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Principia Mathematica, Fold-out Diagram

Isaac Newton · 1687

A fold-out engraved diagram from Newton's 1687 Principia illustrating his geometric treatment of motion and force.

This diagram, from Newton's own Principia, illustrates the mathematical methods he devised to explain motion.

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Engraved diagram on a cream page within a book, showing a curved comet path from Sol at left, with dated positions such as Nov. 25, Dec. 12, Jan. 5 and Mar. 5, labeled orbit lines and a sphere intersection line.
Isaac Newton, Philosophiae Naturalis Principia Mathematica, fold-out diagram, 1687. Wellcome Collection, London.

About this source

What it is

This fold-out page from Newton's Principia Mathematica (1687) contains an engraved diagram showing a curved path, likely tracing a comet's motion from the Sun, with dated positions and orbit lines. It is held by the Wellcome Collection in London.

Why it matters

Newton used geometric diagrams like this to demonstrate his laws of motion and gravitation mathematically. Such diagrams reveal how he combined observation, dates and geometry to prove his physical ideas rather than relying only on words.

Look closer

  • Why would Newton use a diagram instead of only writing in words?
  • What might the dated positions along the curve represent?
  • Why do you think this page folds out rather than sitting flat in the book?

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Title page of the 1687 first edition of Newton's Principia. Large capitals read PHILOSOPHIÆ NATURALIS PRINCIPIA MATHEMATICA, with author credit, Imprimatur by S. Pepys, dated Julii 5, 1686, and London printing by Josephi Streater, Anno MDCLXXXVII.Book

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Philosophiæ Naturalis Principia Mathematica

Isaac Newton · 1687

Title page with a page number marked [1] at top, reading PHILOSOPHIAE NATURALIS Principia MATHEMATICA, followed by the heading Definitiones and Def. I, with a Latin definition of quantity of matter in italic type. Faint bleed-through text from the reverse page is visible.Book

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Principia Mathematica, Page 1: Definitions

Isaac Newton · 1687

Black-and-white line engraving of an elderly man with long, wavy white hair seated in a dark armchair, wearing a dark coat, waistcoat, and white cravat, with his hands resting on his knee. A column appears at the right. Inscribed beneath: 'ISAACUS NEWTON EQ. AUR. ÆT. 83', with 'I. Vanderbank pinxit 1725' at lower left and 'Geo. Vertue Sculpsit 1726' at lower right.Painting

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Sir Isaac Newton, line engraving by Vertue, 1726

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Engraved portrait of Sir Isaac Newton, a man with long curled wig and dark robe, bust-length, against a shaded background. Caption below reads 'SIR ISAAC NEWTON' and publisher 'William Collins Glasgow & London'.Painting

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Sir Isaac Newton, stipple engraving by J. Scott after Kneller, 1702

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Title page of the 1704 first edition of Newton's Opticks. Red and black letters read 'OPTICKS: OR, A TREATISE OF THE REFLEXIONS, REFRACTIONS, INFLEXIONS and COLOURS OF LIGHT', followed by 'Also Two Treatises of the Species and Magnitude of Curvilinear Figures'. Imprint: London, printed for Sam. Smith and Benj. Walford, MDCCIV.Book

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