- 1947 . The Seventeenth Century , 2nd edition 234 – 234 . Oxford
- 1723 . The Construction and Principal Uses of Mathematical Instruments Translated from the French of M. Bion London It is relevant to note here that Stone's interest in mathematics was fostered by John, Duke of Argyll, who shared the interest, and in whose household Stone's father was gardener. The debt is acknowledged in his Preface, pp. v–vi.
- ‘… at the time of Henry VIII's death few Englishmen could navigate a merchant or royal ship across the great ocean to a known landfall. None could navigate to the East … Nor had any Englishman penetrated the vast spaces of the Pacific Ocean …’, Waters, p. 79. For abbreviations used see pp. 65, and 68. By 1631 however it was appreciated that for good navigating, ‘what was most necessary was for a man to have a good grasp of the principles of the sciences of geometry, trigonometry, and astronomy, and the ability to add, subtract, multiply, and divide simple figures accurately’. Ibid., p. 498. Since any gentleman pursuing a career at court in the late sixteenth and seventeenth centuries might easily find himself appointed to command of a ship, it behoved him, if he were not to be entirely at the mercy of the master, at least to know enough to be able to check the navigation. Progress in education was however slow. Compare with these comments those of Sir William Monson (1569–1643), on the great disagreements between master and pilots over the position of a ship after it had been some time on the open sea. Navy Records Society 1913 45 391 396
- For a discussion of this last problem see Evelyn John Sylva , 3rd edition London 1679 180 197 who estimated that most assessments of the size of standing timber were at least a fifth too small.
- Thirsk , Joan . 1969 . Younger Sons in the Seventeenth Century . History , 54 : 358 – 377 .
- Although Pepys's father came of a good family, his father traded in London as a grocer. That Pepys felt uncertain about his own social status is reflected by the satisfaction he felt in March 1660, when he saw himself officially designated ‘Esquire’. Two years later, on 4 July 1662, he engaged a tutor to read mathematics to him. Diary Wheatley Henry B. London 1904 ii 275 275 8 vols.
- Wilson , Charles . 1965 . England's Apprenticeship 1603–1763 226 – 226 . London Sir George Clark provides an excellent survey of the adoption of statistical and quantitative procedures in later Stuart administration in Science and Social Welfare in the Age of Newton, 2nd edition, Oxford, 1949, especially chapter 5. For wider discussions of the craze for mathematics and a mathematically based method of argument, see W. Voise, ‘Social Mathematics in the Seventeenth Century’, Contributions to the Third Session of the Prague Symposium, 1968, and Louis I. Bredvold, ‘The Invention of the Ethical Calculus’ in The Seventeenth Century: Studies in the History of English Thought and Literature from Bacon to Pope by Richard Foster Jones and Others Writing in his Honor, Stanford, 1965. Examples from other areas may be added to these, in particular the sharp controversy evoked by Alexander Pitcairne's Apollo Mathematicus, Edinburgh, 1695, an attempt to apply mathematics to medicine. In Dublin, the minutes of the Philosophical Society there record that on 9 June 1684 ‘Mr [Samuel] Foley read a discourse, which he calls Computation universalis seu logica rerum, wherein he endeavours to bring the value of all things to a certain standard, and to lay down some mathematical rules for good husbandry’. Thomas Birch, The History of the Royal Society, 4 vols., London, 1756–7, vol. iv, p. 320. On Foley and the Dublin Philosophical Society see K. Theodore Hoppen, The Common Scientist in the Seventeenth Century: A Study of the Dublin Philosophical Society 1683–1702, London, 1970, especially pp. 117–123.
- 1719 . Mathematical Lectures Being the First and Second That were read to the Mathematical Society at Manchester Manchester
- For a discussion of the privileges, rights and duties of the gentleman and the sort of training considered desirable for him, see Kelso Ruth The Doctrine of the English Gentleman in the Sixteenth Century Illinois Studies in Language and Literature 1929 xiv The quotation from the Institucion of a Gentleman, London, 1555 f C5a is cited on p. 39.
- 1864 . The Whole Works of Roger Ascham now collected together and revised with a life of the Author by the Rev. Dr. Giles Vol. iii , 100 – 100 . London 3 vols.
- Elyot , Thomas . 1880 . The Booke named the Gouernour (1531) Edited by: Herbert , Henry and Croft , Stephen . Vol. i , 28 – 28 . London 2 vols
- ‘Queene Elizabethes Achademy (by Sir Humphrey Gilbert)’ Early English Texts Society Furnivall F.J. 1869 viii extra series There were of course other institutions, such as Gresham College and the Mathematical Lectureship of the City of London held by Thomas Hood, which helped to provide some of the practical skills which were felt lacking in Elizabethan society. These however were aimed at slightly different social groups and for reasons of space cannot be discussed here. For the Mathematical Lectureship, see F. R. Johnson, J. Hist. Ideas, 1942, 3. For Gresham College, John Ward, Lives of the Professors of Gresham College, London, 1740. See also the comments in Waters, pp. 243–6.
- ‘Queene Elizabethes Achademy (by Sir Humphrey Gilbert)’ Early English Texts Society Furnivall F.J. 1869 viii 10 10 extra series
- ‘Queene Elizabethes Achademy (by Sir Humphrey Gilbert)’ Early English Texts Society Furnivall F.J. 1869 viii 10 10 extra series
- ‘Queene Elizabethes Achademy (by Sir Humphrey Gilbert)’ Early English Texts Society Furnivall F.J. 1869 viii 4 4 extra series
- ‘Queene Elizabethes Achademy (by Sir Humphrey Gilbert)’ Early English Texts Society Furnivall F.J. 1869 viii 5 5 extra series
- Circles of Proportion … Sig A3 r.
- 1633 . Grammelogia … part iii, not paginated, Sig B3 v.
- 1633 . Grammelogia … B4 r.
- 1633 . Grammelogia … B4 r.
- 1633 . Grammelogia … B4 v.
- 1652 . Clavis Mathematica denuo limita sive potius fabricata Oxford
- Just Apologie … Sig A4 r.
- Just Apologie … Sig D2 r.
- Bodleian Library Ms Aubrey 10. The treatise has recently been published in a seriously defective and misleading edition by Stephens J.E. Aubrey on Education: A hitherto unpublished manuscript by the author of Brief Lives London 1972 All citations in this paper are taken directly from the manuscript. For earlier accounts of the treatise see Anthony Powell, John Aubrey and his Friends, new edition, London 1963. Appendix A, pp. 282–287: W. J. Battersby, ‘John Aubrey's “Idea of Education”’, Brit. J. Educ. Studies 1958, 2, and J. E. Stephens, ‘John Aubrey's Idea of Education of Young Gentlemen’, J. Educ. Admin. and Hist., 1968/9, 1.
- There were however some hopes for it. See for example the comments by Evelyn and the long letter to Aubrey by Andrew Paschall, Rector of Chedsey in Somerset, 25 August 1684, added by Rawlinson to The Natural History and Antiquities of the County of Surrey London 1718/9 xiv xx
- Aubrey . 10 7 – 7 .
- Aubrey . 10 7 – 7 .
- Aubrey . 10 7 – 7 . f 36a. Seth Ward (1617–1689), Bishop of Salisbury, was a noted mathematician, and founder-member of the Royal Society. D.N.B. and Walter Pope, The Life of Seth Ward Bishop of Salisburg, edited by J. B. Bamborough, Luttrell Society Reprints No. 21, Oxford, 1961. Lord John Vaughan (1640–1713) was 3rd and last Earl of Carberry: Governor of Jamaica 1674–8 and President of the Royal Society 1686–1689. See D.N.B.
- Aubrey . 10 f 8a.
- Aubrey . 10 f 29a.
- Aubrey . 10 30 – 30 .
- Circles of Proportion … 2 – 2 .
- In 1633 the treatise was augmented by An Addition unto … the Circles of Proportion, For the Working of Nautical Questions The instrument was specially fitted for use at sea by the addition of meridional parts, being engraved in degrees, and having readings for a nocturnal. Taylor, p. 349.
- 1947 . Circles … 129 – 130 . Paris part ii, and see H. Michel, Traité de l'Astrolabe Delamain also claimed the invention of this instrument.
- 1670 . A Tutor to Astronomie and Geographie Or an Easie and speedy way to know the use of both the Globes Coelestial and Terrestrial in Six Books … , 2nd edition London First published in 1659, the book was dedicated to Samuel Pepys. Taylor, [228].
- Taylor and Richey . 90 – 93 . see also references in Waters.
- 1679 . A Catalogue of Globes, Celestial and Terrestrial, Spheres, Maps, Sea-Plats, Mathematical Instruments, and Books, with their prizes, made and sold by Joseph Moxon, on Ludgate Hill, at the sign of the Atlas This catalogue is found bound up with some copies of Moxon's works.
- 1679 . The English Globe Being a Stabil and Immobil one, performing what the Ordinary Globes do, and much more. Invented and described by the Right Honourable, the Earl of Castlemaine London and now publish't by Joseph Moxon, Member of the Royal Society, and Hydrographer to his most Excellent Majesty. Sig A2r.
- 1679 . The English Globe Being a Stabil and Immobil one, performing what the Ordinary Globes do, and much more. Invented and described by the Right Honourable, the Earl of Castlemaine London and now publish't by Joseph Moxon, Member of the Royal Society, and Hydrographer to his most Excellent Majesty. B1
- The English Globe … 135 – 135 .
- A Catalogue of Globes …
- The English Globe … 121 – 121 . and Scholium 43.
- In 1723 Stone refers to a later form of such instruments, the Orrery, developed c. 1700 although not so named until 1717, as the Copernican Sphere. For an outline of the history of planetary instruments and the Orrery see Francis Maddison, ‘An Eighteenth Century Orrery by Thomas Heath and Some Earlier Orreries”, The Connoisseur, vol. cxli, No. 569, April 1958 For Power's instrument showing the Copernican theory of the sun see Gunther R.T. Early Science in Oxford Oxford 1930 vi 159 159
- Taylor, [202], Aubrey Brief Lives ii 237 239
- Aubrey . 10 103 – 103 .
- Description … 4 – 4 . The point of the system was that the planets, seen in their places, ‘All sing the Makers praise, and show his power In due proportion moving every hour’. Ibid., p. 26.
- The Planetary Instrument or the Description and Use of the Theories of the Planets: drawn in true Proportion, either in one, or two Plates, of eight Inches Diameter; by Walter Hayes, at the Cross-Daggers in Moor-Fields John Palmer was Rector of Ecton, and the subtitle goes on to indicate a specifically educational use; ‘Being excellent Schemes to help the Conceptions of Young Astronomers; and ready Instruments for finding the Distance, Longitudes, Latitudes, Aspects, Directions, Stations, and Retrogradations of the Planets; either Mechanically or Arithmetically; with Ease and Speed’
- This seems to have been the idea behind Jagger Robert Edward Wright revived, or Mr Ed. W's Projection so illustrated both by Instrumentall and Logarithmicall operations as it may be most easily understood even of the meanest capacity, together with divers mapps and descriptions of several Ports, Islands and Places in the East Indies 1660 But no copy of this is known. Taylor, p. 368.
- For some examples of what are apparently teaching diagrams used in the Savilian Lectures see Bodleian Library Ms Savile 105. These are listed in Madan F. Summary Catalogue of Western Manuscripts in the Bodleian Library Oxford v Nineteenth Century and Miscellaneous Collections Oxford 1905 192 193
- Brief Lives , ii 79 – 79 .
- 1562 . Claudii Ptolemaeii Liber de Analemmate A Frederico Commandino Vrbinate instauratis & commentariis illustratus Romae
- 1685 . The Use of the General Planisphere called the Analemma In the Resolution of Some of the Chief and most Useful Problems of Astronomy London The treatise was published and sold by Walter Hayes; it had been written, at least in part, some 40 years earlier. For Twysden, who was a physician, see D.N.B. and Taylor, [162]. For the ‘Rojas-Projection’ see Francis Maddison, ‘Hugo Helt and the Rojas Astrolabe Projection’, Agrupamento de Estudos de Cartografia Antiga Seccao de Coimbra, 1966, vol. xii.
- 1585 . The Mathematical Iewell Shewing the making, and most excellent use of a singular Instrument so called: in that it performeth with wonderfull dexteritie, whatsoever is to be done, either by Quadrant, Ship, Circle, Cylinder, Ring, Dyall, Horoscope, Astrolabe, Sphere, Globe, or any such like heretofore devised: yea or by most Tables commonly extant: and that generally to all places from Pole to Pole London The copy of this work in the British Museum (C60 0 7) belonged to Gabriel Harvey and has his manuscript additions. For Blagrave's life and other works see Gunther, op. cit. For a full treatment of the astrolabe see H. Michel, op. cit.
- Frisius , Gemma . 1556 . de Astrolabio Catholico Antwerp
- Mathematical Iewell … 17 – 17 .
- 1658 . The Catholique Planisphaer which Mr Blagrave calleth the Mathematical Jewel; Briefly and plainly described in Five Books London The book was printed and sold by Moxon, and at the end of it Palmer added a short description of the Cross-staff (see number 12 below).
- 1553 . Elucidatio Fabricae vsvque Astrolabii, Ioanne Stoflerino Iustingensi authore Lutetiae
- 1843 . Biographie Universelle , Nouvelle Edition Vol. xl , Paris and Leipzig Allgemeine Deutsche Biographie, Leipzig, 1893.
- Goldstein , B.R. 1969 . Preliminary Remarks on Levi ben Gerson's Contributions to Astronomy . The Israel Academy of Sciences and Humanities: Proceedings , 3 : 9 – 9 .
- It is described and shown in use for measuring inaccessible heights and depths, for example by Fine Oronce Protomathesis: Opus varium, ac scitu non minus utile quam iucundum, nunc primum in lucem feliciter emissum Paris 1532 67v 68v See also Kiely, pp. 83–86 and 194–202.
- Taylor and Richey . 37 – 40 . a full account is given by Stone, 202–4, who calls it a fore-staff.
- For a discussion of terminology see Maddison Francis Mediaeval Scientific Instruments and the Development of Navigational Instruments in the XVth and XVIth Centuries Agrupamento de Estudos de Cartografia Antiga Secção de Coimbra 1969 30 47 47
- 1590 . The Use of two Mathematicall Instruments, the Cross Staffe … and the Jacob's Staffe … the one most commodious for the Mariner, and all such as are to deale in Astronomicall matters; the other, profitable for the Surveyor, to take length, height, depth or breadth, of any thing measureable , Second edition London 1596. The full title is given in Waters.
- Raphson , Joseph . 1703 . Mathematical Dictionary London translated from the French of J. Ozanam,
- Aubrey . 10 f 41a.
- Stone . 193 – 197 . describes the construction of the instrument and gives examples of problems. A pamphlet to accompany the instrument, which was made by Elias Allen, The Description and Use of a Small portable Quadrant, for the more easie finding of the Hour of the Azimuth, was published in 1623, receiving a fourth edition in 1662. An expanded discussion was given by John Collins, The Sector on a Quadrant, London, 1658.
- Aubrey . 10 30. – 30. .
- Moxon . Catalogue …
- Rathbone , Aaron . 1616 . The Surveyor 186 – 187 . London and see Kiely
- Raphson . Mathematical Dictionary Thomas Tuttell engraved the plates for this work; a sinical quadrant is shown in Figure 43.
- For use as a navigating instrument, see Taylor Richey 67 69 and Stone, pp. 206–7.
- Waldseemüller's instrument is described and illustrated in Reisch Gregor Margarita Philosophica Strasburg 1512 1512
- Kiely . 193 – 194 .
- Digges , Leonard . A Geometrical Practise named Pantometria 1571 – 1571 . London
- For a survey of the history of the instrument see Kiely 180 194 Stone, pp. 106–108 and 126–127 describes both the continental and English forms.
- Stone . 127 – 129 . Kiely, pp. 209–212.
- Stone . 127 – 131 . Kiely, pp. 228–235.
- This was the well known Museum Minervae established in 1635/6 to teach ‘the Sciences of Navigation, Riding, Fortification, Architecture, Painting and such like …’. Designed, like Aubrey's schools, exclusively for the ruling classes, it emphasized the useful and graceful studies with which the universities were not primarily concerned, and also, like Aubrey, it had an equipment of charts and instruments as well as of books. See The Constitutions of the Museum Minervae London 1636 The copy of this work in the Bodleian Library (Gough, London, 225) belonged to Hearne and has numerous Ms annotations in a later hand.
- Speidell , I. 1627 . A Breefe Treatise of Sphaerical Triangles, Wherein is handled the sixteen Cases of a right angled Triangle 42 – 43 . London Of an earlier work by Speidell, his Geometricall Extraction …, 1616, Aubrey commented that it ‘made young men have a love to Geometry’, Brief Lives, vol. ii, p. 231.
- For Hooke's usage see Derham W. The Philosophical Experiments of Robert Hooke London 1726 298 298 Diary 1672–1680, edited by Henry W. Robinson and Walter Adams, London, 1935, p. 107, 11 June 1674. On the meteoroscope see J. D. North, ‘Werner, Apian, Blagrave and the Meteoroscope’, Brit. J. Hist. Sci., 1966, 3.
- See Powell Anthony John Aubrey and his Friends 253 258 op. cit. G. C. Moore-Smith, The Letters of Dorothy Osborne to William Temple, Oxford, 1928, Letter 2 n 14, p. 212 and appendix iv: and Taylor, p. 361.
- 1684 . Bibliotecha Mathematica Optimis Libri Diversarum Linguarum Refertissima Una cum variis philologicis, historicis, & Geographicis Adomata Honoratissim. Equitis Jonae Mori … nuper defuncti London
- It was published in 1674 by Nicholas Stephenson. Taylor, [380] and p. 373 in A Mathematical Compendium or Useful Practises in Arithmetick, Geometry, and Astronomy, Geography and Navigation, Embattelling, and Quartering of Armies, Fortifications and Gunnery, Gauging and Dyalling … collected out of the Notes and Papers of Sir Jonas Moore
- Dalton , Charles , ed. 1892 . English Army Lists and Commission Registers, 1661–1714 Vol. i , 190 – 190 . London and 226: C.S.P.D. 1679–80, pp. 112, 113, 322, 326: Calendar of Treasury Books, vol. vi, pp. 382, 383, 385–6. E. S. de Beer, ‘The President, General Council and Earliest Fellows of the Royal Society’, Bull. Inst. Hist. Res., 1937, 15.
- Aubrey . 10 37 – 37 .
- See Plate IX. C.S.P.D. 1611–1618 337 337
- The Arithmeticall Jewell, containing the Use of a small Table whereby is speedily wrought as well all Arithmetic works in whole Numbers as all fractional operations without fractions or reductions. Invented by William Pratt For the context of these arithmetical calculating machines, see Bryden, op. cit.
- For Mercator see Taylor, p. 195 and J. E. Hoffman, ‘Nicolaus Mercator (Kaufman) Sein Leben und Wirken, varzugsweise ab Mathematiker’ Akademie der Wissenschaften und der Litteratur im Mainz Abhandlungen der Mathematisch-Naturwissenschaftlichen Klasse 1950 No. 3. For the use of a sector to calculate an eclipse, see Stone, 258–264.
- Stephens , J.E. 1972 . Aubrey on Education: A hitherto unpublished manuscript by the author of Brief Lives 85 – 85 . London 176, 198. On Samuel Cradock see A. G. Matthews, Calamy Revised, Oxford, 1934 and J. C. Whitebrooke in Trans. Congregational Hist. Soc., 1911/12, 5, no. 3.
- Whinney , Margaret and Millar , Oliver . 1957 . English Art 1625–1714 281 – 281 . Oxford n 3
- Croft-Murray , Edward and Hulton , Paul . 1960 . Catalogue of British Drawings I XVI and XVII Centuries 198 – 199 . London and 291. On Mary Beale see D.N.B.
- J.Venn and Venn , J.A. 1922 . Alumni Cantabrigiensis Vol. i , Cambridge Part I
- Osborne , Harold . 1970 . The Oxford Companion to Art 1096 – 1098 . Oxford See also Whinney and Millar, op, cit., pp. 176, 180, 280–282.
- Vertue , G. 1930 . Notebooks . Walpole Society , 18 : 93 – 93 . i
- 1668 . Diary , viii October : 133 – 133 . 29
- Diary , viii 219 – 219 . Taylor, [266]
- Birch , Thomas . 1756/7 . The History of the Royal Society of London for Improving of Natural Knowledge Vol. iii , 127 – 127 . London
- Venn . 1922 . Alumni Cantabrigiensis Vol. i , Cambridge Part I
- 1702 . The Natural History of Animals containing the Anatomical Description of Several Creatures Dissected by the Royal Academy of Sciences at Paris … London
- Aubrey . 10 135 – 135 .
- 1589 . Magiae naturalis, sive de miraculis rerum naturalium libri xx Naples This was poorly translated into English by an anonymous hand in 1658 as Natural Magick … in Twenty Books. For a full discussion of the development of the camera obscura—which was known in the Middle Ages, being used, for example, by Levi ben Gerson (Goldstein, op. cit.)—see Helmut Gernsheim in collaboration with Alison Gernsheim, The History of Photography, revised and enlarged edition, London, 1969.
- 1651 . Reliquiae Wottoniae 413 – 413 . London
- Styles , P. 1955 . A Letter of William Dugdale 1653 . University of Birmingham Historical Journal , 5
- Taylor . 105 – 105 .
- Boyle , Robert . 1669 . Of the Systematicall and Cosmical Qualities of Things Oxford
- Waller , Richard , ed. 1705 . Posthumous Works of Robert Hooke 127 – 127 . London Derham, op. cit., pp. 292–296.
Annals of Science
Volume 30, 1973 - Issue 1