- Biographical information about Longomontanus can be found in Andersen K. An Impression of Mathematics in Denmark in the Period 1600–1800 Centaurus 1980 24 316 334 (pp. 318–9); DBL, IX, 109–10 and DSB, XII, 332. The information about Albert Burgh and his son Coenraed stems from J. E. Elias, De Vroedschap van Amsterdam 1578–1785, 2 vols (Haarlem, 1903–5), I, 327–9, 453–4.
- Glorioso , Giovanni Camillo . 1572–1643 . Profcssor of Mathematics at Padua.
- Dybvad , Christoffer . 1572–1622 . DBL , IV : 74 – 75 . Danish political dissident, who published some mathematical works (e.g. in 1602 Decarithmia, the first publication in Denmark to treat decimal fractions)
- In fact Pell reopened the correspondence, since he and Cavendish in 1641 and 1642 had also exchanged some letters (Pa-Pd and Ca-Cf). Parts of the correspondence have been published in Vaughan R. The Protectorate of Oliver Cromwell London 1838–9 2 J. O. Halliwell, A collection of letters illustrative to the progress of science in England from the reign of Queen Elizabeth to that of Charles the Second (London, 1841); H. Hervey, ‘Hobbes and Descartes in the Light of some Unpublished Letters of the Correspondence between Sir Charles Cavendish and Dr. John Pell’, Osiris, 10(1952), 67–90, and in MC, X, XI, XIII and XIV. Biographical information about the correspondents is to be found in F. L. Bickley, The Cavendish Family (London, 1911); J. Jacquot, ‘Un amateur de science, ami de Hobbes et Descartes: Sir Charles Cavendish (1591–1654)’, Thalès, 6(1949–50), 81–8; DNB, Supplement I, 399–400 (about Cavendish); F. L. R. Sassen, ‘Levensberichten van hoogleraren der Illustre School te Breda’, Jaarboek van de Geschied- en Oudheidkundige Kring van Stad en Lande van Breda ‘De Oranjeboom’, 19(1966), 123–57; C. J. Scriba, ‘John Pell's English Edition of J. H. Rahn's Teutsche Algebra’, in For Dirk Struik, edited by R. S. Cohen et al. (Dordrecht/Boston, 1974), pp. 261–74; DSB X, 495–6 with further references (about Pell); Hervey (1952) and in the later volumes of MC (about both). It is not known with certainty when Pell was born. Most authors give the year 1611 without mentioning their source. Here 1610 is chosen since Pell notes on the draft of his letter P26 of 1/11 March 1647/1648 (which is 11 March 1648, New Style) that it was written on his 38th birthday. Assuming that Pell knew his own age, one must conclude that he was born on 11 March 1610 New Style.
- Dijksterhuis , E.J. 1931/2 . John Pell in zijn strijd over de rectificatie van den cirkel . Euclides , 8 : 286 – 296 .
- Dijksterhuis . John Pell in zijn strijd over de rectificatie van den cirkel . MC , XIII 200 – 200 .
- Petty , William . 1623–1687 . English economist, author of the Political Arithmetic (1677).
- According to von Braunmühl A. Geschichte der Trigonometrie Leipzig 1900–3 2 reprint: Niederwalluf, 1971), II, p.43, who take Van Schooten 1661, p. 368 (see Sources) as his source. See also Section 17 of this paper.
- Pell had bought from Ravius the manuscript of Conica V, VI and VII that Nicolaus Petri had bought in Istanbul for Ravius (nowadays manuscript Oxford Bodleian: Thurston 3). The copier was ‘Abdel Melik of Schiraz in Persia though he write Arabick (the manuscript is above 450 yeeres old)’ as Pell writes to Cavendish on 29 October 1644 (P6, 109vb). As a matter of fact (‘Abd al-Malik al-Shīrāzī produced a revised edition of the Conica. Later on Ravius tried to buy the manuscript back (letter from Ravius to Pell of 24/08/1651; BL Add. MS 4278 f.2). Gool possessed a copy of Pell's manuscript and another Arabic manuscript of Conica V, VI and VII (the Thābit 'ibn- Qurra translation from the Greek, now Oxford Bodleian: Marsh 667), and both Gool and Pell had plans to publish a Latin translation. In P11 there exists even a report by Pell on a visit that Gool had paid to him to discuss their mutual plans. See also Witkam J.J. Jacobus Golius (1596–1667) en zijn handschriften Oosters genootschap in Nederland 1980 10 49 74 (pp. 57–8).
- I have been unable to locate the piece that Guldin (1577–1643) wrote against Longomontanus; it does not feature in the Guldin bibliography by Sommervogel Bibliothéque de la Compagnie de jésus Brussels Paris 1892 1946 1947 either.
- Reference to the Refutatiuncula 73 73
- Reference to the Refutatiuncula 74 74
- Biographical information about Juan Alphonso Molina Caro is scarce. Zelder Universal-lexikon xx col. 920) says that he was from Estremadura in Spain, that he lived in the second half of the sixteenth century and that he published Descubrimientos geometricos (Antwerp 1568 and 1596), of which a Latin translation appeared in Arnhem in 1620.
- MC , XIII 497 – 497 . n. 1. Pell (in Pell 1647, p. 55; see Sources) published an extract from Mersenne's letters (of 5 October 1645 and about 8 November 1645). Both letters are discussed in Section 13. In MC, XIII, p. 463 this extract has been republished as stemming from one (non-existing) letter, dated ‘fin juillet ou début aoˆut 1645’.
- MC , XIII 164 – 165 .
- The letter was published on the basis of the autograph, which is in the Paris Bibliothèque National MC XIII 497 499 but the refutation (BL Add. MS 4278 f. 221r) was not added.
- Mersenne's letter (BL Add. MS 4279 f. 181r) was enclosed in Petty's letter to Pell of 8 November 1645 (BL Add. MS 4279 f. 183r). The editors of Mersenne's correspondence, who have published Petty's letter MC XIII 511 512 however, regard Mersenne's enclosure as lost. For the Latin text see the following note.
- The first one published partly in MC XIII 522 523 (but not following the autograph in the British Library), the second one in full, MC, XIII, p. 540. Our quotations are taken from the autographs: C18 and C19.
- BL Add. MS 4278 f. 232r. Sir William Boswell (?–1649) was the English ambassador at The Hague. He had a keen interest in art and science. See DNB v 440 440
- MC , XIV 125 – 125 .
- MC , XIV 143 – 143 .
- MC , XIV 366 – 366 . Elements VI, 3 is about the bisector: if in a triangle ABC line AD (with D on BC) bisects angle CAB, then BA:CD. Using this theorem one can (as Roberval and Van Schooten show, see also Section 17) prove Pell's fundamental theorem easily.
- Hervey . 1952 . Hobbes and Descartes in the Light of some Unpublished Letters of the Correspondence between Sir Charles Cavendish and Dr. John Pell . Osiris , 10 : 77 – 79 . and MC, XIV, 134–5.
- Nicely depicted by Thomas Ernst van Goor in his Beschrijving der Stadt en Lande van Breda … 's-Gravenhage 1744 185 186 The house where Pell lived at Breda still stands today (Grote Markt 11).
- Marginal note by Huygens in Baillet's biography of Descartes (Paris 1691, p. 275), as cited by H.-J. Hess, ‘Bücher aus dem Besitz von Christiaan Huygens (1629–1695) in der Niedersächsischen Landesbibliothek Hannover Studia Leibnitiana 1980 12 1 51 (p. 29); see also Christiaan Huygens, Oeuvres Complètes, II, p. 566.
- See Sommervogel Bibliothéque de la Compagnie de jésus Brussels Paris 1892 1946 1947 and 54.
- Van Schooten . 1661 . : 341 – 420 . (see Sources)
- Van Schooten . 1661 . : 366 – 368 . (see Sources)
- Compare von Braunmühl A. Geschichte der Trigonometrie Leipzig 1900–3 2
Annals of Science
Volume 43, 1986 - Issue 4