Early English Books Online 2
 All Digital Collections  spacer  Login  
 
Add to bookbag
Author: Blagrave, John, d. 1611.
Title: The mathematical ievvel shewing the making, and most excellent vse of a singuler instrument so called: in that it performeth with wonderfull dexteritie, whatsoeuer is to be done, either by quadrant, ship, circle, cylinder, ring, dyall, horoscope, astrolabe, sphere, globe, or any such like heretofore deuised: ... The vse of which iewel, is so aboundant and ample, that it leadeth any man practising thereon, the direct pathway ... through the whole artes of astronomy, cosmography, ... and briefely of whatsoeuer concerneth the globe or sphere: ... The most part newly founde out by the author, compiled and published ... by Iohn Blagraue of Reading gentleman and well willer to the mathematickes, who hath cut all the prints or pictures of the whole worke with his owne hands. 1585.
Series: Early English books online text creation partnership. Navigations series.
Rights/Permissions: This text has been selected for inclusion in the EEBO-TCP: Navigations collection, funded by the National Endowment for the Humanities. The University of Michigan Library provides access to these keyboarded and encoded editions of the works for educational and research purposes. These transcriptions are believed to be in the public domain in the United States; however, if you decide to use any of these transcriptions, you are responsible for making your own legal assessment and securing any necessary permission. If you have questions about the collection, please contact eebotcp-info@umich.edu. If you have concerns about the inclusion of an item in this collection, please contact LibraryIT-info@umich.edu. This statement does not extend to any page images or other supplementary files associated with this work, which may be protected by copyright or other license restrictions. Please go to http://www.textcreationpartnership.org/ for more information.
Print source: The mathematical ievvel shewing the making, and most excellent vse of a singuler instrument so called: in that it performeth with wonderfull dexteritie, whatsoeuer is to be done, either by quadrant, ship, circle, cylinder, ring, dyall, horoscope, astrolabe, sphere, globe, or any such like heretofore deuised: ... The vse of which iewel, is so aboundant and ample, that it leadeth any man practising thereon, the direct pathway ... through the whole artes of astronomy, cosmography, ... and briefely of whatsoeuer concerneth the globe or sphere: ... The most part newly founde out by the author, compiled and published ... by Iohn Blagraue of Reading gentleman and well willer to the mathematickes, who hath cut all the prints or pictures of the whole worke with his owne hands. 1585.
Blagrave, John, d. 1611.
Imprinted at London: by Walter Venge, dwelling in Fleetelane ouer against the Maiden head, [1585]
URL: https://name.umdl.umich.edu/A73520.0001.001
How to cite: For suggestions on citing this text, please see Citing the TCP on the Text Creation Partnership website.

Table of Contents
View entire text
title page
MARGARITA MATHEMATICA.
illustration
To the Right Honorable Sir VVilliam Cycill Knight Baron of Burleigh, Lord high Tresurer of Englande, Master of her Maiesties Wards and Liueries, Knight of the most honorable order of the Garter, and of her heighnesse most honorable Priuie Counsel.
The Author to the curteous Reader.
The Authour in his owne defence.
The Authours dumpe.
¶ A Table of the Contents of all the Chapters contained in this worke.
An Index or Table directing any man vnto such places in this booke where al the termes hereafter following, are defined and expounded. The first number signifiyng the booke, the second the chapter.
Of certaine supplies for the better finishing of the figure of the Iewell ioyned to this booke, and first for the Mater and his Limbe.
Now for the Reete.
Of the Theoricke or Calender.
Faultes escaped.
The first booke of the Mathemati∣call Iewel: set foorth by Iohn Blagraue of Reading, Gentleman, Conteineth very needfull Geometricall principles, which may be called the rules of the compasse: it containeth also after that, the principles and Rudiments of Astronomie and Cosmographie, set downe as the first footesteppe for the vnlearned, which I aduertise the learned to passe ouer.
Of certaine Deffinitions Geometricall.
part
The first conclusion. How to erect a perpendiculer vppon any point of a groundline assigned: and thereby to make a right angle.
2. Conclusion. To make a right angle another way and easier.
3 Conclusion. To deuide any streight line or arch of a circle into two equall parts verie speedilie.
4 Conclusion. From a point proposed to draw a perpendiculer to any groundline.
5 Conclusion. From a point proposed to draw a perpendiculer to any groundline a redier way where the groundline lacketh length.
6 Conclusion. From thextreame or end of a groundline to draw a perpendiculer verie easily where the same groundline cannot be extended.
7 Conclusion. To do the same more redily another way with once opening of your compasse.
8 Conclusion. From a point proposed to draw a line parallel to any line proposed.
9 Conclusion. To make a triangle of any three lines proposed.
10 Conclusion. To make a square of any side giuen.
11 Conclusion. To make an angle equall to any angle proposed.
12 Conclusion. To find the very point where a touchline toucheth any circle.
13 Conclusion. To diuide speedily and exactly any line into many equall parts.
14 Conclusion. To prepare a triangle to be alwayes readie for deuiding of lines exactly into as many euen parts as shalbe required.
15 Conclusion. Another speedie way to diuide a line into many equall parts.
16 Conclusion. The same a third way and rediest.
17 Conclusion. Any three prickes set downe howsoeuer, not being in a streight line: how to discribe a circle that shall cutte them all three.
18 Conclusion. How to finde the centre of any circle or arch proposed.
19 Conclusion. To make an angle equall to any angle assigned otherwise then in the 11. conclus.
20 Conclusion. To diuide easily a very small circle into a number of equall diuisions.
Heere follow the principles and rudiments of Astronomy and Cosmographie with the vnderstanding of euerie circle of the Spheare and their vocables.
What Cosmographie Geographie and Topographie are. Chapter 1.
Of the placing of the spheares and the diuision of the world. Chapter 2.
What a sphere or Globe his axtree and poles are. Chapter 3.
Of the six chiefe great circles of the Sphere. Chapter 4.
Of the fower chiefe lesser circles of the Sphere. Chapter 5.
Of the Zodiacke and his diuision into degrees and signes and their carecters. Chapter 6.
A farther discourse of the circles of the Sphere. Chapter 7.
Of other circles of the Sphere, changeable with euery horizon, as Azimuthes, Almicantares and such like. Chapter 8.
Of the motions of the Speere and all the tenne Spheres. Chapter 9.
In what time euery Speere and planet finisheth his course and of the carrecters of the planets. Chapter 10.
Of Zones, Climats, parallels and meridians. Chapter 11.
Of the longitudes and latitudes of places. Chapter 12.
Chapter 13. Of the theorickes of the planets.
The seconde booke of the Mathe∣maticall Jewel: compiled by Iohn Blagraue of Reading, Gent. shewing the composition and making of the Jewel: being a most ne∣cessarie and profitable worke for all those to be well seene in, which shall indeuour to describe mappes or sea cards, or to proiect artificially the globe or any part thereof into a plaine or platforme, as exact and perfite for any purpose as the globe it selfe.
Secondly it conteineth the inuention, definition and explanation of this Iewel, and of euery circle and thing therein contained with their vocables and names, most necessarie to be foreknowne.
Chapter 1. A necessarie discourse which Gemma Frisius vsed as a preamble to his Booke, De Astrolabio Catholico by what reason the globe is brought into a flat or plaine forme.
Chapter 2. What materiall this Iewel were best to be made of.
Chapter 3. The meridians and parallels drawne how to finish the Mater.
Chapter 4. How to finde the centres of the meridians three seuerall wayes.
Chapter 5. How to finde the centres of the parallels artificially.
Chapter 4. How to make the Reete with all his lineaments.
Chapter 7. How the zodiacke of this reete may be diuided diuerse other wayes.
Chapter 8. How to place the fixed starres in the Reete.
Chapter 9. How to finish and cut out the Reete of this Iewel.
Chapter 10. How to make the Label for the Mater and the rule to the backeside with sightes.
Chapter 11. How to furnish the backe of the Iewel with the Theoricke of the sunne and other necessaries.
Chapter 12. How to set togither all this worke of the Iewel.
Here followeth the inuention, definition, and explanation of the Iewel, and of euery circle, part and thing therein conteined.
Chapter 13 VVhat moued the author to his inuention of this Iewel, and whence he obtained it.
Chapter 14. Of the definition of the Iewel and his principall parts.
Chapter 15. Of the diuision or two seuerall distinctions of this Iewel.
Chapter 16. Of the dispositions of the circles both in the Mater, Reete, and Limbe, for the first and chiefest distinction of this instrument.
Chapter 17. The circles seruing the first and chiefest distinction knowne by the last Chapt. how to place them to the latitude of your countrie, where it shall rest fixed to all conclusions, a few excepted euen in manner of the globe or spheere with a farther exposition of the lineaments of the Iewel so placed.
Chapter 18. Of the dispositions of the circles both in the Mater, Reete, and Limbe, for the second distinction of the Iewel.
Chapter 19. A farther declaration concerning the second part of this Iewel for the zodiacke, generall horizons, and fixed starres.
Chapter 20. How to choose out which of the 90. horizons serueth to euery countrie.
Chapter 21. How the Zodiacke and fixed starres rise and set on the horizon now found.
Chapter 22. Of the backe of the Iewel, and his lineaments.
The third booke of the Mathe∣maticall Jewel: gathered and set foorth by Iohn Blagraue of Reading Gentleman: conteineth al the propositions, and con∣clusions of Iohannes Stophlerus, Iohannes Sconerus, Iohannes Roijas, G. Frisius, or any other, written on their seuerall Astrolabes, set downe heere in the selfesame order that Gemma Frisius hath done them on his Catholicon, but all of them applied to this Iewel, and altered to a more plaine and briefe Method, both in writing, working, and vnderstanding, by reason of the Authors new deuised reete, which performeth them fixed as redie, as by any tables, without any of those tedious profers, or doubtfull assaies, which Gemma Frisius is driuen to vse, by his Cursor, or Brachio∣lum: who also hath annexed diuerse new additions to most of the Chapters.
Chapter 1. How by this Iewel to take the altitude of the Sunne, Moone, or Starres.
Chapter 2. How to get or rather examine the Sunnes greatest declination, and distance of the Tropickes, and thereby also to learne the latitude of any countrie.
Chapter 3. How by the theoricke on the backe of the Iewel, to get the sunnes place or degree in the zodiacke any day.
Chapter 4. How to finde the sunnes declination for euery day in the yeare, and also the declination of euery part of theclipticke.
How to do the same a new way by the zodiacke of my Reete.
Chapter 5. How to finde the latitude or poles eleuation, any day proposed in any place, or countrie whatsoeuer.
Chapter 6. How to know what it is a clocke at any time the sunne shining, and in any region in the world.
Chapter 7. The latitude of any place knowne, how to get the declination of the sunne, or any starre, planet, or comet, by obseruation.
To do the same, the starre being in any place of the skie by obseruation and helpe of the Iewel.
Chapter 8. How the latitude or poles eleuation may be had in any region by the starres that neuer set.
Chapter 9. The latitude knowne, how to finde what day of the moneth it is, though it were lost, as they say, by the sunne shining at noone.
Chapter 10. To finde the right ascension for any portion of the eclipticke, and what degree of the Equinoctiall doth coascend, or rise togither with euery degree of theclipticke in a right sphere.
Chapter 11. The same more compendiously by the Reete.
Chapter 12. What point of theclipticke it is, as well in the first quadrant as in the rest also, that hath the greatest difference betweene the arch of theclipticke, and the arch of thecquinoctiall coascending with him.
Chapter 13. Of the difference of ascensions.
Chapter 14. The same very plainely by the Reete.
Chapter 15. To know the oblique ascenscions.
Chapter 16. Of descentions both right and oblique, that is, what degree of thequinoctiall doth descend with theclipticke.
Chapter 17. The longitude and latitude of any starres proposed, to know their right or oblique ascention, and how much they decline from thequinoctiall, and how to place starres in the Mater of the Iewel.
Chapter 18. The declination of fixed starres proposed with their latitude, which neuer altereth, how to finde their longitude in the zodiacke.
Chapter 19. The difference of ascension of any part of the zodicke or fixed starre proposed, or the oblique ascension to know what the latitude of the countrie is.
Chapter 20. To finde the amplitude of the rising and setting of the sunne or starres.
To do the same another way on the Horizons.
Chapter 21. The amplitude of the rising of any knowne starre giuen, or of the sunne, with his place in the Zodiacke to know the latitude of the countrie agreeable.
To finde the same by the Horizons.
Chapter 22. To know the rising and setting of the sunne, and the semidiurnall arch of the sunne and starres.
Chapter 23. The quantitie of the longest day of any countrie proposed, how to get the eleuation of the pole there, and of the distinction of the climates and parallels.
To doe the same by the Reete and Horizons.
subpart
Chapter 24. To know what houre of the day or night the Moone, or any planet or starre riseth or setteth on the horizon.
Chapter 25. To know what starre neuer rise or set to euery region, and which are verticall.
Chapter 26. Of the Cosmicall Eliacall and Acronicall rising and setting of the starres.
Chapter 27. How to know what it is a clocke in the night time by the starres.
Chapter 28. Of the vnequall or planetarie houres.
Chapter 29. How by the Iewell to know the Meridian or greatest altitude of the sunne and starres.
The same another way.
Chapter 30. How to finde the degree of Medium Coeli, or Culmination called midde∣heauen at any time proposed.
Chapter 31. To know how much any degree or point of the heauen is distant from the Meridian at any time by degrees of the Equinoctiall.
Chapter 32. How by the Iewell to know the height of the Sun aboue the horrizon euery houre and time of the yeere sitting within dores: and thereby to make tables to any latitude, for making of particuler Dials, as Cylinders, ringes, quandrants, & such like.
Chapter 33. How to know the height of any starre aboue the horizon sitting close within dores, and thereby to learne to know the starres in the skie.
Chapter 34. How to finde the Meridian line, and the foure quarters of the worlde called cardines, diuers wayes, and specially by the Astro∣labe.
Chapter 35. The meridian founde, to finde the Azimuth of the Sunne or starres by sight without the houre.
Chapter. 36. The verticall circle of the Sunne or any starre, the degree of the Sunne, with their al∣titude aboue the horizon, giuen howe to knowe the latitude and what it is a clocke.
Chapter 37. The latitude, the Sunnes Azimuth and almicantare giuen to finde his place in the Zodiacke.
Chapter 38. To know what houre the Sunne or any Starre commeth to any azimuth proposed.
Chapter 39. A Comet, a Planet, or an vnknowen starre being seen in the skie, how to get his longitude and latitude in the Zodiacke, and how by the right ascension and declination of any stare to get his longitude and latitude.
Chapter. 40. Howe to knowe the quantitie of the angles which the Eclipticke maketh with the meridian at any moment.
Chapter 41. To doe the same another way.
Chapter. 42. How to finde the horoscope, called the Ascendent at anytime appointed.
Chapter 43. How to finde the horoscope or ascendent another way by the Mater.
Chapter 44. Of the twelue houses, and what a circle of position is.
Chapter 45. To finde the circle of position according to Io. Regiomontanus and Campanus, of any point proposed, and howe much the pole is eleuated aboue any such circle.
Chapter 46. Of the other eight houses according to Regiomontanus, and how to set a figure.
Chapter 47. Of the other eight houses, according to Companus and Gazulus.
Chapter 48. To know in what house any starre is at any instant and to place the chiefe starres in the 12. houses.
Chapter 49. Of directions, what direction is, and by what meanes it is performed.
Chapter 50. Of conuerse or euerse direction, or dimission.
Chapter 51. How farre, or into what part of the zodiacke, Dymission or direction shall come any yeare.
Chapter 52. To finde what degree of theclipticke occupieth any circle of position at any time.
Chapter 53. To know the quantity of the angle of the inclination of the Elipticke to the ho∣rizon at any degree of the Eclipticke.
Chapter 54. how to finde the altitude of the Sun or any point of the Ecliptick aboue the horizon at any time otherwise then hath yet bin shewed.
Chapter 55. To find what angles the circle of altitude maketh with the Eclipticke at any point thereof assigned.
Chapter 56 How to finde the parallaxis or diuersity of the sight of the moone in the circle of altitude.
Chapter 57. How to finde the parallaxis of the moone or any other planet, or starre in longi∣tude and latitude of the Eclipticke.
Chapter 58. Howe to finde when the Eclipse of the Sun shall be.
Chapter 59. Another manner to finde out the parallaxis in longitude and latitude, as wel in the ☉ as the ☽.
Chapter 60. To finde the latitude of the moone.
Chapter 61. How much of the Sunne shall be darkened.
Chapter 62. How long the Eclipse of the sunne shal endure.
Chapter 63. Of the Eclipse of the moone, the greatnesse and duration of the same.
Chapter 64. How to get the parallaxis of the Moone out of the heauens at any houre proposed, the latitude knowne with the longitude and latitude of the ☽.
Chapter 65 To know the greatest, or horizontall parallaxis of the Moone when she is to be seene.
Chapter 66. The Longitude and Latitude of two Starres giuen, how to know the distance betweene them.
Chapter 67. How the distance of any two starres vnknowne may be had.
Chapter 68. To know how long the taile of a Comet is.
Chapter 69. Another way to serch the distances of starres one from another.
Chapter 70. The longitude and latitude of two starres giuen, to get the angle of station of one from another.
Chapter 71. To know whither three starres or cities be in one great circle.
Chapter 72. That the taile of a Comet extendeth it selfe directly from the Sunne, and howe you may try it.
Chapter 73. To knowe what point of the heauen is in the Meridian of any place at any in∣staunt proposed, and what it is a clocke in any other countrie.
Example.
Chapter 74. How to direct a ship by the starres in any voyage.
The fourth booke of the Ma∣thematicall Jewel: newly compyled and set foorth by Iohn Blagraue of Reading Gentleman: conteineth diuers Astronomicall Propositions, and vses of the Iewell, of his owne inuention, no lesse pleasant and commodious, then those whiche by other Authours haue beene founde heretofore on their sundrie Instruments.
Chapter 1. An aduertisement of the Authour concerning necessarie Instrumentes.
Chapter. 2. How to make an instrument of three streight rules better then any compasses to describe any arch with, be his center neuer so farre off.
Chapter 3 The vse of the former instrument in drawing of any Arche.
Chapter 4, Of a certaine secrete in diuiding the meridians of great Instruments.
Chapter 5. Another secrete founde by the Authour indeuiding the parallelles of great Instrumentes.
Chapter. 6. Of drawing and dyuiding of the eclipticke line on the Mater.
Chapter 7. By the verticall circle or azimuth of the Sunne or Starres, taken to knowe what it is a clocke, very certainely and exactly.
Chapter 8. By the latitude of any planet and his distaunce from any knowen fixed starre had: how to get his exact longitude.
Chapter 9. How at all times you may beholde on the Mater of your Iewel the whole circum∣ference of the ecliptike, according to his cituation, aboue the horizon, which bringeth with it pleasant vses as followeth,
Chapter 10. By the Eclipticke circle constituted as in the last Chapt. how to get the altitude and azimuth of the sunne or any point of theclipticke, and thereby also of the other planets so they haue no latitude.
Chapter 11. By the same constitution of theclipticke circle how to finde his Nonagessimus gradus with the altitude thereof, being the quantitie of the angle made betweene theclipticke and the horizon.
Chapter 12. How by the same constitution of theclipticke to see all the circles of position liuely on the Iewel, and what degree of the zodiacke is in any of them.
Chapter 64. How by the same constitution of theclipticke circle to set a figure verie sensible and apparantly.
Chapter 14. How to set a figure with more pleasure and ease, the last Chapter well vnderstood, so that you may beholde your whole 12. houses in their being altogether on your Iewel.
Chapter 15. How to get the altitude of the Nonagessimus gradus more readily then in the 11. Chapter is expressed.
Chapter 16. How to place theclipticke aboue the Finitor after another sort then is shewed in the 9. Chapter, and in the same constitution to finde out euery needfull circle, whereby most excellent conclusions are to be performed.
Chapter 17. How by the constitution of the 16. Chapter to get both the altitude and azimuth of the sunne or any point of theclipticke, or of any other planet or starre how much soeuer they shall be in latitude.
Chapter 18. How by the constitution of theclipticke as in the 16. Chapter to get the longitude and latitude of any starre or planet, that is to be seene in the skie, and thereby also his right ascension and declination.
Chapter 19. The altitude and azimuth of the sunne, or any planet or starre giuen, how by the constitution of the 16. Chapter, to get their exact longitude.
Chapter 20. How to get the true and exact azimuth of any planet, comet, or starre vnknowne.
Chapter 21. The moone shining on any sun diall to know in the night, what it is a clocke, very speedily by helpe of the Iewell.
Chapter 22 A speedy way to know what it is a clocke by the starres without taking their altitude.
Chapter 23. The vse of the three tables comprehended in the 2. figure of the second booke 13. Chap.
By the first table to get the Dominical letter for euer.
By the 2. table to get the Prime and Epact for euer.
By the third table to finde Easter day for euer.
Example of all three tables.
The conclusion of this fourth Booke.
The fifth book of the Mathe∣maticall Jewel, newly inuented, compiled and set forth by Iohn Blagraue of Reading, Gentleman: teaching most plainely to performe on the Iewell the whole art of sphericall triangles, without a∣any whit of that great toyle by synes supplementes, tables, proportions, Arithme∣ticall calculations, and such like: by which Ptolomeus, Regimontan. Copernicus, and all other Authors before me, haue wrought them, here pefourmed by ocular inspection with surpassing facility, and maye bee called the key of the knowledge of the sphere, in that it vnlocketh all spherical questions whatsoeuer: and is a singuler introduction vnto the Sinicall woorking.
Chapter 1. Of the Exposition of a Sinicall quadrant, and al thinges thereto appertay∣ning.
Chapter 2 Of certayne definitions needfull to the vnderstanding of this woorke.
Chap. 3. Of cereaine Theoremes needeful to be premised for the better vnderstanding of this my present worke of Sphericall trian∣gles.
Chapter 4. If of a right angled spherical triangle, two sides shalbe knowne how to get the quantity of the third side, and the other two angles.
In briefe.
Chapter 5. The declination of the Sunne, Moone, or any other planet or starre from the Equi∣noctial, giuen together with the Latitude of the countrey, how by the 4. chap. to get the amplitude, the difference of ascension, the ob∣lique ascension, and the diurnal arch of any of them.
Chapter 6. To perfourme the 4. chap. on the Iewell by another manner of woor∣king.
Chapter 7. To perfourme the same by the Iewell after a thirde man∣ner.
Chapter 8. The quantity of the longest day in any countrey giuen, to know the latitude, and in what climate the same is.
Chapter 9. If one side of a right angled sphericall tryangle, with one of the two angles not right be giuen, how to finde the other two sides and angle.
Chapter 10. If you would make an horizontall or verticall Dyall to any countrie, how by this last Chapt. to finde what number of degrees euery houres space containeth.
Chapter 11. If the three sides of any sphericall triangle whatsoeuer shall be giuen to finde the quantitie of euerie of his three angles.
Chapter 12 The declination of the sunne giuen at any time togither with her altitude aboue the horizon, how by meane of the 11. Chapt. to get what houre and minute it is, and in what azimuth the sunne then is.
Chapter 13. If of aspherical triangle two sides containing any one knowne angle shalbe giuen, how to finde the other side and angles.
Chapter 14. How by helpe of the 13. Chapt. to know the height of the sunne at any houre, and minute proposed in the whole yeare, and also in what azimuth he is.
Chapter 15. Ioannes Regiomontanus, Lib. 1. Cap. 51. and lib. 4. cap. 29. proposeth and sayth that the knowing of two sides of a triangle not right angled, with one angle subtended by one of those sides, cannot serue to get the other side and angles.
Chapter. 16. The azimuth of the Sunne giuen or taken at any time by Instrument, with his declination, how by helpe of the fifteenth Chapter, to knowe what height the Sunne is of, and what it is a clocke.
Chapter 17. If of any sphearical triangle, not right angled, two angles shalbe giuen with the side lying betweene those angles or els the side subtending one of them, how to get the other two sides and thirde angle.
Chapter 18. Howe by the helpe of the 17. chap. to make any declining diall, that is to say, a dial to any wall shouldring or bending from the ful beholding of the South.
Chapter 19. How to let downe a perpendiculer arche from any angle of a knowen sphea∣ricall triangle vnto his base or subtending side, and to know the quan∣titie of the same perpendiculer, and of the parts whereinto hee deuideth the base.
Chapter 20. To doe the same after another manner of working, yea though one of the other two angles, and one of the other two sides, of the triangle were vnknowen.
Chapter 21. If two great circles of the spheare crosse one another, making a knowen angle howe to get the perpendiculer arche, falling from any poynt assigned of the one circle vnto the circumference of the other, together with the arche of the same circle, betweene the perpendiculer, and the crossing.
Chapter 22. How by helpe of the 21. chapter to knowe both the height of the cocke, to any decli∣ning dial, and how much he must be placed byas from the perpendiculer which I call his deflection.
Chapter 23. In a right angled sphearicall triangle where one of the angles shal chaunce too bee but certaine min. as it often hapneth, how to get the side subtending that angle presisely notwithstāding.
Chapter 24. If the three angles of a right angled sphearicall triangle shall bee giuen, howe to get the quantitie of the three sides vnknowen.
Chapter 25. If by the crosse staffe or other Instrument, you shall take the true distance of any planet, co∣met, or starre vnknowen from twoo knowen starres, how by helpe of this my woorke of sphericall triangles, to get the longitude and latitude in the zodiacke of the same planet, comet, or starre, and also his declination and right as∣cension: and what you had need to do in al sphearical questions.
The conclusion of this worke of triangles.
The sixt book of the Mathe∣maticall Jewel, newly compiled, deuised, and set foorth by Iohn Blagraue of Reading, Gentleman: shewing the Theoricall reason and grounde of all Dialles and Horizons, and the practicall making of all sortes of horizontall, murall, declining, reclining, and inclining Dials, by the onely helpe of this Mathematicall Iewell, and that most plainely, rea∣dilie, and exactly, as hereafter shall followe: which worke, besides the art of Diall making, bringeth a man acquainted with the full vnderstanding of the spheare, and is the dore into the same.
Chapter 1. Of certaine prenmbles to bee noted in vnderstanding this worke following.
Chapter 2. Of the distinction on Dials into two kinds, Instrumentall and Sphericall.
Chapter 3. Of the definition and deriuation of Dyals and the grounde of them all.
Chapter 4. What the cocke or Gnomon of euery Dyall is, and by what reason they giue the true shade to the Dyall.
