सिद्धान्तदर्पण (महामहोपाध्याय सामन्त चन्द्रशेखर सिंह - नग्न-नेत्र खगोल वेध एवं गणित महाकोश)

गणित क्रिया शब्द v
(४) ऋ (छोड़ना)- ऋण
(५) क्षि (नष्ट होना, कम होना) क्षय
(६) ग्रह (छीनना)- प्र गृ ह्य
(७) चि (कम करना)- अपचय, अपचयात्मक, अवचीयते, अपचीयन्ते
(८) त्यज (छोड़ना)- त्यक्त्वा, त्यजेत्, त्यज्यन्ते
(९) नि (लेना)- अपनयन, अपनयेत, अपनीते, अपनीय, अपनीयते अपनीयन्ते,
समपनीय
(१०) पत् (गिरना)- निपातित, निपात्य, पतित, पातयित्वा, पातित, पात्यते
(११) युज (जोड़ना) वियोग, वियुक्ति
(१२) रह् (छोड़ना)-रहित विरहित
(१३) वृ (खोलना)- विवर, विवरकम्
(१४) वृज (बाहर करना) वर्जित, विवर्जित
(१५) शिष् (बाकी रखना) अवशिष्ट, अवशेष, विशिष्ट, विशिष्यते, विशेष,
विशेषण, विशेषित, विशिष्यते, शिष्ट, शिष्यते, शेष शेषयेत् ।
(१६) शुध् (धोना, साफ करना)- परिशुद्ध, परिशोध्य, प्रविशुद्ध, प्रविशोधयेत्,
प्रविशोध्य, विशुद्ध, विशोधयेत्, विशोध्यन्ते, विशोध्या, शुद्धम्, शुद्ध,
शुद्धि, शुद्धे, शुद्धयति, शुद्धयन्ति, शुद्धयन्ते, शुद्धेयेत्, शोधित, शोधनम्
शोधनीयम्, शोधयित्वा, शोधयेत, शोध्यम्, शोध्य, शोध्यते शोध्या,
संशुद्धि, संशुद्धि
(१७) श्लिष् अलग करना)- अविशिष्ट, विशिष्ट, विश्लेष, विश्लेषित
(१८) हा (घटाना, कम करना)- परिहीन, विहीन, हित्वा, हीन
(१९) हस् (कम होना)- हास
(२०) अन्य शब्द-अग्र (शेष), अन्तर
३. गुणा -
(१) अस् (दुहराना,) अभ्यस्त, अभ्यस्य, समभ्यस्त, समभ्यस्य
(२) क्षुद् (कुचलना, मारना) क्षुण्ण, संक्षुण्ण
(३) गुण् (गुणा करना)- गुण, गुणक, गुणकार, गुणना, गुणयित्वा, गुणयेत्,

सिद्धान्त दर्पण
गुणित, गुण्या, गुण्यते, गुण्या, गुण्यात्, संगुण, संगुणय्य, संगुणा, संगुणित,
संगुणा, संगुण्य
(४) ताड् (पीटना)- अभिताड़ित, ताड़ित
(५) वृत् (बार बार करना) उद् वर्त ना
(६) हन् (वध करना, मारना), अभिनिघ्न, अभिहत, अभिहत्य, आहत, आहत्य,
आहन्यात्, घात, घ्न, निघ्न, निहत, निहत्य, प्रणिघ्न, प्रणिहत्य, विसंहति,
संहति, संहत्य, संहन्यात्, समाहत, हत, हतम्, कृत्वा, इतहित्वा ।
४. भाग -
(१) खण्ड (तोड़ना) खण्ड्यात्
(२) छिद् (काटना, तोड़कर अलग करना, बांटना) -छित्त्वा, छिद्यते, छिन्द्यात्
छेद, छेद्य, संछेद
(३) भज् (बांटनां, भाग करना)- प्रविभजेत्, भक्त, भक्ते, भक्तव्या, भक्तूवा, भजन,
भजित, भजेत्, भाग, भागहार, भागे हते, भाजयेत, भाजित भाज्यम, भाज्य,
भाज्या विभक्त, विभजेत्, विभजेत, विभज्य विभज्यते विभाजित
विभाजयेत्
(४) भञ्ज् (फाड़ना, टुकड़ों में तोड़ना)- भंक्त्वा
(५) वृत् (अपने साथ)- अपवर्तन
(६) हृ (छीनना, बांटना)- अपहृत, आहरेत्, उद्धृत, उपाहर, विहृत, संहृतम्,
संहृत, संहृता, समद्धृत, हरतु, हरेत, हर्तव्या हृत, हृति, हते, हृत्वा, ह्रियते,
ह्रियमाण
५. वर्ग-कृति, याव, वर्ग, वर्गितम्, वर्गणा
६. वर्गमूल-द्विगतमूल, पद, मूल, वर्गमूल
७. घन-धन, त्रिगत, वृन्द, सदृश, त्रयाभ्यास
८. घनमूल-घनमूल, त्रिगतमूल

viii सिद्वान्त दर्पण
आत्मा के पर्याय-रूप
२. द्वि - जोड़ा के पर्यायवाची-युग्म, द्वितय, यमल, यम, उभ जोड़ा। अश्विनी
कुमार (२) के पर्यायवाची-अश्विन, दस। आंख (२) के पर्यायवाची
शब्द-अक्षि, ईक्षण, दृक्, चक्षु, दृक्, नेत्र, नयन, चक्षुष, लोचन, विलोचन।
हाथ के पर्यायवाची- बाहु, भुज, पंख या पक्ष (शुक्ल और कृष्ण)-पक्ष
३. (त्रि) गुण (सत्व, रज और तम) के पर्यायवाची- गुण। राम (परशुराम,
रामचन्द्र और बलराम)-राम। अग्नि (दावाग्नि, जठराग्नि, बड़वाग्नि)
अग्नि, ज्वलन, वह्नि, दहन, ऋतुभुक्, पावक, हुताशन, शिखि, अनल।
अन्य-त्रि, त्रितय
४. चतुर, तुरीय (चेतना की चतुर्थ अवस्था-सुषुप्ति, जाग्रत, स्वप्म, समाधि),
चातुर्य
वेद (ऋक्, साम, यजुर, अथर्व) के अर्थ में -वेद। कृत (सत्ययुग जिसमें
धर्म के ४ चरण थे), निगम, श्रुति। समुद्र (जल, लवण, क्षीर और श्वेत)
के अर्थ में-अब्धि, पायोधि, अम्भोधि, कूपार, वारिधि, रत्नाकरं रत्नभणार),
अम्भोनिधि, समुद्र अम्बुनिधि, उदधि, अहम्बुधि, पयोधि, अर्णव सागर,
अम्बुराशि सिन्धु, वार्द्धव
५. (पञ्च)- अर्थ (शब्द के पांच प्रकार के अर्थ होते हैं, संपत्ति पांच प्रकार की
है) के पर्याय अर्थ। इन्द्रिय (पांच कर्म या ज्ञान की इन्द्रियाँ) अर्थ में -
इन्द्रिय, विषय। बाण (कामदेव के पंचबाण) अरविन्द, अशोक, आम्र,
नवमल्लिका, नीलोत्पल) के पर्यायवाची-शर, बाण, मार्गण, इषु, अक्ष,
आशु, आशुग, विशिख, शिलीमुख, पृषत्क, सायक, पत्रिण। तन्मात्रा (५
तन्मात्राए या ५ मूल स्वरमात्राए-अ,इ,उ,ऋ, लृ)-अर्थ में- तत् (३
अध्याय १५४ श्लोक)
६. षड्, रस (६ रस भोजन के तिक्त, मधुर, लवण, काषाय, समअम्ल)। अंग
(५ कर्मेंद्रिय और मन), ऋतु (ग्रीष्म, वर्षा, हेमन्त, शिशिर, शरत्, वसन्त)
तर्क (षड् दर्शन)
७. सप्त। घोड़ों के अर्थ में (सूर्यकिरण के सात रंग सूर्यरथ के सात घोड़ों
के समान है)- वाजि, अश्व, हय, तुरंग। मुनि (सप्तर्षि)-मुनि दिति। स्वर
(संगीत के सात स्वर-षड्ज, ऋषभ, गान्धार, मध्यम, पञ्चम, धैवत और
निषाद), सर। पर्वत (भारत के सप्त पर्वत)-महीध्र, महीधर, भूमिधर,

