The central aim of the work is to compose a history of celestial motions based on careful study and observations, and then to devise geometric models or hypotheses that can provide a reliable basis for computing these motions accurately for both the past and the future5. The author was motivated to seek a different system because existing astronomical theories did not agree among themselves and contained significant "absurdities" when compared with observations.
The modelling relies heavily on geometry and mathematical calculation. Key mathematical principles and tools include:
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The universe and celestial bodies are considered spherical.
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Motions are fundamentally assumed to be uniform, eternal, and circular, or compounded from circular motions. Straight-line motions (librations) are also used but potentially understood as resulting from circular motions.
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The principles of plane and spherical triangles are essential for calculating positions, distances, and angles. A key question is how to obtain sides from angles and angles from sides.
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The use of straight lines subtended in a circle (chords) is a fundamental technique for relating arcs and lengths.
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Tables are extensively used to provide pre-calculated values for various phenomena and motions.
The geometric models employed include:
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Historically, eccentrics and epicycles were used to account for apparent nonuniformities, although the author finds issues with these traditional models5....
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Under the new hypothesis, the motion of the Earth itself accounts for many phenomena previously explained by complicated epicycles or eccentricities, such as the apparent nonuniformity of planetary motions and retrogradations. The Earth moves on a "great circle" around the sun.
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Specific motions like librations (appearing as straight-line oscillations) are introduced to explain phenomena such as the variation in the obliquity of the ecliptic.
The concept of prosthaphaereses (or equations) is central to reconciling the theoretical uniform motions with the observed apparent nonuniform motions; these are calculated differences that are added or subtracted to find the true position or motion.
The author stresses that these hypotheses are primarily tools for computation that provide a calculus consistent with observations, rather than necessarily representing the absolute physical truth, particularly because the true causes of apparent nonuniform motions were considered unknown. The work aims to make astronomical computations easier to understand and more enduring.
