ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

or something, or it'sऋतुचिह्नं रिदं? Wait, what is that dot above ह्न? Let's look at the dot above ह्न: it's an anusvara! Wait, if it has an anusvara, then it's ऋतुचिह्नं. Then what is the mark next to it? Wait, look at: ऋतुचिह्न- is that a repha overह्न? No, ह्नhasहandन. Wait, above ह्न, there is a small vertical tick or a dot? Wait, look at line 16: ऋतुचिन्हैर्ज्ञानं. There it is न्हैर्withैandर्. In line 24: 'ऋतुचिह्न- wait, is thatह्नorन्ह? In line 24, it is हwithनinside:ह्न! And above it, there is a small tick. Wait, could that tick be a quote mark? No, look at the quotes in this book: Line 3: 'क्रान्ति...- single quote before क. Line 8:'आद्येपदे...- single quote before आ. Line 24:'ऋतुचिह्न...- single quote before ऋ. Then what is'afterह्न? Wait, could it be

( १४ )
त्यक्त्वा भास्कराचार्येण ऋतुवर्णनद्वारा पदज्ञानं समीचीनं ज्ञात्वा कृतमिति ।
चन्द्रग्रहणाध्याये रविचन्द्रभुवां योजनबिम्बानि, रविचन्द्रयोर्योजनात्मककर्ण-
स्पष्टीकरणं, भूभा बिम्बानयनं, ग्रासमानाद्यानयनं, परिलेखप्रकाराश्चाचार्यैरुक्ताः,
श्रीपतिना भास्कराचार्येण च कथनक्रममादाय विशेषतया तथैवानूदितः । ब्रह्म-
गुप्तकृत एव सूर्यग्रहणाधिकारः श्रीपतिना प्रायः श्लोकान्तरैरुक्तः । उदयास्तमया-
ध्याये आयनदृक्कर्मसाधनं कृतं परं तन्न समीचीनं श्रीपतिनाऽपि प्राचीनरोक्तं
तदानयनं कृत्वा—
खनभोधृतिभिः समाहतं प्रथमं दृक्फलमायनाह्वयम् ।
द्युचराश्रितभोदयासुभिर्विहृतं स्पष्टमिह प्रजायते ॥
इत्यनेन तत्स्फुटीकरणं कृतं, एतदवलोक्य भास्कराचार्येण 'आयनं वल-
नमस्फुटेषुणा सङ्गुणमि' त्यादिना तदेव

( १५ )
इन्दूच्चोनार्ककोटिघ्ना गत्यंशा विभवा विधोः ।
गुणो व्यर्केन्दुदोः कोट्यो रूपपञ्चाप्तयोः क्रमात् ॥
फले शशाङ्कतद्गत्योर्लिप्ताद्ये स्वर्णयोर्वधे ।
ऋणं चन्द्रे धनं भुक्तौ स्वर्णसाम्यवधेऽन्यथा ॥
इत्यनेनैतादृश एव चन्द्रसंस्कारो मुञ्जालाचार्येण 'लघुमानस'नामके
करणग्रन्थे कथितः । परमेतयोः सहशत्वाभावात् -- श्रीपतिना वेधेन दृष्ट्वा ततो
भिन्नोऽयं कथित इति प्रतिभाति । श्रीपत्युक्तोऽयं संस्कारो भास्कराचार्येणासकृद्-
दृष्ट्वा विवेचितस्तत्र स्वोपलब्धेर्विस्तारपूर्वकं प्रतिपादनार्थमेको 'बीजोपनय'
नामको ग्रन्थः ५६ श्लोकात्मकः सिद्धान्तशिरोमणि रचनैकवर्षानन्तरं—
मयाय बीजोपनये यदन्ते सूर्योक्तमाद्यं परमं रहस्यम् ।
प्रकाशये गोप्यमपीह देवं प्रणम्य बीजं जगतां हितार्थ

ब्राह्मस्फुटसिद्धान्तोत्तरार्धे परिकर्मविंशतिः (सङ्कलितम्, व्यवकलितम्,
प्रत्युत्पन्नो गुणनम्, भागहारः, वर्गः, वर्गमूलम्, घनः, घनमूनम् । पञ्चजातयः,
त्रैराशिकम्, व्यस्तत्रैराशिकम्, पञ्चराशिकम्, सप्तराशिकम्, नवराशिकम्, एका-
दशराशिकम्, भाण्डप्रति भाण्डं चेति) कथिताऽस्ति, सर्वत्रैव चतुर्वेदाचार्य्योक्ता
उद्देशकाः (उदाहरगानि) सन्ति । सिद्धान्तशेखरेऽपि परिकर्मविंशतिः (अभित्ना-
ङ्कानां गुणन-भजन-वर्ग-वर्गमूल-घन-घनमूलानीति षट् ६, भिन्नाङ्कानां योगान्तर-
गुणन-भजन-वर्ग-वर्गमूलानीति षट् ६, भाग प्रभाग-भागानुबन्ध-भागापवाहाराख्य-
जाति चतुष्टयम् ४, विलोमकर्म १, त्रैराशिकम् १, व्यस्त त्रैगशिकम् १, पञ्च-
राशिकम् १, इति ) ब्रह्मगुप्तश्रीपत्युक्त विंशत्यां परिकर्मसु विषयवर्णने महानेव
[L1