सिद्धान्त दर्पण में प्रयुक्त अंकों के पर्याय शब्द
अंकों को शब्द में लिखने के अतिरिक्त गणित ज्योतिष में उन्हें दो और प्रकार
से व्यक्त किया जाता है । सूर्य सिद्धान्त, सिद्धान्त शिरोमणि तथा ब्रह्मस्फुट सिद्धान्त
में किसी अंक के लिए वैसे अर्थ के शब्द का प्रयोग हुआ है जिनकी गिनती उतनी
होती है । आर्य भट्ट ने अक्षरों की स्थान संख्या के अनुसार उनका अंकीय मान दिया
है, दशमलव पद्धति में उनका स्थान दिखाने के लिए उनके साथ उपयुक्त स्वर वर्ण
लगाये हैं ।आर्य भट्ट की तरह 'कटपयादि' विधि केरल में प्रचलित है जिसमें 'कट'
से आरम्भ (आदि) कर क वर्ग और च वर्ग के अक्षरों का अर्थ से ० तक है । इसी
प्रकार 'ट' आदि ट वर्ग, त वर्ग का १-१० अर्थ है । प वर्ग का अर्थ १-५ य से ह
तक १-८ हैं ।
शब्द पर्याय द्वारा संख्या लिखने पर शब्दों का क्रम बायें से दाहिने होता है
पर उनके द्वारा निर्दिष्ट अक्षरों का क्रम दाहिने से बायें होता है । (इकाई से आरम्भ)
होता है । 'कट पयादि' अक्षरों का क्रम दाहिने से बायें होता है । आर्य भट्ट में सिर्फ
सार्थक अंक (शून्य नहीं) लिखे जाते हैं जिनके साथ लगे स्वर के अनुसार उनका
दशमलव पद्धति में स्थान निश्चित होता है ।
शब्दों की तालिका इस प्रकार है-
० (शून्य)- आकाश तथा उसके पर्याय खाली स्थान में कुछ नहीं या शून्य
होता है)-ख, अभ्र, नभ, गगन, अम्बर, वियद्, व्योम आदि ईश्वर अनन्त
या पूर्ण अर्थ)-पूर्ण, अनन्त, विष्णुपद वामन के पद द्वारा नापा था, या विष्णु
अर्थात् सूर्य का मार्ग), पुष्कर
१/४ - पाद, अंघ्रि
सपाद या सांघ्रि +१/४, आप्त, आय आदि उपसर्ग और प्रत्यय भी
लगते है)
व्यंघ्रि -१/४ (ऊन, हीन आदि प्रत्यय भी लगते हैं ।
१/२ अर्द्ध, दल (इसे जोड़ने के अर्थ में स, प्राप्त और आय् शब्द लगते हैं,
घटाने के अर्थ में ऊन, हीन आदि लगते हैं ।
१. एक - पृथ्वी के पर्याय वाची शब्द-भुव, भू, क्षिति, कु, धरणी, स्थिरा,
वसुधा, भूमि, क्ष्मा, वसुन्धरा, महीधरा । चन्द्रमा के पर्याय वाची-चन्द्र,
शीतग, क्षपेश, इन्दु, अब्ज, विधु, सुधांशु, शशधर, शशि, शीतकर,
शीतभानु, सितांशु, निशानाथ, सितभानु, रजनीश

सिद्धान्त दर्पण में प्रयुक्त अंकों के पर्याय शब्द ix
भूभृत्, कुभृत् क्ष्माभूत्, गिरि, ग्रौ, मग, अग, अद्रि, इभ, शैल, पर्वत, वाद्धर्वग,
शिखरि ।
८. अष्ट, हाथी अर्थ में (आठ दिग्गज आठ दिशाओं को धारण किये हुए
है)- स्तम्भे रमा, दन्ति, द्विप, गज, मतंगज, कुञ्जरु द्विरद । सर्प अर्थ में
(आठ दिशाओं के सर्प)- नाग, भुजंग, फणभृत, व्याल, अहि, सर्प ।
वसु (आठ वसु थे)-उनमें एक के अवतार भीष्म थे । रूसी भाषा में यह
शब्द अभी तक व्यवहार होता है)
९. नव, अंक (१ से ९ तक अंक होते है), रन्ध्र छिद्र-(शरीर में छिद्र हैं- दो
आंख, दो कान, दो नाक, मुंह, मलद्वार, मूत्रद्वार) गो, नन्द नन्द (नवीं निधि
या सम्पत्ति है)
१० दिशा (दस दिशायें, चार दिशा, चार कोण, ऊपर नीचे), अर्थ में- दिश
आशा ३ । ५० तथा २ । १३ मे), दिक्, काष्ठा, २ । १२ तथा ३ ।४९ मे), हरित
३ । २३ में ।
११. ११ रुद्र प्रसिद्ध हैं अतः शिव के पर्याय वाची शब्द-रुद्र, गिरिश ईश,
शिव, भव, हर, ईश्वर, शंकर, पिनाकी
१२. अदिति के १२ पुत्र आदित्य (सबसे छोटे वामन या उपेन्द्र थे) । आदित्य
का अर्थ सूर्य भी होता है अतः सूर्य के पर्याय वाची शब्द-अर्क, आदित्य,
सहस्त्रांशु, सूर्य, रवि, प्रभाकर, तपन
१३. विश्व
१४. ब्रह्मा के एक दिन में १४ मनु या इन्द्र होते हैं अतः उनके पर्यायवाची
शब्द-मनु, इन्द्र, शक्र, त्वाष्ट्र
१५. तिथि (एक पक्ष में १५ तिथि होती है ।)
१६. भूप (आठ लोक पाल और आठ दिकपाल-पृथ्वी या भू के १६ पालने
वाले हैं) नृप (भूप का पर्याय) अष्टि (आठ आठ)
१७. घन (कम्पास द्वारा वृत्त के भीतर सबसे ज्यादा इतनी भुजाओं का समक्षेत्र
बन सकता है), अत्यष्टि (अष्टि या १६ से ज्यादा)
१८. धृति
१९. अतिधृति
२०. नख

x सिद्धान्त दर्पण
२१. वैश्व (६ ।६२)
२२. आकृति, वैष्णव (६ ।६२), विष्णु
२३. धनि (७ ।८९)- धनिष्ठा नक्षत्र अश्विनी से २३ वां है ।
२४. सिद्ध, जिन, प्रचेतस् (२४ जैन तीर्थकर, २४ प्रचेता के पुत्र थे)
२५. तत्व (महत्तत्व, तन्मात्रा, इन्द्रिय और पंचभूत कुल २५ है)
२७. भ (२७ नक्षत्र है)
३२. दन्त, रद (दांत ३२ हैं)
३३ देवताओं के अर्थ में (देवता ३३ या ३३ कोटि है)- सुर, निर्जर, देव,
गीर्वाण
४९. मरुत् (४९ पवन हैं)

Introduction¹
In his Brihat Samhita, Varaha-mihira
enumerates the requisite qualifications of an
astronomer. According to him, an astronmer should
be able to explain the differences in the various
Siddhantas, to demonstrate with the help of
instruments the moment of the Sun's turning to the
north or to the south, and of his entering the prime
vertical and the meridian, and to make calculation
agree with observation.
Unfortunately, the true science of astronomy
has been ousted by the pseudo-science of astrology,
whose votaries are to be found in almost every town

1. Tycho Brahe (1546-1601 A.D.), a Dane, born at
   Knudsthrop, near the Baltic, three years after Copernicus
   (1473-1543 A.D.) teminated his career. The fame of Tycho
   has been obscured by his rejection of the Copernican
   doctrine, and the construction of a system of his own,
   combining the elements of the Ptolemaic and Copernican
   theories. He maintained the earth to be the immovable
   centre of the universe, but supposed the planets to revolve
   round the Sun, and to be carried with their centre in
   revolution round the earth. Samanta Chandrasekhar,
   contrary to Tycho's university education royal favour, was
   conserevative and well versed in Hindu - Astronomy by
   the study of Siddhantas without any royal patronage and
   was far from modern education even in 19th century i.e.
   300 years after Tycho. But strangely enough
   Chandrasekhar adopts the planets' orbit as conceived by
   Tycho, who was usually deemed discreditable in those
   days for his hypothesis. Despite this late Prof. Jogesh Ch.
   Roy, an admirer of Chandrasekhar, however finds
   pleasure in comparing with Tycho.

xii सिद्धान्त दर्पण
and village of India at the present day. No doubt,
there are men who have committed to memory some
stray couplets from Siddhantas, and can perhaps
compute an almanac with the aid of tables. But, as
Bhaskara has well said, an astronomer without a
knowledge of spherics is what food is without
clarified butter, a monarchy without its monarch,
and an assembly without a speaker.
Astronomy as a science is not cultivated by
those whose business it should be to do so. They
would rather learn to read the thoughts of simple
persons and pretend to predict future events, than
dive into the mysteries of Kalpas and Yugas, for
less observe the heavens. Those that have a desire
to study the science have no means of doing it,
while those that have the means have no desire to
watch the movements of the planets. Our students
of the English colleges are busy in cramming the
answers to expected questions and our university
men are too busy to have leisure to think about the
revival of the indigenous sciences and arts of the
country. It is not strange therefore that the
mathematical science of astronomy has been
relegated to the halfread, illiterate, fortune-tellers
who are not ashamed to assume the title of
mathematician. For, the name mathematician (गणक)
has been degarded to mean only an astrologer.
In this state of indigenous sciences, it is singular
to find a man born and brought up in the recesses
of the hills of Orissa, far removed from all
educational activity and the influence of imported
western civilization, silently trading his way into
such a difficult science as mathematics. It is a unique
experience in the department of national
development to find a man really striving after

Introduction xiii
knowledge for its own sake, under difficulties
whose magnitude is no less startling than the
boldness of his attempt.
This is my apology for bringing before the
public, a Sanskrit work written entirely in the way
of our ancient Siddhantas and never meant to see
the light. It is the life-long labour of Chandrasekhara
Simha Samanta of Orissa, written in a language
which few men care to study in these days of
English education.
Modern Europe boasts of discoveries, one of
which alone would have been the glory of the past.
The science of astronomy has been developed to so
great an extent as to shed a lustre on the bright
records of original and patient researches in the
domain of Physical Science. The telescope, the
spectroscope, and last but not the least, the art of
photography, have gone hand in hand in the service
of dillgent workers. In these days of "scopes" and
"meters", it may be thought useless to put forward
the poor work of a Hindu whose education is in no
way superior to that of an astronomer of
pre-telescopic Europe. And there are men, too, who
have thought that much nonsense has already been
written about him.
Let them but calmly take stock of the present
state of Hindu astronomy. Let them find out a
couple of mathematicians, brought up wholly in
sanskrit studies, who can intelligently attack the
intricate calculations of a solar eclipse. Nor is there
any noticeable endeavour to revive the science.
What with natural apathy, and what with want of
encouragement by endowments, no addition to the
stock of the world's knowledge has been made by
my countrymen for many a long year. If in these

xiv सिद्धान्त दर्पण
circumstances something, however poor, is laid
before us, something, however crude, is evolved
from within, we should rejoice over it.
Whatever may be thought of the merits of the
work, I regard it as a misfortune that the author
has not found a man to introduce his work, better
qualified than myself, whose daily avocations run
in a different groove. For my part, I shall deem my
efforts amply rewarded, if my countrymen, to
whom original researches are as yet a thing of the
future, find in the life and doings of my author a
living example of what patient inquiry after truth
and diligent struggle after knowledge can achieve.
But I caution them again against high hopes. To
apperciate the man, one must compare his work
with others produced under similar conditions. It
will be unfair to expect anything new in the work
which will be useful to those who have studied
European Science. Let me therefore briefly recount
a few bright names from the annals of our ancient
astronomy that the present work may be taken and
its true worth.
Not to dive into the antiquity of Hindu
astronomy, which is as old as the Vedas and
regarding which abler men have measured swords,
let me begin the story from the point where we
tread on the firm ground of history. It begins with
Aryabhatta of Kusumapura (Pataliputtra), the
Andubarius of the Greeks, the Arjabhara of the
Arabs, and the Indian founder of the theory of the
earth's daily rotation. He was born in the Saka year
398 (A.D.476) and wrote his famous work at the age
of twenty-three. It was he in whose work we find,
as far as our present knowledge goes the first
successful attempt to solve indeterminate equations

Introduction xv
of the first degree. He enjoyed a wide reputation
which can only be explained by supposing that he
was an original observe and made improvements
upon older astronomy.
Hindu astronomy was then passing through the
state of childhood, and a few years later, we find
Varaha-mihira of Avanti (Ujjayini), adoring the court
of Vikramaditya the Great, about whom many a tale
of adventure and narrow escape from death has
been recounted. Varaha's encyclopaedic knowledge
made him famous. But he is remembered more as
a compiler than as an original worker. His
astronomical compilation, named Panchasiddha-
ntika was written about the Saka year 427 (505 A.D.)
Next, the name of Brahmagupta, son of Jishnu,
introduces an important chapter in the history of
Sanskrit astronomy. He wrote his work,
Brahmasphuta-siddhanta in Saka 550 (628 A.D.) at
the age of thirty, somewhere near Rewa. He was a
practical astronomer, and made several corrections
in the older astronomy. Indeed, the form in which
we find Hindu astronomy at the present day, dates
from him. He was a consummate algebraist, from
whom the Arabs got their knowledge of the science.
An indeterminate equation of the second degree, of
which he gives solution, was a prize problem in
Europe as late as the 17th century.
But the fame of Bhaskar born in the Saka year
1036 (1114 A.D.), near the Sahyadri (Western
Ghats), threw all his predecessors into the shade.
He is a glory to us, a wonder among Europeans.
His great work Siddhanta-Siromani, is one of the
standard treaties of the present day. He appears to
have made use of the Differential Calculus.

xvi सिद्धान्त दर्पण
With the death of Bhaskara, the living breath
of mathematical science parted from India. Repeated
invasions by a barbarous nation poured forth an
abundance of calamities and in the troubled times
the sacred muse of learning fled and hid herself
among a herd of commentators in the Deccan. In
the dark ages that followed, amidst the petty
dissensions of a host of semi-indepndent States, we
find intellectual effort at a stand-still; men were
content to chew the cud of what their predecessors
had thought and done. At last, one name of this
period is worth mentioning. This is Ganesa of
Nandigrama who wrote his Graha-laghava in Saka
1442 (1520 A.D.), a work which has been employed
as an easy hand-book of astronomy in some parts
of the country. Arab influence and, latterly, the
contact with Europeans did not benefit the science
much. It was during the reign of Jayasimha of
Jayapura so late as the 17th century, that the Arabic
Almagest and Euclid were translated into Sanskrit,
and it was he at whose instance five observatories
were built at various places in Northern India.
The long chain of astronomers was snapped
asunder for a period of at least four hundred years.
No doubt, there were astronomers, as there are
now, and some of them may have for a time enjoyed
a reputation, however local in character. But they
have hardly left any permanent mark on the
progress of the science.
Will it be estimating this work too highly if we
regard Chandrasekhara as forming a link in the long
chain ? Be that as it may, it is a most gratifying
thing that Chandrasekhara has not laboured in vain.
His work has already exercised an influence upon
Hindu astronomy, and hence upon Hindu society.

Introduction XVII
I say upon Hindu society, to which a correct
knowledge of the ever-changing positions of the
heavenly bodies is neither a matter for the
inquisitive, nor one which may be safely let alone.
For, Hindu life is nothing if not a routine of religious
practices, due observance of which necessitates a
knowledge of the positions of the planets and the
stars. Indeed, a correct almanac is an indispensable
equipment of every Hindu household. All religious
observances and rites are regulated by the almanac,
and some of these require very accurate
determinations. For instance, a Hindu must know
the exact moment when a particular position ends
and another begins.
It has, however, been observed that no two
current almanacs agree in their computations. A .
fierce controversy is going on between the
conservatives and the liberals in Hindu India about
the correction of almanacs, and therefore about the
data of the Siddhantas. The orthodox of the Hindu
community refuse to believe in the existence of
errors that have crept into the figures of the old
Siddhantas in course of time. To use the foreign
Nautical Almanac to regulate the religious
observances is out of the question. Any correction,
if necessary, must come from within, from a Hindu
uninfluenced by foreign education. It is not for
Europe, with all her brilliant scientific discoveries
and wonderful inventions of labour-saving
machinery, to take the place of the old Rishis, whose
hallowed names are associated with every
department of useful knowledge. Europe may be
our guide in matters temporal, but must not dictate
a work in matters spiritual. Materially, a Hindu is

xviii सिद्धान्त दर्पण
hardly of old days, though spiritually, I believe, he
is still the same.
The value of the Siddhanta-darpana, the work
of an orthodox Hindu, showing errors in our
current almanacs, cannot thus be over-rated. Here
is a man who has practically tested the elements
hitherto followed, and found reasons for correction.
And he has authority for doing so from the
honoured Rishis, who have given their sanction to
the adoption of such corrections as may be
necessary for the purpose of making calculation
agree with observation.
The influence which Chandrasekhar’s work has
already exerted upon society is not inconsiderable.
Some twenty-three years ago a meeting of learned
Panditas and Hindu astronomers was called at Puri
to select an almanac according to which the
numerous daily rites of worship were to be
conducted in the temple. The meeting decided in
favour of the almanac computed after this work.
One of the Chandrasekhar’s pupils has been
computing an almanac every year, which is used
not only at Puri but throughout the greater part of
Orissa. Another pupil of his publishes a Bengali
almanac which has a by no means insignificant sale.
Thus Chandrasekhara has already gained a
foot-hold in Hindu society and has inaugurated
silently but effecually an advance upon the current
almanacs. At any rate, he has silenced all
opponents, and has made the question of correction
possible in the near future.
To fully apperciate him, it is necessary to say
a few words on his early life and education. Some
four years ago, I first made his acquaintance, and
from conversation with him on astronomical

Introduction xix
subjects, I was surprised to find in him a man of
genius and extraordinary merit. Since then I have
looked into his work, Siddhanta-darpana, written
on palm leaves in Oriya character, the result of his
life-long labour in the field of astronomical research.
Two years ago¹ he was honoured by Government
with the title of Mahamahopadhyaya, a title hitherto
enjoyed only by Brahman versed in Sanskrit lore.
Chandrasekhara however, is not a Brahman but a
Kshattriya by caste.
He was born in the Saka-year 1757 (1835 A.D.)²
in the small village of Khandapara, some 50 or 60
miles West of Katak, amidst the hills and jungles
for which Western Orissa is famous. It is the chief
town of the Raja of Khandapara - one of the
tributary chiefs of Orissa. Chandrasekhara belongs
to the Raj family, the present Raja, Natabara
Mardaraj, Bhramaravara Ray being a son of
Chandrasekhara's eldest cousin. The full name of
the author is Chandrasekhara Simha Samanta
Harichandana Mahapatra. Harichandana and
Mahapatara are mere titles bestowed by the Raja of
Puri, whose influence upon the destinies of the
Rajas of Orissa is still as unbounded as was that of
the Pope of Rome on the vassals of medieval
Europe. He is styled Samanta as befits a member
of the Raj family. In Orissa, however he is best

1. The sanad conferring the Mahamahopadhyaya to Samanta
   Chandrasekhar bears the date 3rd June, 1893. Hence this
   portion was written by late Prof. Jogesh Ch. Ray in the
   year 1895 and the article was complete and printed finally
   in the year 1899.
2. Prof. Jogesh Ch. Roy has simply added 78 to the Saka
   era 1757 to get the A.D. But actually the date of birth
   when calculated comes to be 11th January, 1836 A.D.

xx सिद्धान्त दर्पण
known by the familar name of Pathani Saanta
(corrupted from Pathan and Samanta), a nickname
given him by his parents on account of their first
two children having died in infancy.
At an early age Chandrasekhara received
instruction in Sanskrit. For sometime he studied
Sanskrit Grammar, Smritis and Puranas, logic and
medicine, and read all the important Kavyas in the
original. His education has thus been varied and
many sided. But it has stood him in much better
stead than the modern elaborately arranged
curriculum of the English schools, through which
he would have been thrust, had he lived nearer a
town.
At the age of ten, one of his uncles¹ taught him
a little of astrology. He shewed the young
Chandrasekhar some of the stars to satisfy his
curiosity so natural in young children and thus
gradually initiated him into the mysteries of
astrology. At this age, his extraordinary desire to
test for himself the position of the stars as they
changed night after night was predominant. The
determination of lagnas is a very frequent necessity
in horoscopy; and the varying position of the
planets among the stars, without a knowledge of
which astrological predictions could not be made,
led him to watch their movements. This idle
curiosity exhibited in star-gazing developed into the
habit, of a really fruitful study of astronomy. There
was, however, no teacher who could instruct him
in the science, and he was quite ignorant of any
language save Sanskrit and his mother-tongue

1. It was his father but not uncle according to the biographer
   Pt. Chandrasekhar Mishra of Khandapara:

Introduction xxi
Oriya. He found, however, a few Sanskrit
Siddhantas in the family library, and applied
himself diligently to master them with the help of
commentaries.
At the age of fifteen, when he came to learn
the meaning of lagna and the rules for calculating
ephemerides of planets, he was surprised to find
that neither did the stars apear on the horizon at
the right moment, nor could the planets be seen in
their right places. Again and again, he measured
with a graduated rod the relative distances of the
heavenly bodies in the vain hope of finding an
agreement between calculation and observation,
and, again and agian his hopes were dashed to the
ground. Was it possible that the rules and the
figures of the famous Siddhantas were not accurate
enough, or was it possible that he had made errors
in his daily observations? Correct observation was
the only test to settle the question. There were no
mathematical instrument-makers to supply him with
the requisite instruments. The old Siddhantas give
brief instructions for constructing them, and he had
no other alternative than to make for himself, a few
primitive instruments for measuring time and
angular distance.
Some of my readers may be desirous of
knowing something of his observatory. It was the
clear, blue vault of the heavens that was his
observatory; and its equipment consisted of an
armillary sphere and a vertical wheel as substitutes
for modern transit and alta-azimuth, and the
time-honoured clepsydra took the place of the
sidereal clock. Of course, the all-useful gnomon
found a place in the observatory, and I am
informed, he had also a self-revolving instrument

xxii सिद्धान्त दर्पण
made of the pericarps of the Bottle-Gourd
(Lagenaria Vulgaris) with water and mercury. But
it was more of the nature of a curiosity than of
much practical use. The instrument, of which he
made constant use, was one devised by himself.
This, which he is fond of calling his Manayantra
(measuring instrument), may be properly called a
tangent-staff, it consists of a thin rod of wood,
twenty-four digits long, at one end of which is fixed
another rod at right angles in the form of a T. The
cross-piece is notched and also pierced with holes
at distance equal to the tangents of the angles
formed at the free extremity of the other rod. Of
course, such a rude instrument did not admit of
being so divided as to enable him to measure a
degree with any accuracy.
But it is a real pleasure to see him handling his
Manayantra with a precision marvellous to behold.
Constant practice has given him such facility with
it, that he would not care to have recourse to his
other instruments although better suited for
measurement of vertical angles. Indeed, in most
cases, mere inspection is often sufficient to enable
him to hit the angle to the nearest degree.
One instance of the perfection he has attained
by practice came before us when I saw him for the
first time. Some of my friends doubted his
pretensions to practical astronomy, and were
desirous of testing his knowledge. One evening
when Mars and Venus were about 6° apart in the
western sky, he was requested to show, if he could,
with the help of any improvised instrument the
actual distance between the planets. After a
moment’s pause, he made his manyantra out of a
stick 42 digits long, attaching a crosspiece of 4-1/2

Introduction xxiii
digits to one end. The trigonometrical functions of
sines and cosines were all committed to his memory.
The necessary calculations were mentally made, and
his instrument was ready in a few minutes.
On this occasion, he saw a telescope for the
first time. He had heard of its wonderful powers,
but had no idea of its performances. He requested
me to show him the planets through one.
Unfortunately, I had with me then a telescope no
bigger than a refractor of 3-1/2″ diameter. This was
adjusted for him with a power of 80. The keen
delight with which he looked at the varied and
picturesque appearance of the moon, absorbing him
for sometime can better be imagined than described.
When the novelty of the aspect had abated a-little,
he wanted to know the magnifying power. He was
told to find it out for himself, if he could. The
question is itself puzzling, and I did not expect any
answer. But he startled me by saying that the
instrument magnified about one hundred
diameters. He had measured the enlarged image of
the moon as seen through the telescope and had
compared it with the appearant to diameter
well-known to him.
The planet jupiter was next shown through the
telescope. I should rather say that he directed the
instrument to the planet and saw it himself. The
apparent motion of the planet quickened by about
a hundred times through the instrument, was
followed by him for sometime till he could see the
belts and the satellites to his heart’s content. It was
at this moment that he gave vent to his bitter regret
that he had not the advantage of such instruments
in his younger days.
Next morning we had a talk about tithis. I said

xxiv सिद्धान्त दर्पण
that the almanac-makers of Bengal would not be
believe in any variation in accepted duration of the
tithis. Hearing this, he was silent for a minute or
two, as if he doubted the fact. Being pressed for
his opinion, he quoted a line from his work,
meaning that arguments can never defeat the results
of direct observation.
He had read in a vernacular text book that the
sun sometimes exhibited dark spots on his radiant
orb, and was anxious to see if it was really so. I
asked him to accept the fact as true; but he said he
would not believe it unless he saw spots with his
own eyes. To this I retorted by asking if he had
ever believed in the existence of the seven
atmospehrs of the Siddhantas. His reply was that
the statement was to be taken at what it was worth,
and he had no opinion of his own to give. The
minimum sun-spot period had been passing; but a
few that he saw made him reflect upon them a long
while.
None can read his life without gaining a fresh
insight into the marvellous thoroughness with
which our ancestors devoted themselves to their
studies, our universitymen being only surface-deep
in subjects more than one. The living breath of
science has departed from India with the departure
of men whom Chandrasekhara had made his ideal.
He is an adherent of truth obtained by direct
observation, and with all his respect for the
ancients, would not hesitate to denounce a Sastric
authority, if a proof to the contrary were obtained.
Were he placed in a well-equipped observatory of
modern days, I doubt not he would enrich science
with his assiduous labour and valuable obser-
vations.