Elliptical or azimuthal horologiography comprehending severall wayes of describing dials upon all kindes of superficies, either plain or curved, and unto upright stiles in whatsoever position they shall be placed / invented and demonstrated by Samuel Foster ...

Title

Elliptical or azimuthal horologiography comprehending severall wayes of describing dials upon all kindes of superficies, either plain or curved, and unto upright stiles in whatsoever position they shall be placed / invented and demonstrated by Samuel Foster ...

Author

Foster, Samuel, d. 1652.

Publication

London :: Printed by R. & W. Leybourn for Nicholas Bourn ...,

1654.

Rights/Permissions

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Subject terms

Horology -- Early works to 1800.

Sundials.

Link to this Item

https://name.umdl.umich.edu/A40031.0001.001 content_copy

Cite this Item

"Elliptical or azimuthal horologiography comprehending severall wayes of describing dials upon all kindes of superficies, either plain or curved, and unto upright stiles in whatsoever position they shall be placed / invented and demonstrated by Samuel Foster ..." In the digital collection Early English Books Online. https://name.umdl.umich.edu/A40031.0001.001. University of Michigan Library Digital Collections. Accessed April 28, 2025. content_copy

Contents

• title page
• To the READER.
• ERRATA.
• instructions
  • Declinations of the Sun from the Aequinoctiall.
  • Tangents of the Suns decli∣nation from the Aequinoctiall.
• SECT. I. Of the Elliptical Dial, where the Index stands perpendicular to the Plain: How to draw it for an Horizontal Plain, or any other Plain that declineth not.
  • How to divide the Ellipsis into its requisite parts.
  • How to make the Zodiac, or dayes of the yeare, whereby the Ellipsis and Index are to be set in a right position, that they may daily stand true to shew the houre.
  • Another way to describe and divide the same Zodiac, or Scale of Moneths.
  • How to divide the Annuall Circle into its requisite parts.
  • Concerning the Index.
  • Of the place for the Suns Annual course or Zodiac.
  • The Vses of the Elliptical Dial.
    • There may other uses be made of it, if it have other Scales adjoyned to the Zodiac.
    • A Table of Amplitudes, with their answerable Declinations, for the Latitude of 51 gr. 30 min.
    • Another Table of Amplitudes, with the Tangents of their answerable Declinations, for the Latitude of 51 gr. 30 mi.
• SECT. II. How to frame the Elliptical Dial to other Plains which are not direct but declining: To an Index that standeth perpendicular to the plain.
  • How to limit and draw the Ellipsis.
  • How to divide the Ellipsis into such requisite parts as the plain shall require.
  • How to limit the Ellipsis, and divide it, without Calculation.
  • Note: that
• SECT. III. Another way to prick down the Ellipsis upon an Horizontal Plain.
  • Note.
• SECT. IV. Here follow some Vses and Varieties of this Ellipticall Diall.
  • USES.
• SECT. V. Some varieties of the structure of it do here follow.
  • There remains yet one structure more, by which it is fitted for some uses that follow after, and is made a portable Instrument, not at all to be used in observation.
  • Being thus far prepared, you may take away the lesser plate, and divide the Scales upon the greater plate, in this manner.
  • The reason why this Instrument is thus contrived.
  • The uses of it do here follow, which by reason of the Semi∣ellipsis will not be so easie, because many changes are required. In generall note thus much.
  • 1. By having the Azimuth to finde the Houre.
  • 2. By having the Houre in which the Sun or any Star is, the Azimuth thereof may be found.
  • 3. To finde the Ascensionall difference, the Semidiurnall and Seminocturnall arkes, with the time of their risings and settings.
  • 4. To finde the Amplitude of their Risings and Settings.
  • Note here.
  • 5. To finde the Declination of the Sun.
  • 6. How to make an Horizontall Diall by this Instrument.
• SECT. VI. AN ADVERTISEMENT Concerning sme oter uses of the Instrument that was last described.
  • 1. Having the Suns Declination and Alti∣tude to finde the Houre and Azimuth.
  • A DEMONSTRATION of the Ellipticall Diall upon an Hori∣zontall Plain: shewing the reason why the same Diall, by an upright Index should shew the true Houre.
    • LEMMA I.
      • COROLLARY.
    • LEMMA II.
      • COROLLARY.
    • LEMMA III.
  • The application of these things to the purpose intended.
  • The next thing to be shewed, is how the Ellipticall Equino∣ctiall may supply the use of all the Parallels.
  • The next thing to be enquired is, what the line A G is, or how it must be found and estimated.
  • Sect. 2. Pag. 22, &c. Of framing it to Declining Plins.
  • Sect. 3. Pag. 29, &c.
  • Sect. 5. Pag. 37, &c.
  • Sect. 6. Pag. 47, &c.
• SECT. VII. 1. How to draw and divide the Ellipsis upon any Plain, to an Index that stands upright (not to the Plain, but) to the Zenith line of the place, or perpendicular to the plain of the Horizon.
  • 2. The manner of the work.
  • 3. Concerning the motion that is to be made either by the Index, or by the Ellipsis it selfe.
  • 4. Concerning the Place of the Suns Annuall course or Zodiac.
  • 5. Of what limitation or length the Zodiac must be, and how to be described, and where to be set.
  • 6. What the Meridians inclination meaneth, and how to finde the quantity of it.
  • 7. Other things to be noted concerning the Zodiacall Scale.
  • 8. Another Observation.
  • SECT. VIII. Hitherto of Ellipticall Dials to all Superfi∣cies whether plain or curved, whose In∣dexes stand upright in the Zenith line of the place: There now followeth some other directions how the same thing may be done to any Superficies, and to an Index set casu∣ally in any position whatsoever. But first are premised some usefull Propositions tend∣ing to the same purpose.
    • 1. An Index or streight line being set casually, how to finde the Re / In-clination and declination thereof.
