Euler’s Argument for the Tide-Raising Force, Reconstructed

One segment of one source

• Euler, Inquisitio physica in causam fluxus ac refluxus maris (Eneström 57), chapter II
• The end of §22 and §§24–29: seven pages, 33–39 of Opera omnia II 31
• The question: by what force does the sun or the moon tend to move a particle of the earth relative to its centre?

“propria vis, qua quaeque particula agitabitur, innotescet, si a vi acceleratrice illam particulam sollicitante auferatur vis acceleratrix, quam centrum Terrae patitur” (§22)

The page: source beside reconstruction

• Twelve passages, nine parts of the argument
• One action per passage: open its page in the edition, in a separate window
• A compact figure stays in view and shows what the selected step speaks of

Nothing of the source is typed

• Latin: from the page of the edition, between a first and a last phrase that must be found exactly once
• English: the edition’s stored page translation, compared with the Latin; three wordings corrected, all at a page break
• Reference: from a checked record; paragraph addresses from the reference register
• The page is not built when a passage is not found, or a step stands beside no passage

Euler’s figure and the model

An emendation, tested

• Opera omnia: 4xx + yy, “Correxit EJA”; first edition and manuscript: 4xx − yy
• Against Euler’s exact component: 4xx − yy is of second order (1.8 · 10⁻⁴, 10⁻⁶, 10⁻⁸); 4xx + yy of first order only (2.0 · 10⁻², 10⁻³, 10⁻⁴)
• Euler’s sign was right; his results, which use the first term, are untouched

Where the reconstruction does not follow Euler

• §26: the resolution through QV and the similar triangles QVM, MPC is compared with its result, not rebuilt
• §25: the first resolution, with the diagonal MO, is left out; nothing later cites it
• §28: 54°45′ “circiter” is 54°44′ to the nearest minute
• The notes say each of these at its passage

The exposition as a format

• One file: passages, the steps beside them, notes
• One element, <astra-exposition>: Latin · English, Overview · Steps · Full, Notes, Figure
• The same file gives the page and the print
• Any segment of any source of a Famulus collection can be taken through its argument in this way