Chapter 5. Of the diuision of Horizons, and especially into three sortes.
Chapter 6. Of the diuision of all Dials into three sorts, and whie they make shew of greater diuersitie then there is.
Chapter 7. How to make the first kinde of dial to the Equinoctial horizon, that is, where one of the poles is zenith.
Chapter 8. How to make the second kinde of dial to a right horizon, that is, where the Equi∣noctiall cutteth the zenith, together with the ground and reason of al dials to any right horizon.
Chapter 9. How to make the third kind of diall to an oblique horizon, which they commonly cal an horizon diall, and that very easily.
Chapter 10. How to make a diall to a perpendicular wall beholding the South fully, called of some Authors Horologium verticale.
Chapter 11. To make a diall to a ful North wall.
Chapter 12 How to make a diall to an East wall.
Chapter 13. How to make a Diall to a West wall.
Chapter 14. Of declining walles, and what circles of the spheare they represent.
Chapter 15. How to know the scituation of any wall, and to finde how much he declineth.
Chapter 16. How by the declination of any wall knowne, to finde his eleuation with his angle of deflexion.
Chapter 17. To perfourme the last chap. a second way by the 6. chap. of spherical triangles.
Chapter 18. To performe the same a third way.
Chapter 19. How to make a diall to any declining wall, respecting the South.
Chapter 20. How to make a Dyall to any declining Wall respecting the North.
Chapter 21. How to order Dyals that decline very farre East and west.
Chapter 22. Of uals reclining and inclining, and of the diuersitie of them.
Chapter 23. How to take the reclination, or inclination of any wall or flat, togither with his declination if any be.
Chap. 24. How to make a Dyall to a south or north reclining or inclining wall, bancke or flatte.
Chapter 25. How to make a Dyall to an East and West wall, bancke or flat reclining or inclining.
Chapter 26. How to finde the angles of the poles eleuation, dials deflection, and meridians ascension, to any reclining or inclining wall declining.
Chapter 27. How to perfourme the last chapter by sphearicall triangles very easily, and with great pleasure and profite.
Chapter 28. The angles of reclination, delination, eleuation, deflection, and ascension had as before, how to make the dial to a reclining wall, bancke, or flat declining.
Chapter 29. Of inclining dials reclining.
Chapter 30. Howe to knowe in what countrie any declining, reclining, or inclining diall, woulde or of right shoulde serue as an horizon diall, and also to make him shewe the houres of the same place together with yours.
Chapter 31. How to place a flat representing the horizon of any countrie, citie or place in the worlde both according to the longitude & latitude of the same.
Chapter 32, To perfourme the same by sphearicall triangles.
Chapter 33. To describe dials to al maner of declining walles, and also to all East and West reclining and in∣clining flats more at plaesure then yet hath been shewed without foreknowing the angles of eleuation or deflexion.
Chapter 34. To reduce all reclining and inclining flats declining vnto East and West, reclining and inclining flattes to some one latitude or other, and thereby most easily to make the Dyall.
Chapter 35. To do the same somewhat easier.
Chapter 36. To performe the 31. Chapter somwhat more easily, or at the least more pleasingly.
Chapter 37. A most easie and briefe way to reduce all reclining and inclining flats declining, vnto East and West reclining flats to a new latitude, otherwise then in the 34. & 35. Chap. by helpe of sphericall triangles.
Chapter 38. A briefe note how East and West reclining or inclining Dyals are to be made two seuerall wayes.
Chapter 39. How to make a diall to any East or West, reclining or inclining flat, by helpe of spherical triangles most easily.
Chapter 40. Most excellently and easily to make dialles to al maner of reclining or inclining flats declining, by the Iewell and helpe of spherical triangles.
Chapter 41. To know in what Longitude and Latitude our horizon or any other shall represent any declining wall proposed, or els any circle of position proposed.
The conclusion.
The order of the sixe bookes behinde.
colophon