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Parallelogrammum Prosopographicum

Abstract

This paper investigates the ‘parallelogrammum prosopographicum’ (prosopographical parallelogram), a little-known device for drawing from life using parallel lines. The instrument, described in an article published in 1673 in the Philosophical Transactions, was adapted from Christoph Scheiner’s stereograph and designed as a practical method to bypass the visual effects of perspectival foreshortening. The present paper examines the geometrical and mechanical principles of the parallelogram and the rationale deployed by its inventor. It then locates the implications of the device within a history of orthographic projection through mathematical instruments in late seventeenth-century London. The paper ultimately argues that the programmatic aim of the parallelogram constitutes a relevant case study for a history of early modern architectural representation, a permeable field of research laying on the threshold between projectivity, mathematical practice and instrumentation.

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Notes

  1. In the journal index of the Philosophical Transactions, the title was translated into English: ‘a new way of orthographically delineating by parallel visual rays the posture and actions of an Humane body, exactly preserving the symmetry and proportion of the parts; by Mr. John Saint-Clare’ [sic].

  2. The name of the author as presented in the journal is John St. Clare (Ioanne de Sancto Claro). According to Rupert Hall and Marie Boas Hall however, his name was George (Hall and Hall 1975: 139). George Sinclair may have been the nephew of the mathematician of the same name, author of The Hydrostaticks and party to a controversy with James Gregory (Craik 2018).

  3. In a letter to Gregory from July 1672, Collins mentioned Sinclair’s parallelogram made ‘so as to designe an Object at a distance’. Sinclair had seen a similar instrument designed by instrument maker Hilkiah Bedford ‘after the common mode’, which he apparently did not like. Later that year, Sinclair purchased a similar ‘very good ordinary Parallelogram’ for the bargain price of 40 shillings, which was supposed to be sent to Gregory at St. Andrews University (Turnbull 1939: 239–40).

  4. Partes enim Autographi æquales, transcriptæ sunt in planum prorsus ineæquales. Unless otherwise indicated, all translations from Latin are by the author.

  5. In a later Italian edition of Scheiner’s book, the editor Giulio Troili suggested to use this device to ‘Draw in plane anything that is seen by us from afar, be it Village, Mountain, Sea, Island, Fortress, City, Villa, Square, Hamlet, House, Man, Beast, Stars’ (‘Disegnare in piano ogni cosa da noi veduta da lontano, sia Paese, Monte, Mare, Isola, Fortezza, Città, Villa, Piazza, Borgo, Casa, Huomo, Fiera, Stelle’) (Troili 1653: 18). In order to adapt his device to different positions of the model, Scheiner had equipped his machine with a series of hinges, allowing the projection plane to be rotated at will. This, however, allowed the readjustment of the drawing board but didn’t reduce the effects of foreshortening (Carpo 2011: 142, n.71).

  6. Menimi enim, cum effigiem cuiusdam in horto sedentis, cuius imago per lentem convexam in chartam transmissa fuit, ducerem, crura & depes multum ultra reliqui corporis proportionem, ut pote propriores, crescere.

  7. Expertus sum tamennequaquam inter partes Ectypi in planum, eam esse symmetriam, quæ inter partes Prototypi dissiti.

  8. Ex quo luculenter cernere est differentiam, inter rei Apparentiam, ejusque Projectionem.

  9. Apparentia ex duorum duntaxat habitudine pendet, rei nempe objectæ, & intuentis oculi; Projectio vero insuper (quae est rei solidæ in planum transcriptio), planum deposcit, in quod profusi radii varie incidunt.

  10. quo propieres enim sunt noctu candela, manus aut pedes aut cætera membra eo majorem in parte em oppositum umbram effundunt.

  11. Sicut enim se habet Parallelogrammi planum ad imaginem corporis describendi, sic & paries ad umbram.

  12. ecce tibii aliud imaginis parallelae exemplum in umbris, quæ oriente vel occidente Sole in parietibus radiis solaribus ad angulos rectos oppositis conspiciuntur, quaeque licet tenebrosae, multum tamen lucis in praesenti negotio afferunt, cum Geometrice corporibus, unde fluunt, æquales sint.

  13. Hisce præmissis, fingamus ab omnibus Prototypi punctis radios parallelos prætendi, & ad angulos quam fieri potest rectissimos in planum Pantographicis incidere; qua ratione fiat, ut Index Stereographicus omnia illa puncta saltem præcipua percurrat, nunc inquirendum restat.

  14. sit oculus in Prosopographia liber & solutus.

  15. vero mere rationale, sive mathematicum.

  16. Sinclair may have been familiar with this system, as Royal Society member John Evelyn had reproduced it in his De Sculptura (1662: 121–124).

  17. For a more theoretical/general discussion on how mechanisation can clarify the principles of parallel drawing, see (Astengo 2020).

  18. Locke seems to have been referring here to the Stereograph and the Epipedograph, rather than Sinclair’s version.

  19. Sed cum Astronomi decant Sphæram Parallelam, cur non & mihi imaginem Parallelam dicere liceat? A parallel sphere indicates the celestial sphere seen from either the north or the south pole of the earth, where all the celestial bodies seem to move in small circles parallel to the horizon (Blaeu 1668: 40-41).

  20. This resembled a more complex device, designed by Robert Hooke, which included a second eyepiece and a rotating vertical parallelogram to rescale the image. In June 1663 Oldenburg presented the device to Balthazar de Monconys during his journey to London and shipped the machine to him in Paris the following year (Hall, Hall 1966: 285–91; Monconys 1666: 62; Hunter 2015).

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Correspondence to Gregorio Astengo.

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Astengo, G. Parallelogrammum Prosopographicum. Nexus Netw J 22, 735–753 (2020). https://doi.org/10.1007/s00004-020-00497-x

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Keywords

  • Orthographic drawing
  • Prosopographical parallelogram
  • George Sinclair
  • Christoph Scheiner
  • François D’Aguillon
  • Projective geometry