रागुया

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भाचात्रिद्वादा सोसामेकादशान |

कुत्रिद्वानसा बुद्वादासाचष ||

ग्वैकानषट्चत्रि शुदासाचत्रैका |

शनषचैकाद्वा रागुया ||
#SAH20140820 

Audio: https://soundcloud.com/hari-tirumalai/raguya

First letter => Day

दीर्घ => Add 0.5 except for द्वादश

Single letter notations except of 10 => दश

Ignore म् and  च but not चा

Now, if we know our सन्धि-s correctly, it’s easy!

Lets start:

रागुया => रा + गु + य + अ

ð  राहुकाल गुलिककाल यमगण्डकाल अर्धप्रहारकाल

And the first word:

भाचात्रिद्वादा => भा चा त्रि द्वा दा

भानुवासरः चा => च+1/2 सार्धचत्वारिवादने त्रिवादने द्वादशवादने द+1/2 सार्धदशवादने

सोसामेकादशान => सो सा एका दशा न

सोमवासरः सार्धसप्तवादने सार्धेकवादने सार्धदशवादने नववादने

ग्वैकानषट्चत्रि => ग्वैका => गु एका न षट् त्रि

गुरुवासरः सार्धेकवादने नववादने षड्वादने त्रिवादने

Easy isn’t it!

Quiz:

Q_1: Can you tell me when is राहुकाल on Wednesday? 2mns!

Q_2: Can someone tell me when is अर्धप्रहारकाल on Tuesday? 2mns!

Let’s make it a little tough .. or is it?

Q_3: Now can someone tell me when is it a good-time on Saturday? 2mns!

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Interjections in #Sanskrit ..

Something to aid memory ..
आहा स्तोभ हन्त हळा भो | अयि तु अये हा धिक्चाहो || आम् किल हुम्फट् रे हे एते | इह खलु ननु वै हि संस्कृते ||

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आहा Wow! aHaa! (like when a breath of fresh air felt)
स्तोभ Hurruh!
हन्त Damn!
हळा Hello!
भो also hello! अयि ay! (maybe when missed something)
अये ay!
हा Haa (when hurt)
धिक् pity/curse
अहो oh! (surprise) आम् yes 
किल वै हि all mean: indeed/surely
हुम् hmmm..
फट् crack!
रे showing disrespect
हे hey! 
इह now then.. 
खलु  isn't it 
ननु not at all and without-doubt/certainly (more often)  
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कोर्भवान्

A student really wanted to learn सम्स्कृत-व्याकरणम् from पाणिनि and went to pay respects. पाणिनि was very old at that time and was only doing तप and योग. But he directed the young boy to पतञ्जलि. When the boy asked how would he find him, पाणिनि says, the person who gives the right answer to this question, "कोर्भवान्" would only be "पतञ्जलि"!! 
Surprised but ordered by the revered पाणिनि, the boy goes in search of पतञ्जलि. Wherever he went, people made fun of him for a not knowing simple grammar!

Finally, he meets an old man teaching व्याकरणम् to many students at the same time!!
With due respect and a little hesitation, he asks:
Boy: "कोर्भवान्" |
Old man: "सपोsहम्" |
Boy: रेफः क्वगतः| Where did the रेफ go?? (in सर्प) 
Old man: त्वयापहृतः| (Stolen by you!) 

Astonished and happy, the boy prostrates before the guru saying he could be none other than "पतञ्जलि" and prays to learn सम्स्कृत-व्याकरणम् from him!

Notable thing in the story is an example where रेफ not included in विसर्ग-सन्धि |
Will you now keep that in mind!?

PS: पतञ्जलि is considered by many as आदिशेषावतार and hence referred here as सर्प!

RekhAgaNitam-tweets

अस्मद्गुरुभ्यो नमः -> Salute to our gurus!

Today, I'll take up रेखागणितम्


रेखागणितम् or Science of Geometry in संस्कृतम् was written by जगन्नाथ साम्राट् (1652–1744) under the order of राजा जयसिंह of Jaipur

In रेखागणितम् are similarities with Arabic-work by Nasir Eddin, raising the question whether it was an original work or just a translation..

Author says in opening verses saying of another work of his ‘सिद्धान्त साम्राट्’ that it is a translation of Arabic-language-book-मिजास्ती


Although Pandit जगन्नाथ साम्राट् defends saying it was orally transferred through generations in his family…

...evident from the primitive language in the grantha But, it is generally agreed that both these works are translations from Arabic.

However, शिल्पशास्त्रम् - the science of Geometry, misunderstood as for only sculpting, was first cultivated in India, ..

.. imported to Greece and other countries, and probably was lost in time.

Which raises the next question whether geometry itself originated in India or Greece?

The point of contact of classical-geometry is Alexandrian-Geometry and Sulba-Sutras.

Alexandrian-mathematicians Hero (215 BC) the earliest from Greece, and Pythogoras are known to have drawn parallels to Sulba-sutras but,..

.. the Sulba-Sutras are part of Srauta-sutras of Bodhayana and Apastamba (date debated 800-200BC).

However, Yajurveda+Taittiriya-BrahmaNa lay strict rules for construction of altars, bricks, arrangement, etc.Sulba-sutras are prior to them!

Anyway, mere translation/original work comprised from a collection of oral-renditions through generations, the merit needs to be appreciated

So let's star the journey!

In the author’s words, any book dealing with geometry or solid-geometry cannot be clear unless "theory of numbers" and terms used.

Here are some basic definitions:

Number अङ्क 
Unit रूप 
Even सम 
Odd विषम 
Prime-number प्रथमाङ्क 
Multiplier गुणक 
Multiplicand गुण्य

Point बिन्दु 
Line रेखा 
Plane क्षेत्र 
Arm/Side भुज, बाहु 
Square-number वर्गाङ्क or just वर्ग
Cube-number घनाङ्क or just घन

Proportional सजातीय 
Perfect-number पूर्णाङ्क
.. goes on .. lets take more of them as they appear

Some Geometry-specific definitions before we take a couple of astonishing Theorems ..

Ready?

Definition #1: बिन्दु : point 

यः पदार्थो दर्शनयोग्यो विभागानर्ह: स बिन्दुशब्दवाच्यः| 

#SanskritAppreciationHour

Lets do the पदच्छेद and W2W

यः Which पदार्थो object दर्शन-योग्यो capable of being seen विभागानर्ह: not eligible for division (into parts) ..

स that वाच्यः is to be called as/by बिन्दुशब्द the word-बिन्दु nka 'point' 

kna - now-known-as :)

Interesting definition isn't it? Apt too, I suppose! A point is one, that is capable of being seen (minutest) & cannot be divided further!

As usual, after the first definition, here is Quiz1: Can you split विभागानर्ह:, what sandhi?

OK, next definition:
चतुर्भुजम् : Quad-Arm kna Rectangle :)


Definition#2
चतुर्भुजम् : यस्य बाहुचतुष्टयम् समानं कोणचतुष्टयमपि समानं तञ्चतुरश्रं समकोणं समचतुर्भुजम् ज्ञेयम् | 
#SanskritAppreciationHour

पदच्छेद and W2W now: यस्य Whose बाहु arms चतुष्टयम् all-four समानं are equal कोण angle चतुष्टयमपि all-four also are समानं are equal

.. तञ्चतुरश्रं that quad-cornered figure (from अश्रि) is ज्ञेयम् to be known as समकोणं equi-angular समचतुर्भुजम् equi-armed (figure)

समचतुर्भुजम् equi-quad-armed (figure):)

Definition clear? Question?

Quiz2: What sandhi is तञ्चतुरश्रं ?

Now to real stuff, प्रथमोsध्यायः एकानविंशतितम क्षेत्रम् Pg88 of रेखागणितम् vol1
Note क्षेत्रम् here means property/theorem

Greatest/Shortest sides of त्रिभुजम्–Tri-Arm 
तत्र त्रिभुजे योsधिककोणस्तत्सम्मुखभुजोsपि महान् भवति योsल्पकोणस्तत्सम्मुखभुजोsपि लघुर्भवति |

त्रिभुजम्–Tri-Arm NKA => Triangle :)

Don't bother about the long compounds, lets split them!


{ Now to real stuff, प्रथमोsध्यायः एकोनविंशतितम क्षेत्रम् Pg88 of रेखागणितम् vol1
Note क्षेत्रम् here means property/theorem

पदच्छेद and W2W: 

तत्र There त्रिभुजे in Tri-Arm
Let’s break the compound: योsधिककोणस्तत्सम्मुखभुजोsपि => य:+अधिक+कोण:+ तत्+सम्मुख+भुज:+अपि

य:which अल्प meagre/smaller कोण: angle तत् that(it’s) सम्मुख opposite भुज: arm/side अपि also भवति will be लघु: small!
Easy isn't it?
#SanskritAppreciationHour

Meaning .. य:which अधिक greater कोण: angle तत् that(it’s) सम्मुख opposite भुज: arm/side अपि also भवति will be महान् great!

Similarly- योsल्पकोणस्तत्सम्मुखभुजोsपि => य:+ अल्प+कोण:+ तत्+सम्मुख+भुज:+अपि

य:which अल्प meagre/smaller कोण: angle तत् that(it’s) सम्मुख opposite भुज: arm/side अपि also भवति will be लघु: small!

Complete meaning: Arm opposite to the largest angle is the largest side, and arm-opposite to the smallest-angle is the shortest!

Orally, easy to pass it on to generations!
तत्र त्रिभुजे योsधिककोणस्तत्सम्मुखभुजोsपि महान् भवति योsल्पकोणस्तत्सम्मुखभुजोsपि लघुर्भवति |

Of course, need to decipher the meaning!

Quick theorem:
तृतीयोsध्यायः एकविंशतितम क्षेत्रम् 

वृत्तद्वयस्य संस्पर्शः एकस्मिन्नेव चिन्हे भवति नान्यत्र |
#SanskritAppreciationHour

BTW, these are non-intersecting-planes. Lets do पदच्छेद and W2W:

द्वयस्य two वृत्त circles’ संस्पर्शः touch भवति happens एकस्मिन्नेव only-at-one चिन्हे point नान्यत्र not-anywhere-else!


That was easy to understand, wasn't it?

BTW, Quiz3: What sandhi is: एकस्मिन्नेव

Shall we take another interesting theorem now?

द्वितीयोsध्यायः द्वादशक्षेत्रम् from Pg156

यत्त्रिभुजमधिककोणरूपमस्ति तत्कोणसम्मुखभुजस्य वर्गोsवशिष्टभुजद्वयवर्गयोगादाधिको भवति|

Again, quite easy when we break it, lets do the पदच्छेद and W2W ..

यत्त्रिभुजमधिककोणरूपमस्ति => यत्+त्रिभुजम्+अधिक+कोण+रूपम्+अस्ति

यत्+त्रिभुजम्+अधिक+कोण+रूपम्+अस्ति यत् In which त्रिभुजम् Tri-Arm अस्ति there is अधिक+कोण greater-angle => Obtuse-Angle रूपम् appearance

तत्+कोण+सम्मुख+भुजस्य तत् that कोण angle’s सम्मुख opposite भुजस्य Arm’s वर्गः+अवशिष्ट+भुज+द्वय+वर्गात्+अधिकः वर्ग: square भवति will be …

अवशिष्ट remaining भुज+द्वय two-arm’s वर्ग squares अधिकः more than योगात् sum 

As you can see, just breaking it up makes it a cake-walk!
Attaching a pic showing the proof .. pic.twitter.com/OdpfhY3OXp

(https://twitter.com/haritirumalai/status/4318039727901450250)

Of course, the proof draws root from रज्जु-सूत्र of बोधायन-सुलभ-सूत्राणि rather than plagiarizing from आचार्य-Pythogoras :)

That’s I have for today .. time's up as well!

Thanks for those who attended, hope you’ve enjoyed and are encouraged to look into रेखागणितम्/शिल्पशास्त्रम् in #Sanskrit!

I often ask myself, what did #Sanskrit not have? I’ll hang-around for a bit if any interactions, over-to रोहिणी महोपाध्याया @rohinibakshi


BTW, Quiz-Answers: 
Quiz1: विभागानर्ह: =>विभाग अनर्ह: => सवर्णदीर्घ-सन्धिः @PnNamboo

Quiz2: तञ्चतुरश्रं => तम् चतुरश्रम् => अनुनासिक-सन्धिः 
Quiz3: एकस्मिन्नेव => एकस्मिन् एव => ङमुडागम-सन्धिः


@RohiniBakshi Thanks for the opportunity!

Have a great weekend everyone! And see you next week for more #Sanskrit with #SanskritAppreciationHour

सुभाषितम्: #२१

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सुभाषितम्: #२१

मनसि वचसि काये पुण्य पीयुष पूर्णाः
In their minds, words and body, fully filled with nectar or virtues

    त्रिभुवनमुपकार श्रेणिभिः प्रीणयन्तः |
    Pleasing the worlds with string of charity and good-deeds

परगुणपरमाणून् पर्वतीकृत्य नित्यम्
 Everyday making(highlighting) even minute-ones of others' merits as big as a mountain

    निजहृदि  विकसन्तः ख्यापयन्तः कियन्तः ||
    and depositing, collecting, (them) in their own hearts and explaining,
      how many are there in this world?

तात्पर्य: -> Good men, embodied with plenty of good virtues, highlight even the minutest good-deeds of others and learn, deposit those inside their hearts. Such people are very rare in this world!

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सुभाषितम्: #२०

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सुभाषितम्: #२०

उपदेशो हि मूर्खाणां प्रकोपाय न शान्तये |
Advise to fools, leads to increased anger and not peace.
(just as ..)
पय: पानं भुजङ्गानां केवलं विषवर्धनम् ||
Feeding milk to snakes only increases their poison!

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सुभाषितम्: #१९

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सुभाषितम्: #१९

गुणावज्जन संसर्गात्  याति नीचोऽपि गौरवम् |
With the company of good-people, even an inferior person achieves respect..
(just like ..)
पुष्पमाला प्रसङ्गेन सूत्रं शिरसि धार्यते ||
In the company of a floral-garland, a (simple) thread gets worn on the head!

तात्पर्य: -> Company of good people has the power of getting respect even to an inferior, lowly person.

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