁၈-၁၂-၀၇ at the Wayback Machine "one yojana measures about eight miles"

[8] Alexander Cunningham, Measures of Distance. Yojana, Li, Krosa. in The Ancient Geography of India: I. I. The Buddhist Period, Including the Campaigns of Alexander, and the Travels of Hwen-Thsang, Trübner and Company, 1871, pp. 571-574

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