ि'त्यादेर्विलोमेन परिधितो व्यासानयनवदस्ति,-> wait,'तद्वर्गतो दशगुणात्पदं परिधिरि'त्यादेर्विलोमेन`

• श्रीपतिनापि 'कालः स्यात्परिवेर्वर्गाद्दिग्भक्ताच्च पदं त्विहे'ति प्रकारानुकूलैव त्रिज्या- -> wait, is it स्यात्परिवेर्वर्गाद् or स्यात्परिधेर्वर्गाद्? Look closely at परिधेर्वर्गाद्: the letter has the loop at the top left characteristic of ध, but no top line across it. Yes, it's ध! But wait, does it look like वे? No, look at व in वर्गाद्: व has a rounded belly on the left with vertical line on right and full top line. ध in परिधेर् has the characteristic curly left horn of ध! So it is परिधेर्वर्गाद्.
• तिथियुगाग्नि ३४१५ मिताऽस्तीति स्वीकृता भास्कराचार्येण 'व्यासे भनन्दाग्नि-
• हते विभक्ते खबाणसूर्यैः परिधिः सुसूक्ष्मः' इत्यनेन व्यासात्परिध्यानयनं कथ्यते ।

वलोकनात्स्फुटमस्ति । भास्करेण 'अन्त्यज्योत्पत्तौ' बहवो विशेषाः प्रतिपादिताः
सन्ति ।
स्फुटगतिवासनायां—मन्दफलसाधनेऽपि कर्णानुपातेन यत्फलं तदेव समी-
चीनमिति कर्णः कथं न कृत इत्यस्य कारणम्—
त्रिज्याभक्तः परिधिः कर्णगुणो बाहुकोटिगुणाकारः ।
असकृन्मान्दे तत्फलमाद्यसमं नात्रकर्णोऽस्मात् ॥
कथितम् । सिद्धान्तशेखरे—
त्रिज्याहृतः श्रुतिगुणः परिधिर्यतोदोः कोट्योर्गुणो मृदुफलानयनेऽसकृत्स्यात् ।
स्यान्मान्दमाद्यसममेव फलं ततश्च कर्णः कृतो न मृदुकर्मणि तन्त्रकारैः ॥
इति श्रीपत्युक्तश्लोक आचार्यो ( ब्रह्मगुप्तो )क्त श्लोकस्यानुवादरूप एव,
भास्कराचार्येणापि—
स्वल्पान्तरत्वान्मृदुकर्मणीह कर्णः कृतो नेति वदन्ति केचित् ।
त्रिज्योद्धृतः कर्णगुणः कृतेऽपि कर्णो स्फुटः स्यात्परिधिर्यतोऽत्र ॥
तेनाद्यतुल्यं फलमेति तस्मात् कर्णः कृतो नेति च केचिदूचुः ।
नाशङ्कनीयं न चले किमित्थं यतो विचित्रा फलवासनाऽत्र ॥
इह कर्णेन यत्फलमानीयते तदेव समीचीनम् । यन्मन्दकर्मणि कर्णो न
कृतस्तत्स्वल्पान्तरादिति कथ्यते । मन्दकर्मणि मन्दकर्णतुल्येन व्यासार्धेन यद्वृत्तं
तत्कक्षावृत्तम् । तेन ग्रहो गच्छति । यो मन्दपरिधिः पाठपठितः स त्रिज्यापरिगतः ।
अतोऽसौ कर्णव्यासार्धे परिणम्यते । यदि त्रिज्यावृत्तेऽयं परिधिस्तदा कर्ण-
वृत्ते क इति स्फुटपरिधिः । ततः स्वेनाहृते परिधिना भुजकोटिजीवे भांशैरित्यादिना
यत्फलमागच्छति तत्रिज्यया गुणितं कर्णेनभक्तं यल्लब्धं तत्पूर्वफलतुल्यमेव
फलमागच्छतीति ब्रह्मगुप्तमतम् । अथ यद्येवं परिधेः कर्णेन स्फुटत्वं तर्हि किं
शीघ्रकर्मणि न कृतमित्याशङ्क्य चतुर्वेदः कथयति—ब्रह्मगुप्तेनान्येषां प्रतारण-
परमिदमुक्तमिति । तदसत् । चले कर्मणीत्थं किं न कृतमिति नाशङ्कनीयम् ।
यतः फलवासना विचित्राऽस्तीति । अन्यत्सर्वं पूर्वकथितमेवेति ।
ग्रहणवासनायां—छादकनिर्णयं कृत्वा राहुकृतं ग्रहणं न भवतीति वराह-
मिहिरादीनां मतं प्रतिपाद्य संहितामतमवलम्ब्य तन्निराकृतम् ।
राहुकृतं ग्रहणद्वयमागोपालाङ्गनादि सिद्धमिदम् ।
बहुफलमिदमपि सिद्धं जपहोमस्नानफलमत्र ॥

