Geometrical reasoning in the history of astronomy
Astronomers from Ptolemy to Euler argue from figures. Famulus Astra writes the model out, sets down the argument step by step with the rule that licenses each step, and checks it.
See an argument reconstructedA source beside its reconstruction
One segment of a source, passage by passage: the author's text in the original or in English, beside it the step that says the same thing explicitly, notes in a third column, and a link from every passage to its page in the edition.
Euler's argument for the tide-raising force
12 passages in Latin and English, each beside its reconstruction.
Open the source and its reconstruction →Arguments
Three reconstructions from three centuries. Each opens as an outline that unfolds: sub-arguments and cases are indented, a selected step is shown in the figure.
About the centre of its circle the planet moves unequally
Model, hypotheses, every step with its rule, and what the checks say. Overview first; open what you want to see.
Open the argument →Eccentric and epicycle place the sun at one point
Model, hypotheses, every step with its rule, and what the checks say. Overview first; open what you want to see.
Open the argument →The tide-raising force, to first order
Model, hypotheses, every step with its rule, and what the checks say. Overview first; open what you want to see.
Open the argument →Further: The emended second-order term of Opera omnia II 31, tested · The equation of centre is the angle at the sun, with tan c = e sin κ̄ / (R + e cos κ̄) · The two forms show the sun in the same direction when R'/r = R/e · The eccentricity and the apogee follow from the lengths of spring and summer
Papers
Each as PDF for reading, as HTML with the live argument for browsing, and as slides for presenting.
14 pp.
Geometrical Reasoning in the History of Astronomy
What an argument is about, what it says and what it does; what licenses a step; what the figure supplies; hypotheses, cases, equivalence, approximation; a vocabulary, a display format, a procedure, a table of rules.
10 pp.
Reconstructing Kepler's Reasoning in the Astronomia Nova
The argument about the equant in chapter 4: one figure, six points, about ten steps. The inequality holds in every position, and the hypothesis BC = BA is needed by no step.
12 pp.
Two Geometrical Arguments Reconstructed
Euler on the tide-raising force (E57), with an editorial emendation tested and found wrong; and the equivalence of eccentric and epicycle in Swerdlow's exposition of Ptolemy, argued in three cases.
10 pp.
Euler's Argument for the Tide-Raising Force, Reconstructed
One segment of a source, E57 §§22–29, passage by passage: Euler's Latin or English beside the step that says the same thing explicitly, with notes and a link to every page in the edition.
28 pp.
astra/1: A Language for Historical Astronomical Models and the Geometrical Reasoning about Them
Model, parametrisation, superposition, figure and derivation as five kinds of text; the four checks; reference objects; Ptolemy's solar model as the case study.
9 pp.
Reading Five Pages Deeply
Swerdlow on Ptolemy's solar model, checked assertion by assertion: 45 assertions, each with its address and a result that is recomputed.
The package
The language astra/1 and its tools: five kinds of text, four checks, figures, and the argument pane.
Documentation
The language, the kinds of text, derivations, arguments, checking, outputs, reference objects.
Read the documentation →Rules of derivation
22 rules: propositions of Euclid with Heath's wording and page, lemmas, and what each takes from the figure.
See the rules →On the command line
famulus-astra check famulus-astra derive kepler-equant-unequal-motion famulus-astra argument solar-equivalence-equal-radii --format html
In a page
<script src="assets/astra-argument.bundle.js"></script> <astra-argument src="argument.json" depth="overview"></astra-argument>
Famulus Lettre · Astra
Studies and reconstructions from this edition, published as numbered issues.