    • 2. By having the Re / In-clination and Declination of any right line, to finde the Longitude and Latitude thereof.
    • 3. How to finde a Meridian line, and to erect a true Axis of the World from the foot of the Index.
    • 4. Having an Axis raised from the foot of the Index, how to finde in what Longitude and Latitude the Index it selfe lyeth, by a way easier and differing from the former, without looking after any re / in-clination or declination of the said Index.
    • 5. How to forme the Angles at the Pole.
    • 6. By knowing the angles at the Pole, and the Latitude of the place or Horizon, how to finde the Horizontall Spaces thereto belonging.
    • 7. By knowing the angles at the Pole, and the Latitude of the plain or Horizon, how to finde the Equinoctiall Altitudes or depressions (above or under the same Horizon) due to the said Angles at the Pole or points of the Equinoctiall.
    • 8. How to finde the proper Meridian line duly belonging to any Zenith line casually placed, and to draw it upon the plain.
    • 9. How to draw and divide the Ellisis into houres and quarters, to an Index casually set, whose Latitude and difference of Longitude is discovered by the former works.
    • 10. Concerning the motion that is to be made, either by the Index, or by the Ellipsis it selfe.
    • 11. Of the place of the Suns Annuall course or Zodiac.
    • 12. How the Zodiac is to be limited in regard of length, and how to be described and set in its true place.
    • 13. How to finde what angle is made between the Index and that part of the proper Meridian which is projected upon the plain whereon the motion is made, or which drawn upon the foot of the Index which maketh the same motion.
    • 14. Further observations concerning the motion and daily fitting of the Diall and Index, for setting them true.
    • A briefe DEMONSTRATION of the 7th. and 8th. Sections.
    • To the Reader that shall have the view of this first draught of Precepts.
    • 15. Having placed a Diall plate to move (let the Coast of the motion be casual) how to fit a stedfast Index to it, and to describe an Ellipticall Diall upon the said moving plain.
    • 16. If an Index should be set up and made moveable upon a standing plain, there can no Diall be described thereto,
• title page
• CIRCULAR Horologiography.
  • How to make an Horizontall Diall in a Circle equally divided, to shew the Houre of the day, and Azi∣muth of the Sun.
    • The altitude of the Horary Index may thus be found.
    • The standing and looking of it.
    • The motion of the Horary Index.
    • How the Zodiac is to be limited, and laid, and charactred.
    • The manner how to fashion the Cock which holdeth the Index.
    • How to place this Diall for use.
    • To finde the Houre.
    • To finde the Azimuth.
  • Another way to make the same Horizontall Diall equally divided, to finde the Houre and Azimuth.
  • How to make the like Houres and Azimuths by an equally divided Circle, upon all Plains whatsoever.
    • The first way.
    • The second way.
    • How to divide the Circle of houres.
    • NOTE
  • A briefe DEMONSTRATION of these Circular wayes of making DIALS.
    • NOTE.
    • For the limitation of the Zodiac.
  • APPENDIX.
    • Having the Zodiac limited, how to finde the two extream Diameters of the Ellipsis.
• RECTILINEAL OR DIAMETRAL Horologiography.
• RECTILINEAL OR DIAMETRAL Horologiography.
  • Concerning Dials made upon a finite streight line, with a moveable Index.
    • ¶ 1. How to make a Diall upon a finite streight line, drawn upon any plain, the Index being so ordered that it point up into the Equinoctiall Circle, and into the plains proper Meridian.
    • Concerning the Zodiac and the Index.
    • ¶ 2. How to make a Diall upon a finite streight line, drawn upon any plain, the Index being so ordered, that it point up into the Equinoctiall Circle, and into a just hour point in the same Circle.
  • A DEMONSTRATION of the former way.
  • APPENDIX.
    • How to lay a line that shall point up to any assigned place or point in the heavens.
    • For the houre points.
    • ☞ Upon this Circular way Note thus much.
    • Concerning the Zodiac.
  • For DEMONSTRATION of these things.
    • Of the parallelisme of the Index and Plain.
• title page
• ELLIPTICAL Horologiography.
  • How upon any plain to draw an Ellipticall Diall, to an Index set any , by Sphericall (and not Projective) work.
  • Things that are pre-requisite to this work.
  • Or if you would set an Index so as to fit it to any assigned difference of Longitude, and to any assigned Latitude also, you must work thus.
  • What remains to be done.
  • How to make an Ellipticall Diall upon any Plain, to an Index perpendicular to the Plain.
  • A second way to make the Ellipsis and houres to a slope Index upon a plain: and without trouble of making that Table before men∣ioned.
  • Concerning the Zodiac, how it is to be limited and placed.
  • CORONIDIS LOCO: I shall here further adde; How upon an Horizontal Plain, to describe an Ellipticall Diall to an Index lying aslope, and pointing into some assigned Longitude and Latitude.
  • How the Zodiac is to be placed and limited.
  • Another way for the description of an Ellip∣ticall Diall upon the Horizontall plain of 51 gr. 30 min. Latitude, whose Zodiac, and the motion of the Index is performed upon the oures of 7 in the morning, and of 5 in the afternoon, as the same houres are drawn upon the common Horizontall Diall.
  • For the Zodiac.
  • A Note concerning the framing of Dials to finde the Azimuth.
    • COROLLARY.
• AN INDEX Of the Chief PARTICULARS:
  • Of the Elliptical Diall with an Index stand∣ing in the Zenith-line.
• Courteous Reader, be pleased to take notice of these Books following, which are very usefull and necessary for all Merchants, Tradesmen, Accomptants, they are sold by Nicholas Bourn at the South entrance of the Royall Ex∣change.
  • These following are Books of other sorts: