the Colume M. 5294. which I take from the scale B. and protract it from T. to 30. in the line 2. 10. Now placing one foote of the Compasses in 30. next 10. and extending the other foote to P. the Eclipticke may be intersected in the points of ♉ and ♓ and placed in 30. towards 2. the same extent will Intersect the Eclipticke in ♠and ♠In like manner may the Centers of the rest of the degrees of the Eclipticke be protracted in the line 2. 10. from T. out of the Columes M. and P. and so all the Eclipticke divided from degree to degree but this may be otherwise done Besides that which is delivered touching the drawing of the Parallels Eclipticke and Houre lines there remaines yet how to put on the Callender to graduate the Index and to draw and divide the line of Shadowes This may be easily done from the Table R. Calculated and accommodated to that purpose for the yeare 1640 and may sufficiently serve for many yeares after without any sensible error Having divided the Quadrants Constru ∣ ction E.S. and E.N. as before into the usuall degrees of a Quadrant lay a ruler upon the Center Z. and account the degrees from the point E. in the Quadrant towards N. and S. out of the Table R. according to the severall Columes of the Table R. and Intersect the Quadrants How to inscribe the Callender with small short lines so shall the Arke of the Horizon of the Instrument from E. be divided into the usuall dayes of the Month which is the Callender and the beginning of these divisions may be at the 10. of March and so going on to the 11. of Iune and then againe to begin from the 10. of March and go on unto the 10. of December and these dayes may bee noted upon the inside of the Horizontall Arke with short lines from E. as before and at every Month may bee placed a representative letter for that Month and every 10. and 5. day of every Month may bee noted with a small stroke somewhat longer then the rest to helpe the memory the readier to number In like manner may the rest of the dayes of the Calender be intersected in the out side of the Horizontall Arke towards the Limbe beginning at the 13. of September and so going on to the 11. of Iune then againe from the 13. of September and going on unto the 10. of December and these Months may bee also noted with significant letters appropriate to each Month and each 10. and 15. day of the Month may be also denoted as before with a stroke somewhat longer than the rest according to the Scheme against Page the 1. How to graduate the Index for the Instrument Let the Index be equall to the semidiameter Z. E. and then may it bee divided out of the Table Q. by the helpe of the scale A. beginning at the Center the Index being diuided and placed on the Center of the Instrument at Z. it shall helpe to put on and divide the line of shadowes as followeth Lay the edge of the Index to A. in the Limbe which is neere the 10. of December and move it to any degree in the Table S. and account the like degree in the Index and then make a marke upon the plaine of the Instrument where that degree toucheth and so goe on from point to point untill the whole line bee described and divided according to the Table S. This line might bee placed betweene the Calender and the Limbe or in a Quadrant c. But I have caused it to bee described as is seene upon the Scheme against Page the 1. for expedition and conveniency ☞ Let A. B. C. D. be a plaine divide the length A. B. within halfe an Inch of the higher end and an Inch of the lower end in to 3. equall parts which suppose the line M.N. then divide each part into halfe so the line M. N. shall bee divided into 6. equall parts the middle of which will bee at Z. Then take 4. of these parts for Radius and on Z. describe the obscure Arke A. E. B. and upon Z. erect a perpendicular to the line M. N. to cut the Arke A. B. in E. now from E. to A. protract 40. gr and from E. to B. protract 50. gr so the Angle E. Z. M. shall be 90. and also A.Z.B. shall be 90. Now having made a scale of Z.E. like to the scale A. according to the former directions then out of the Colume C. and by helpe of the said scale A. from Z. you may protract Z. ♋ 2493. Z.Q. 4823. and Z. ♑ 7673. and from the Colume F. y u may protract the distances of the Centers of those intersections from Z. viz. Z. 1.5269 Z. 2.7949 and Z. 3.16217 and so placing the Compasse in these Centers you may describe the Equator and both Tropicks But if Z. M and Z. N. be divided according to the scale A. then from Z. you may account the intersections of the parallels and distances of the Centers and so describe the parallels with greater expedition and so shall you have the Scheme or Trapeziall forme of the Instrument B. A. ♑ ♋ and may bee finished according to that against Page the 1. by the Tables and directions here calculated and delivered to that end Now to augment the Instrument to any proportion assigned as if betweene the Tropickes were supposed to bee 10. Inches the Radius might be found out or if the Radius were 4. foote which is according to mine owne Instrument what distance might there bee betweene the Tropickes the proportion would be as 516. to 1000. so the breadth to the scale or as 1000. to 516. so the scale to the breadth therefore by the Ring bring 516. in the moveable to 1000. in the fixed so right against any Radius in the fixed is the distance betweene the Tropickes in the Moveable or against the distance assigned for the Tropickes in the Moveable is the measure of the Radius or Scale in the fixed So if ♑ ♋ be allotted to be 10. Inches for the distance betweene the Tropickes the Scale or Radius of the Instrument should be 19 4 10. fere but if the scale or Radius were 4. foote or 48. Inches then the distance betweene the Tropickes of ♑ and ♋ will be neere 24 77 100. Inches Thus for the making of the Instrument the description of which followeth The Description of the Horizontall Quadrant THe forme of this Instrument is like a mixt Trapezia as appeares against Page 1. where of two sides are right and the other two sides are Circular which falleth out to bee so from the nature of the Projection and that part which I have thought most convenient for use and is fully sufficient for that which I have deliuered upon it and may be made of any plaine Materiall but fittest in Brasse or Silver the severall parts of which Instrument are five viz. the Backe the Face the
the Instrument being a part of the Horizon the Parallels Meridians Verticall Circles that are contained or may be described in our Latitude sufficiently necessary induceth any one in the understanding of the uses of it that is but indifferently versed in the linaments and principles of the Globe what to speake and what to answere in a Proposition without farther direction And having had this Horizontall Quadrant for many yeares past as a Pocket Instrument diverse about this Kingdome being importunate with me for to have it or to publish the use of it seeing its great facilitie and expedition in comparison of such Pocket Instruments as are now used here or in forraigne parts I was willing at last after I had given order for the making of fower of these Instruments in Silver for severall Noble Personages to disburthen my selfe of Transcribing the uses of the Instrument and Tables for the making of it to satisfie those which were importunate and to let others that are studious in Mathematicall Practices also participate of it Now what I have delivered vpon the accommodating of the Instrument thus the making thereof with the uses that I have delivered in this Tractat upon it following I acknowledge due to none Inferiour assistant but to mine owne Industry search and labour and that 64. 65. and 66. Pages of the Booke of the Sector before specified in which is onely shewne the 2. 3. 19. 22. 25. and 30. Propositions of the Index or Table following as uses of the said Projection But I have extended them to many more and abundantly and plentifully supplied the obscuritie of that Scheme or Diagramme there drawne as for a generall good in the use of this Horizantal Quadrant I deliver therfore first the making of it first by the Sector somewhat different from that of Master Gunters secondly by Geometrie and lastly I shew a third way how it may be Proiected and made by my Mathematicall Ring and by Numbers which I have Calculated and accommodated to that end in Tables for more exactnesse Part of the generall scope and use of which Instrument I deliuer in the Index or Table following An Index or Table of the vses of the Horizontall Quadrant Viz of the Horizon Line of Shadowes Kalender Parallels Aequator Eclipticke Houre-lines Index 1 By the Horizon to shew 1. The Sunne or Starres Altitude at any time Pag. 53. 2. At any Day of the yeare how farre the Sun riseth or setteth from the true East or West Pag. 28. 3. The Suns Azimuth and Altitude at any houre for any day Pag. 62. 4. The Meridian line upon any appearance of the Sunne Pag. 55. 5. The vncertaintie of time by noting the Shadow of things Pag. 63. 6. The Site of a Building or Costing of a Place Pag. 57. 7. The Variation of the Needle Pag. 59. 8. The Declination of a Wall or Plaine the Sunne shining thereon Pag. 71. 9. The Inclination of a Plaine and to place a Plaine Horizontall Pag. 89. 2. By the line of shadowes is had 10. At what houre in any Day of the yeare the shadow of an Altitude is equall double triple c. unto it Pag. 35. 11. Instantly the houre of the day the Azimuth and Altitude of the Sun with the Meridian line without observation or sight of the Sun by knowing the Proportion betweene the length of a shadow upon a Horizontall Plaine that which casts the shadow Pag. 67. 12. At any houre an Altitude of the Sun or Azimuth what Proportion shadowes have to their Bodies Pag. 37. 13. Whether and Altitude be above or below the Iewell of the eye how much 14. The hight of an Altitude accessible or in accessible Pag. 100. 101. 15. The measure of any Part of Altitude not approchable Pag. 102. 3. By the Kalender is knowne 16. The inequality of Time in equall Months or equall number of Dayes Pag. 44. 17. What number of dayes wil make the day and houre longer or shorter at any time Pag. 43. 18. The houre of the Sun rising setting with the length of the day at any time Pag. 23. 19. What dayes are alike in length what day the Sun rising in the one shall be the Sun setting in the other Pag. 24. 20. The inequality of Time between day breake and Sun rising Pag. 41. 4. By the Parallels to search out 21. At any day the Suns declination Pag. 24 22. The Latitude of a Place or hight of the Pole above the Horizon Pag. 60. 23. At what houre in any day the Suns Azimuth and Altitude will be equall and how much the Altitude Azimuth wil be Pag. 42. 5. By the Aequator is seene 24. The Suns equall motion right Ascention and oblique Ascention Pag. 26. 6. By the Eclipticke to give 25. The Sunnes Place at any time of the yeare Pag. 25. 26. The Degree of the Aequator in the Horizon by supposing the degree of the Ecliptick in the Horizon Pag 46. 27. The Degree of the Eclipticke in the Horizon by supposing the degree of the Aequator in the Horizon Pag. 47. 28. The degree of Medium Coeli or the degree of the Eclipticke in the Meridian by supposing the degree of the Eclipticke in the Horizon Vel contra Pag. 47. 