यहाँ पृष्ठ का पंक्ति-दर-पंक्ति पूर्ण एवं शुद्ध प्रतिलेखन प्रस्तुत है:

( १६ )
लोक प्रथेयमिति कथयित्वा राहुकृतं ग्रहणं भवतीत्यत्र स्मृति वाक्यं वेदवाक्यं च
प्रतिपादितम् । युक्त्या राहुकृतं ग्रहणं न भवति । परन्तु स्मृतिषु-पुराणेषु वेदेषु
च राहुकृतं ग्रहणं प्रतिपादितमस्त्यतोऽत्र द्वयोर्मतयोः समन्वयः—
राहुस्तच्छादयति प्रविशति यच्छुक्लपञ्चदश्यन्ते ।
भूछाया तमसीन्दोर्वरप्रदानात् कमलयोनेः ॥
चन्द्रोऽम्बुमयोऽधःस्थो यदग्निमयभास्करस्य मासान्ते ।
छादयति शमिततापो राहुश्छादयति तत् सवितुः ॥
आचार्येण कृतः । सिद्धान्तशिरोमणौ गोलाध्याये भास्कराचार्येण भूभाकृतं
चन्द्रग्रहणम् । चन्द्रकृतं सूर्यग्रहणं प्रतिपाद्य स्मृतिपुराणादिमतेन साकं
समन्वयार्थ—
राहुः कुभामण्डलगः शशाङ्कं शशाङ्कगश्छादयतीव बिम्बम्

( २० )
चेति सप्तानां ग्रहाणाम् = २१, चन्द्रादीनां विमण्डलानि = ६ सर्वेषां योगश्चल-
वृत्तान्येक पञ्चाशत् सन्तीति, सिद्धान्त शेखरेऽप्येवमेवास्ति यथा-
मन्दोच्चनीचवलयानि भवन्ति सप्त शैघ्याणि पञ्च च तथा प्रतिमण्डलानि ।
दृक्क्षेप दृष्टचपमजानि च खेचराणामकं विनैव खलु षट् च विमण्डलानि ॥
पञ्चाशदेकसहितानि च मण्डलानि पूर्वापरं वलयमुत्तरदक्षिणं च ।
क्ष्माजं तथा विषुवदुद्धलयाभिधाने पञ्च स्थिराणि कथितान्युडु खेचराणाम् ॥
इति यन्त्राध्याये-
सप्तदश कालयन्त्राण्यतो धनुस्तुर्यगोलकं चक्रम् ।
यष्टिः शङ्कुर्घटिका कपालकं कर्त्तरी पीठम् ॥
सलिलं भ्रमोऽवलम्बः कर्णश्छाया दिनार्धमर्कोऽक्षः ।
नतकालज्ञानार्थं तेषां संसाधनान्यष्टौ ॥
इत्यने धनुर्यन्त्रम् । तुरीयम् । चक्रयन्त्रम् । यष्टिः, शङ्कुः, घटीयन्त्रम् ।
कपालयन्त्रम् । कर्त्तरीयन्त्रम् । पीठसंज्ञं यन्त्रम् । सलिलं (जलम्), भ्रमः (शाराः),
अवलम्बसूत्रम्, छायाकर्णः, शङ्कुच्छाया, दिनार्धमानम्, सूर्यः, अक्षः (पलांशाः)
नतकालज्ञानार्थं सप्तदश काल यन्त्राणि सन्ति, तेषां यन्त्राणां मध्ये सलिलादीन्यष्टौ
यन्त्ररचना मूलकानि सन्ति, सिद्धान्तशेखरे 'गोलश्चक्रं कार्मुकं कर्त्तरी च कालज्ञाने
यन्त्रमन्यत् कपालम् । पीठं शङ्कुः स्याद् घटी यष्टिसंज्ञं गन्त्री यन्त्राण्यत्र दिक्
सम्मितानी' त्युक्त्य १ गोलयन्त्रम्, २ चक्रयन्त्रम्, ३ धनुर्यन्त्रम् । ४ कर्त्तरी नामक-
यन्त्रम् । ५ कपाल यन्त्रम् । ६ पीठ (फलक) यन्त्रम्, ७ शङ्कुनामकयन्त्रम् ।
८ घटीनामक यन्त्रम्, ९ यष्टि यन्त्रम् । १० गन्त्री (शकट) यन्त्रम् । इति दश-
मितानि यन्त्राणि श्रीपत्युक्तानि सन्तीति । शिष्यधीवृद्धिद तन्त्रे द्वादश यन्त्रा-
ण्युक्तानि यथा-
गोलो भगणश्चक्रं धनुर्घटी शङ्कुकटककर्तर्यः ।
पीठकपालशलाका द्वादश यन्त्राणि सह यष्ट्या ॥
कर्णच्छाया द्युदलं रविरक्षो लम्बको भ्रमः सलिलम् ।
स्युर्यन्त्रसाधनानि प्रज्ञा च समुद्यमश्चैवम् ॥
भास्कराचार्येण सिद्धान्त शिरोमणौ दशैव यन्त्राण्युक्तानि । यथा-
गोलो नाडीवलयं यष्टिः शङ्कुर्घटी चक्रम् ।
चापं तुर्यं फलकं धीरेकं पारमार्थिकं यन्त्रम् ॥ इति ।

( २१ )
सूर्य सिद्धान्तोक्त यन्त्राणि—
तुङ्गबीजसमायुक्तं गोलयन्त्रं प्रसाधयेत् ।
गोप्यमेतत्प्रकाशोक्तं सर्वगम्यं भवेदिह ॥
कालसंसाधनार्थाय तथा यन्त्राणि साधयेत् ।
एकाकी योजयेद्बीजं यन्त्रे विस्मयकारिणि ॥
शङ् कुयष्टिधनुश्चक्रैश्छायायन्त्रैरनेकधा ।
गुरूपदेशाद्विज्ञेयं कालज्ञानमतन्द्रितैः ॥
तोययन्त्रकपालाद्यैर्मयूरनरवानरैः ।
ससूत्ररेणुगर्भैश्च सम्यक् कालं प्रसाधयेत् ॥
पारदाराम्बुसूत्राणि शुल्बतैलजलानि च ।
बीजानि पांसवस्तेषु प्रयोगास्तेऽपि दुर्लभाः ॥
ताम्रपात्रमधश्छिद्रं न्यस्तं कुण्डेऽमलाम्भसि ।
षष्टिर्मज्जत्यहोरात्रे स्फुटं यन्त्रं कपालकम् ॥
नरयन्त्रं तथा साधु दिवा च विमले रवौ ।
छाया संसाधनैः प्रोक्तं कालसाधनमुत्तमम् ॥
मानाध्याये—
मानानि सौरचान्द्रार्क्षसावनानि ग्रहानयनमेभिः ।
मानैः पृथक् चतुर्भिः संव्यवहारोऽत्र लोकस्य ॥
इत्यनेन सौरचान्द्रनाक्षत्रसावनमानानि कथितानि, एभिरेव चतुर्भिर्मा-
नैर्लोकिानां व्यवहारा भवन्ति। केन केन मानेन के के पदार्था गृह्यन्ते इति सर्वे
प्रतिपादिताः सन्ति, ब्राह्मं, दिव्यं, पित्र्यं, प्राजापत्यं, बार्हस्पत्यं, सौरं, सावनं,
चान्द्रं, नाक्षत्रमिति नव मानानि सन्ति, एतेषु नवमानेष मनुष्यलोके मान-
चतुष्टयानां (सौर चान्द्रार्क्ष सावनानां) प्राधान्यम्, यतस्तैरेव तेषां व्यवहारा
दृश्यन्ते । सूर्यसिद्धान्त-सिद्धान्तशेखर-सिद्धान्तशिरोमण्यादिषु सर्वेषु ग्रन्थेषु-
मानानां सम्बन्धे समानरूपेणैव सर्वं प्रतिपादितमस्ति । ब्राह्मस्फुटसिद्धान्तेऽ-
त्राध्याये भूभादैर्घ्यं भूभामानञ्चापि प्रतिपादितमस्ति ।
संज्ञाध्याये—संज्ञाकथनकारणम् । सिद्धान्त एक एवास्ति, कस्मिन्नंशे
सूर्यसिद्धान्तादयो भिन्नाः सन्तीति प्रतिपाद्य स्वसिद्धान्तोत्तरार्धेऽनुक्रमणिकाः
कथिता आचार्येण, नान्येषु-सूर्यसिद्धान्त-सिद्धान्तशेखरादिसिद्धान्तग्रन्थेषु संज्ञा-
ध्यायः । अध्यायोपसंहारात्पूर्वमेकः प्रश्न विशेषः—

( २२ )
आग्नेये नैर्ऋत्ये वेष्टदिने संस्थितस्य योऽर्कस्य ।
शङ्कुच्छाये कथयति वर्षादपि वेत्ति सूर्य सः ॥
कथितोऽस्ति यदुत्तरं कोणाशङ्कोरानयनेन स्फुटमस्ति ।
संज्ञाध्यायकथनस्य किमपि प्रयोजनं नासीत् ॥
आचार्येण कथमेतस्याध्यायस्योल्लेखः कृत इति न जानीमः ।
ध्यानग्रहोपदेशाध्याये—चैत्रादौ मासगणानयनम् । चैत्रादौ दिनादिकं निधि
ध्रुवसाधनम् । इष्टमासादौ रव्यानयनम् । प्रतिमासं शशिकेन्द्रतिथिध्रुवक्षेपयोग-
नयनम् । प्रतिदिनचालनम् । चन्द्रसाधनमौदयिकरविसाधनञ्च । ज्याखण्डकानि
केन्द्रज्या साधनञ्च यथा -
त्रिंशत् सनवरसेन्दुर्जिनतिथिविषया गृहार्धचापानाम् ।
अर्धज्याखण्डानि ज्याभुक्तैक्यं स भोग्य फलम् ॥
गतभोग्यखण्डकान्तरदलविकलवधाच्छतैर्नवभिराप्तैः ।
तद्युतिदलं युतोनं भोग्यादूनाधिकं भोग्यम् ॥
इत्याचार्योक्तभोग्यखण्डस्पष्टीकरणमेव सिद्धान्तशिरोमणेर्ग्रहगणिता-
ध्यायस्य स्पष्टाधिकारे 'यातैष्ययोः खण्डकयोर्विशेषः शेषांशनिघ्नः' इत्यादिना
भास्कराचार्येण कथितम् । भास्कराचार्येण खार्क-१२० मिता त्रिज्या गृहीता,
अत्राचार्येण खतिथि १५० मिता त्रिज्या गृहीता । इत्यतीववैचित्र्यं यत्सर्वत्रैव
श्रीपतिनाऽऽचार्यश्लोकोक्तविषया एव छन्दोन्तरेण लिखिताः परं किं कारणं
यदपूर्वं भोग्यखण्डस्पष्टीकरणं न लिखितम् । चन्द्रे भुजफलसंस्कारः, तिथौ
फलसंस्कारश्च । इत्यादयः सर्वे विषया अपूर्वाः सन्ति । अत्राध्याये ये केचन
विषया लिखिताः सन्ति ते सूर्यसिद्धान्ते सिद्धान्तशेखरे, सिद्धान्तशिरोमणौ न
सन्ति ।
अनुगृहीतोऽस्म्यहं श्रीडाक्टर सत्यप्रकाश डी० एस० सी० महोदयानां
यैराङ्गलभाषायां कृपया ग्रन्थस्यास्य प्रस्तावना समरचि ।
सम्पादकमण्डलस्यान्ये सहयोगिनः ज्योतिषाचार्याः श्रीमुकुन्दमिश्राः,
श्रीविश्वनाथ झा, श्रीदयाशंकरदीक्षिताः, शास्त्रिणः श्रीओंदत्तशर्माणश्च सर्वे एव
मम धन्यवादस्य पात्रतामहंन्ति । एतेषाममूल्यसहयोगेनैवायं महान् ग्रन्थः सुचारु-
रूपेण सम्पूर्णतामगच्छत् ।
'पद्मश्रीप्रकाशनालयस्य' स्वामिने रमेशचन्द्रशर्मणोऽपि धन्याञ्जलिर्भवतु
यस्य महता परिश्रमेण ग्रन्थस्य प्रकाशनं कालेनैवाभवत् ।
अन्येभ्यः सर्वेभ्योऽपि धन्यवादान् प्रददे, यैरल्पमपि साहाय्यं विधायाहं
कृतार्थीकृतोऽस्मि, इति शम् ।
भृगु-आश्रमः } विदुषामनुचरः
३०-३-६६ } रामस्वरूप शर्मा

श्रीब्रह्मगुप्ताचार्य विरचितः
विभिन्नपाठान्तरसहितो
ब्राह्मस्फुटसिद्धान्तः

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Please provide an image that contains the relevant text or page to be transcribed.

CHAPTER I
Astronomy in Ancient
Nations
Brahmagupta's great works like the Khaṇḍakhādyaka and
the Brāhma-sphuṭa-siddhānta took astronomy to Arabs through
whom it spread to many countries of Europe. Al Beruni records
this testimony in his great book on India.. It is doubtful that
astronomy had its birth in Greece and China. From remote ages
China, India, Greece, Arabia and Egypt developed the entire
system in close cooperation. This knowledge must have spread
from their common cradle home where man for the first time
developed his culture and civilisation. In this chapter we pro-
pose to give a review of astronomy as developed in many of
these ancient lands, especially Arabia, people of which land
came in close contacts with India much before any recorded
time.
Dawn of Astronomy
The earliest man must have been the primitive astro-
nomer. The striking spectacles presented to him by the varied
appearances of a sky covered with thousands of twinkling
and non-twinkling objects of different degrees of brightness,
apparently revolving round the Earth, and the daily changing
phases of the Moon must have raised strange feelings of
the most primitive man also. Then he must have in course
of time observed the bright morning and evening stars, and at
a considerably late stage the comets and shooting stars and then
on occasions eclipses of the Sun and the Moon. These phenomena
not only raised feelings of admiration, but in different sections of
human society often feelings of superstitious alarm. By and
by stars became guides for the traveller by land and sea. In
the midst of these observations, one discovered various cycles :
cycle of day and night, cycle of seasons and cycle of other
details. Then there was a striking observation of the tides in a
sea changing with the phases of the Moon.

2 ASTRONOMY IN ANCIENT NATIONS
Earliest Discoveries
We shall briefly sketch out the order of astronomical
discoveries. The first phenomena to be noted must have
been the regularly recurring dawn (for this one may refer
to the Uṣā Sukta of the Ṛgveda), the sunrise and sunset (which
led to prātaḥ and sāyaṁ, i.e. morning and evening prayers of
the Vedic times), daylight, twilight and night concerning
which we have numerous Vedic hymns. Next it led to the
measurement of a day (which was of a short duration in
winters and of a long duration in summers). The Vedic Aryans
also discovered the variations in the duration of the day along
different latitudes, and the time of sunrise in places of different
longitudes. In fact the idea of longitudes and latitudes came suffi-
ciently afterwards. Man discovered month as related to the varia-
tion of light with the Moon's phases. In temperate regions, where
probably the first astronomical observations were systematically
made, the changing length of the day or the direction of the Sun
at rising or setting or the lengths of shadows cast at midday,
would show that the Sun's daily path in the sky altered through-
out the year, a time interval which was already marked by the
changing vegetation. According to Sir W.C. Dampier, "attempts
were made to determine the number of months in the cycle of
the seasons in Babylonia about 4000 B. C. and in the China soon
after. About 2000 B. C. the Babylonian year settled down to
one of 360 days or twelve months, the necessary adjustments
being made from time to time by the interposition of extra-
months." In India, this concept is of even much earlier origin.
The old inspired sages like Dīrghatamas discovered for the
observing man the Vedic Era and intercalation. I have
described this discovery in a special chapter on the subject in my
book the Founders of Sciences in Ancient India and a reference
may be made to the Āsya Vāmasya Suktam of the Ṛgveda. It
is impossible to assign an age to these old traditions. Round the
Yajña, developed the science of astronomy, mathematics,
anatomy and medicine in this ancient land of ours, which in
fact was the common heritage of a large number of people of
the modern world.
One might also say that a considerable period might have
well elapsed before it was noticed that at a particular season of

ZODIAC 3
the year, the same stars are seen at corresponding hours of the
night. Of course this circumstance was less conspicuous than
the regular variation of the Sun's altitude in the sky as the year
progresses. It is the surmise that the striking naked-eye cluster,
the Pleiades, must have been one of the earliest noted star-
groups, and it became the first star-group for providing the first
fairly close determination of the length of the year as approxim-
ately 365 days. The rising of this cluster in the evening was a
mark of the coming winter to primitive man ; and the husband-
man judged the time of reaping by its rising, and of ploughing
by its setting in very ancient times ; Sirius, Arcturus, the Hyades
and Orion were similarly equally useful to him. The passages
in the Taittirīya Saṁhitā and in the Śatapatha Brāhmaṇa clearly
indicate the confusion once created by following the concept of
lunar months without further adjustments :
"Now the seasons were desirous to have a share in the
sacrifice among the gods and said, 'Let us share in the sacri-
fice. Do not exclude us from the sacrifice ! Let us have a
share in the sacrifice !' The gods, however, did not approve
of this. The gods, not approving, the seasons went to the
Asuras, the malignant, spiteful enemies of the gods. Those
(Asuras) then throve in such a manner that they (the gods)
heard of it, for even while the foremost (of the Asuras)
were still ploughing and sowing, those behind them were
already engaged in reaping and threshing : indeed even
without tilling, the plants ripened forthwith for them.
(ŚBr. I.6.1.1-3)
The Zodiac
It is difficult to say how much time it must have
taken, but in fact, it was eventually noted that the Sun and
Moon travel over very similar paths among the stars during
their circuit of the sky. This led to the formation of the Zodiac
and its constellations, the centre of this zone, a belt about 16°
broad, being the annual path of the Sun or Ecliptic. The divi-
sion into twelve parts, each corresponding to a month of the
Sun's movement, was made ; and their connection with the solar
course during the year was found by observations of heliacal
risings or settings. These were the times of the year when certain
bright stars would first be seen to rise before the Sun, or when

4 ASTRONOMY IN ANCIENT NATIONS
they were last seen to set after sunset. In the case of Sirius, the
brightest fixed star, these would happen when the Sun was about
ten degrees below the horizon. For the less bright stars the
angle would be a larger one.
It must have been almost simultaneously observed that the
Moon in going like the Sun round the heavens always in the
same direction from west to east (i. e., opposite to the diurnal
motion which she shares with the other bodies), kept in general
to the same track in the sky. After a time, however, it must
have been noted by careful observers that this path was not con-
stant, but deviated from the centre line of the Zodiac, getting
away from that line up to a maximum deviation on either side
but slowly returning to it. In the course of a number of years, it
must have become evident that the Moon's path among the stars
does not lie always in the same line on the celestial sphere, but
in a zone or band about twenty moon breadths (10°) wide, occu-
pying the middle of the Zodiacal zone itself.
Among the bright stars Mercury, Venus, Mars, Jupiter
and Saturn (the first two of which are never seen very far from
the Sun in the sky) soon must have been noted to be moving in
the Zodiac with varying periods. The English name planet is de-
rived from Greek planetes, meaning a wanderer, since the planets
change their positions among the Zodiacal stars.
There is a word Sṭr which in the Ṛgveda always occurs in
the instrumental plural, Sṭrbhiḥ. The English word star is de-
rived from this word. Parāśara and Gṛtsamada, I have shown
elsewhere, were the first amongst the great observers, inspired by
the Ṛgvedic hymns, and Vāmadeva identified Bṛhaspati or the
Jupiter planet and Vena Bhārgava discovered tht planet Venus
which still bears the name of its discoverer.
Constellations
Long before the Zodiacal belt was divided into "signs" (700
B. C.), a number of asterisms, or the configuration of stars in the
sky had been arranged, the brighter stars of these configurations,
thus identified, proved very useful in indicating the seasons of the
year by the times of their rising or setting, and also in locating
the positions on the celestial vault of such moving objects as
planets, comets and shooting stars and in helping the traveller
by land or sea to determine direction.

CONSTELLATIONS 5
These named constellations date back to very early period.
In India, Gārgya is the name of an astronomer who is associated
with a hymn of the Atharvaveda which for the first time enume-
rates constellations. In many of these constellations, the stars
form a well marked group, clearly separated from other groups,
and the names given to these formations are supposed to have
been suggested by a resemblance to the shapes of certain familiar
objects. Of course, the resemblance is usually very slight, and
depended merely on a fancy.
It is remarkable that different countries devloped almost
similar notions regarding these constellations. The late Dr. A. C.
D. Crommelin considered that there is a reason to believe that
the stars may have been grouped to some extent by the Egyptians
as early as 4000 B. C., and he remarked on their use of the then
Pole Star for orienting the Great pyramid, Again, Chinese are
said to have mapped out the sky into many divisions of stars by
2500 B. C., if one can rely on their records.
The idea of constellations takes us to a date much earlier
than 2500 B. C. even. In total forty-eight have come down from
extremely ancient times, but these do not cover the entire extent
of the sky. The part not occupied by any of them evidently did
not rise above the horizon where the early astronomers to whom
we owe their naming lived; and the stars concerned were there-
fore not included in their constellation schemes. The centre of
this part (near the bright star Achernar) must have been near
the South Pole of the heavens of the time, and its angular radius
from the Pole gives us roughly the latitude of their homes. The
date appears to have been about 2800 B. C., when, owing to the
precession of the equinoxes, the South celestial pole was in the
position indicated. The latitude seems to have been about 38°
North. These are the findings of E. W. Maunder (Astronomy
without a Telescope, p.5, 1902); but from the same considerations
Dr. Crommelin assigns a latitude of 36° and a date 2460 B.C.,
and Proctor 2200 B. C. Maunder also suggested that the presence
of the Lion and Bear among the stellar configurations and the
absence of Elephant, Tiger, Camel and Crocodile seem to ex-
clude India towards the East and the countries towards the
West, the latitude and the longitude indicated being those of
Asia Minor or Armenia. The suggestion that the blank area in

6 ASTRONOMY IN ANCIENT NATIONS
the sky referred to gave an approximate date for the formation
of the constellations appears to have beeen first put forward in
1807 by Carl Schwartz, for some time Swedish Consul at Baku.¹
Indo-Greek Contacts
It is highly improbable that before Alexander, there had
been absolutly no contacts between India and the distant nations.
Even in pre-Alexandrian era, there had been such migration is
clearly evinced by the philological and mythological studies. But
we do not possess historic record of it.
The conquests of Alexander the Great made the Greeks
acquainted with the Eastern world, which had up to that
time been visited probably by very few Europeans, and it
likewise spread Greek culture to all the countries which the
victorious Macedonian had been able to reach. The Indian
province of his Empire became independent soon after
Alxander's death, and though the spread of Buddhism in the
third century B. C. checked the progress of Hellenism in
Northern India, the rise of the Greek kingdom of Bactria and
its gradual extension south and east continued for a long time to
keep alive the connection between India and the West. Not
only (as has beeen asserted) the Greek and Indian drama and
architecture have been strongly influenced by Hellenistic and
Indian contacts, it is beyond a doubt that the entire astronomy
of the two great nations is the offspring of these mutual
contacts.
In earliest times astronomy had only been cultivated in
India and in no other country. Some idea had been acquired
during those days of the periods of the Sun and Moon and the
planet Venus and Bṛhaspati (Jupiter), which were used for chrono-
logical purposes, the lunar motions being specially connected with
the proper times for sacrificial acts. The Vedic era was discovered
during this period by Viśvāmitra, and Gārgya enumerated the
Nakṣatras. Lagadha composed his Vedāṅga Jyotiṣa, which is the
first book on astronomy written in human literature. India dev-
eloped her geometry in connection with the construction of sacri-
ficial altars, and its account is found in the Śulba Sūtras of
Baudhāyana, Āśvalāyana and Kātyāyana. Āryabhaṭa laid the
foundations of algebra. One might still say that there is no sign of

1. See, Peter Doig : A concise History of Astronomy, London, 1950.

INDO-GREEK CONTACTS 7
accurate knowledge of the planetary motions earlier than about
the century of the Christian era. From thenceforth astronomy,
hitherto confined to rituals, appears as a science, treated in the
course of the next thousand years in a series of text-books,
the Siddhāntas,¹ the contents of which, though supposed to be
derived from divine sources are strongly influenced by Greek
authors. Prior to the Greek influence, we had ceremonies like
dvādaśāha (lasting for twelve days), ṣaḍaha (lasting for six days),
tryaha (lasting for three days) besides darśa-pūrṇamāsa ceremo-
nies connected with the New Moon and Full Moon. But the week
of seven days (Saptāha) was unknown in India. This concept of
week and the dedication of each day to the deity of one of the
seven planets, now appears for the first time. It is difficult to say
whether names of the planets were borrowed by Greeks from
India or vice versa, but they became common, e.g., Aśvajit or
Asphudit (Aphrodite), Dyugatiḥ or dyaus or Jīva (Zeus), Heli
(Helios), &c., while the zodiacal signs have superseded the earlier
but totally different twelve star-groups connected with the
Sun's motion, and proclaim their origin by their names:
Kriya, Tāvuri, Jituma, Karkin, Leya, Pāthena, Juka, Kaur-
pya, Taukshika, Ākokera, Hridroga, Ittha,
corresponding to Κριός, Ταῦρος, Δίδυμος, Καρκίνος, Λέων,
Παρθένος, Ζυγόν, Σκορπίος, Τοξότης, Αἰγόκερως, Ὑδροχόος,
Ἰχθύς².
A great many other Greek terms connected with geometry,
astronomy and astrology have also been transferred from Sans-
krit works to Greek and vice versa. This conclusively shows the
mutual influence on astronomy. Indian authors never failed to
acknowledge the ideas they borrowed from Greeks, e.g. Varāha-
mihira quotes the Yavanas or peoples of the west as authorities
for some of the scientific statements he makes. The name of the
Romaka Siddhānta (which is at least as old as A.D. 400) also
points in an unmistakable manner to its origin in one of the pro-
vinces of the Roman Empire.

1. The Romaka or Pauliśa Siddhānta (before 400 A. D.), See Varāhamihira's
   the Pañcasiddhāntikā (about 570 A.D., Varāhamihira died in 587 A.D.). The
   original Sūrya-siddhānta was prior to Varāhamihira, the modern edition is
   perhaps of the 13th century. See J. Burgess "Notes on Hindu Astronomy"
   J. R. A. S., October 1893, p. 742.

8 ASTRONOMY IN ANCIENT NATIONS
Earth as a Sphere
The astronomers of the Siddhāntas taught that the Earth
is a sphere, unsupported in space, and they reject the ancient my-
thological notion that it is supported by some animal like śeṣanā-
ga (serpent), kacchapa (tortoise), or diggajas (elephants) which
in turn rest on another, and so on, until the support of the last
one after all has to be left unexplained. Bhāskara II, about
A.D. 1150, who comments on the absurdity of this, also rejects
the idea that the Earth is perpetually falling, since it would fall
faster than an arrow shot upwards, on account of being heavier,
so that an arrow could never again reach the Earth.¹ Round the
Earth the planets are moving, all with the same linear velocity.
The diameter of the Earth is 1600 yojanas, the distance of the
Moon is 51,570 yojanas (or 64.5 times the radius of the Earth,
nearly equal to Ptolemy's greatest distance, 64⅙), while the dis-
tances of the other planets result from the assumption of
equal velocities.² The equation of centre of the planets
is found by an epicycle and to this arrangment the Hindus
add one of their own invention, by assuming that the epi-
cycle had a variable circumference, greatest when the planet is
at apogee or perigee and least at 90° from these, when the equa-
tion reaches its maximum. This contrivance of an oval epicycle
was by some astronomers applied to all the planets, by others
(Brahmagupta and Bhāskara) only to Mars and Venus, by others
it was altogether rejected.³ Why they complicated the calculation
in this way is not clear. Āryabhaṭa I of Kusumapura or Pāṭali-
putra, born A.D. 476, made another deviation from the Alexand-
rian doctrines, as appears in the Brahma-sphuṭa-siddhānta of
Brahmagupta, wherein he quotes the following from Āryabhaṭa:
"The sphere of the stars is stationary, and the Earth, making a
revolution, produces the daily rising and setting of stars and
planets." Brahmagupta rejects this idea, saying: "If the Earth
moves a minute in a prāṇa, then whence and what route does it
proceed? If it revolves, why do not lofty objects fall?" But his
commentator Caturveda Pṛthudaka Svāmi replies: "Āryabhaṭa's

1. As. Res. XII. p. 229 (Essays, II, p. 394).
2. The distances are proportional to the orbital periods of revolution, but for
   Mercury and Venus to the periods in the epicycles.
3. For further details see As. Res. II. p. 251 (Davis) and XII. p. 236
   (Colebrooke, also Essays, II. p. 401).