Siddhanta Siromani (Ganitadhyaya / Grahaganita quarter only)
Siddhanta Siromani (Ganitadhyaya / Grahaganita quarter only) — what it is, what it added, and what we retired from it.
Siddhanta Siromani (Ganitadhyaya / Grahaganita quarter only) — Bhaskaracarya II, translated by D. Arkasomayaji.
Edition consulted: English Exposition and Annotation in the light and language of modern Astronomy, Kendriya Sanskrit Vidyapeetha, Tirupati Series No. 29, published for the Rashtriya Sanskrit Sansthan, Ministry of Education, Government of India, 1990. .
What kind of text this is
NOT a verbatim translation and NOT the whole work. The editor states his own scope: “I have chosen to keep the commentary away from the Sanskrit text and Bhaskara’s own Vasana Bhasya… this work of mine seeks to present only the mathematical side of Siddhanta Siromani.” The scan covers only the Grahaganita/Ganitadhyaya quarter of four (Lilavati, Bijaganita, Grahaganita, Goladhyaya) and cross-references the others as material NOT present. The famous self-dating colophon lives in the missing Goladhyaya, so no verbatim self-dated verse is quotable here.
What it contributed
circular-reasoning-admitted — novel. Bhaskara’s own Vasanabhasya, under Verses 1-6 of the Bhaganopapatti, admits his proof of the sidereal-revolution constants is anticipated to commit Itaretarasrayadosa (circular reasoning), and states plainly that no mortal lifespan permits observing a full revolution of the slower planetary points - so the base numbers rest on Brahmagupta’s Agama taken on faith.
A named 12th-century astronomer’s self-aware admission that his own key derivation is circular is a stronger self-criticism specimen than any external critique in the corpus - the project’s own epistemic standard (checkability, not doctrine) applied by the author to himself.
dissent-answered-by-smrti — refinement. Per the modern editor, Bhaskara II - six centuries after Aryabhata, and explicitly a Brahmagupta-lineage astronomer - had Aryabhata’s earth-rotation verse available and instead endorsed the fixed-Earth, pravaha-wind model, “apparently for fear of tradition.”
CONTRADICTS the working assumption that Bhaskara II’s habit of correcting predecessors trends toward truth. On this one physical question the correction ran backward, three centuries after Brahmagupta’s generation and six after Aryabhata - a third documented instance of the same suppression, this time inside the very source used as the model’s correcting authority.
predecessor-corrected-by-name — novel. Bhaskara names and mathematically corrects Lalla’s Ayana Valana formula (confusing versed-sine with sine), disputes Lalla/Brahmagupta/Sripati/Madhava’s general Vyatipata rule with two worked counter-examples, and sarcastically dismisses Vateswara’s Brahma-birth-epoch Ahargana proposal - three registers of correction (formula error, worked counter-example, ridicule of an absurd premise) inside one author.
A concrete, checkable, named transmission-and-correction chain inside the ganita branch, exactly the kind of link the lineage thread needs between a 5th/8th-century figure and a 12th-century one - and the modern editor disputes Bhaskara’s own reading in the Vyatipata case, so correction is not shown as a one-way ratchet even within this single source.
samhita-branch-definition — refinement. Bhaskara’s own opening verses (7-8) of the astronomy volume name astrology/Samhita (Muhurta, calamity-omens) as a distinct part of Jyotisha from Ganita, and argue Ganita’s priority with similes; the Patadhyaya’s closing chapter explicitly separates a computed quantity (spherical astronomy) from its “only… astrological significance” (meaning).
Independent, six-centuries-later corroboration that the Ganita/astrology branch boundary Varahamihira states explicitly (Brihat Samhita 1.9-10) was still explicit and load-bearing to a pure-computation author opening his own treatise - and the branch boundary is applied at both ends of the book (opening polemic, closing chapter’s caveat).
ganita-serves-phala — novel. The Spastadhikara’s opening verse states that true planetary positions are computed partly “to decide auspicious moment… astrology and the like”; the Triprasnadhikara’s lagna verses (2-4) are pure rising-time/Ayanamsa computation, with the horoscope-casting application named only in the modern editor’s Comm., never in the verse.
The cleanest single worked example in the corpus of computation feeding, but not containing, interpretation: the verse computes a longitude; a separate, later, and in this text unstated step assigns it meaning for a horoscope.
ayanamsa-choice-argued — novel. Bhaskara is reported to have rejected the (shorter, pre-interpolation) Surya Siddhanta precession verse as giving a rate “too small,” choosing Munjala’s figure instead; the underlying phenomenon is tied to a stated observational method (gnomon shadow at the solstices), not asserted by authority.
Direct counterpoint to the corpus’s ayanamsa-unargued finding (Krishnamurti Paddhati’s KP ayanamsa as a bare, unargued number): a 12th-century author choosing between named rival ayanamsa rates on a stated numerical ground is a stronger epistemic practice than a modern manual that never argues its own zero-point.
denial-over-citation — refinement. Arkasomayaji’s 1990 preface argues at length against Greek-derivation of Hindu astronomy, using Aryabhata’s, Varahamihira’s and Brahmagupta’s own compilation-claims as evidence; his body commentary, confronted with the concrete Rasi/zodiac name correspondence, instead declines to adjudicate (“we shall not enter into the controversy here”).
A fourth instance of a modern Indian editor using his own preface to deny Greek transmission, independent of the classical text - and a documented inconsistency of register within one author: forceful denial where the evidence is general, agnostic non-adjudication where the evidence (matching names) is most specific.
greek-transmission — refinement. Zero yavana/mlechcha hits anywhere in Bhaskara’s own verses or Vasanabhasya; every Romaka/Paulisa/Greek reference traces to the 20th-century editor. Separately, the editor notes Bhaskara’s own 19-year Adhikamasa convergent matches the Romaka-Siddhanta/Metonic ratio - a parallel he draws, not one Bhaskara states.
Second corroboration (after Aryabhatiya) that transmission vocabulary belongs to the horoscopic branch and to modern commentary, not to the ganita branch’s own primary authors - even six centuries later, in an author who names Brahmagupta and Varahamihira by name for everything else.
author-dates-himself — contradiction. The only date evidence in this scan is an unquoted paraphrase (“62 years before his birth”) of Bhaskara’s own Vasanabhasya, pointing at Saka 1036 - the famous self-dated colophon (Saka 1072 composition, age 36) lives in the Goladhyaya, which this scan does not contain.
A weaker dating specimen than Aryabhatiya’s directly-quoted III.10, by exactly one step: paraphrase of a reference to a birth year, versus a quoted self-dated verse. Tier accordingly and do not treat Bhaskara as equally well-sourced from this file alone.
translator-dependence — refinement. This edition is a declared selective “Exposition and Annotation,” not a verbatim translation (“I have chosen to keep silent over passages which do not call for a mathematical elucidation”), and covers only the Grahaganita/Ganitadhyaya quarter of the four-part Siddhanta Siromani - Lilavati, Bijaganita and Goladhyaya are cross-referenced but absent.
A second access-layer caveat stacked on the first: any negative finding from this source (“the text never mentions X”) is scoped to one quarter of the work, filtered through a 20th-century mathematician’s selective exposition - the same truncation hazard already logged for Mansagari, now recurring in a pure-astronomy source.
Reading the text yourself
We quote and cite; we do not republish. Most translations in this corpus are in copyright, and the public-domain ones are better served by the Internet Archive than by a copy here. Citations give chapter and verse so any claim can be checked against your own edition.