29. The Horoscope or the degree ascendant ' or descendant and the Nonagessima degree at any houre Pag. 49. 30. What Angle the Eclipticke makes with the Horizon or the Altitude of the Nonagessima degree and what Azimuth it is in at any houre Pag. 50. 7. By the hour lines to find 31. The houre of the Day and Azimuth of the Sunne Pag. 54. 32. The houre of the day agreeable to any Altitude or Azimuth Pag. 39. 33. The Sunnes Difference of Ascention for any day Pag. 23. 34. The Quarter of the yeare and day of the moneth houre of the day Meridian-line and Azimuth of the Sunne if it were forgotten Pag. 64. 8. By the Index adioyned with other lines you have 35. At what houre Altitude the Sun wil be due East at any day of the yeare Pag. 27. 36. The Suns Azimuth houre without observation Pag. 58. 37. The time of day-breake or end of Twi-light for any day in the yeare Pag. 30. 38. The hight or Depression of the Sun in the Meridian for any day in the yeare here or for any Latitude Pag. 29. 39. The Suns depression Azimuth at any houre of the Night assigned Pag. 40. 40. The houre of the day to our Antipodes by supposing the suns depression under the Horizon Pag. 42. 41. What houre Altitude the sunne commeth upon a declining wall any day in the yeare how long the sun shineth thereon Pag. 32. 42. At what houre and Altitude the Sun must have to be opposite or Perpendicular to a Declination Plaine Pag. 33. 43 The declinatiō of a wall by seing the sun beginning to shine thereon or going from it Pag. 69. 44. The houre Altitude of a stars coming to the Meridian at
Horizon of the world But this may be more accurately done if you place the backe of the Instrument downe upon an Horizontall plaine and the edge of the Index being at the degree of the suns Azimuth observed and the perpendicular erected at the end of the Index as before then moving the Instrument as it so lyeth untill the shadow of the perpendicular fall by the side of the Index so the Meridian of the Instrument shall be in the Meridian of the World and every point and degree in the Limbe of the Instrument shall point out and be opposite and represent his like degree in the Horizon of the world Constru ¦ ctio 39 But here note that this Construction serves only but for the forenoone observation for if the practice be in the afternone the way to finde the Meridian line may be thus Having found the suns Azimuth as before lay the Index upon the houre line of 12. and erect the perpendicular at the end thereof and move the Instrument about Circular untill the shadow of the said perpendicular fall by the side of the Index for then if the edge of the Index be moved unto the suns Azimuth before known the edge of the Index shall represent the Meridian line 90. gr farther shall be the point of East and the Center of the Instrument the point of West therefore if upon the plaine that the Instrument lies upon you make a marke at the edge of the Index which is in the Meridian as before and another marke right under the Center and so place the North and South edge of the Instrument unto these two points then every degree in the Horizon or Limbe of the Instrument shall point out as before his opposite or â—ike degree in the Horizon of the world Fourthly how to finde the sit Pro. 30 of a Building or Costing of a place By the last Pro. finde out or draw the Meridian Constru ¦ ctio 40 line and place the North and South edge of the Instrument unto it if the Building or Place ly in the Easterne semicircle of the world but if it ly in the Westerne semicircle then let the East West edge of the Instrument be placed upon the Meridian line so the eye being over the Center of the Instrument and behoulding the place let the Index be moved untill it be also with the visual line observed by the eye that is opposite to the place so the edge of the Index from the Cardinall points of the Instrument in the Limbe viz. from the East or West North or South shall shew the bearing of that place from you in respect of the Cardinall points of the world in the Horizon but if two sights be placed at the Index which is according to the description thereof then may you observe the place through the sights of the Index by leting the Instrument rest and moving the Index to and fro untill you see the obiect so the edge of the Index in the limbe shall point out the bearing or Position of the place from you in degrees from the East West North or South accounting 11. gr and ¼ as often as you can in those degrees observed you have the point of the Compasse which the place or obiect beares from you Pro. 31 Fiftly to finde the suns Azimuth and houre without observation The Meridian line being drawne first upon a Constru ¦ ctio 41 plaine according to the former directions consider if it be in the forenoone or afternoone if in the forenoone then let the North and South edge of the Instrument be placed unto the Meridian line but if it be in the afternoone then set the edge of East West of the Instrument unto the Meridian line and let the Instrument rest there then erect the perpendicular at the end of the Index move the Index about untill the shadow of the perpendicular fall by the side of the Index so the edge of the Index will amongst the degrees in the Limbe shew the Suns Azimuth at that time and where the edge of the Index meeteth with the parallel of the day of the Month that is the houre of the day at that time But if the Axis be rectified then there is no neede of a Meridian line to be drawne for this Instrument will with great facilitie finde out his owne Meridian by moving it to and fro untill the shadow of the perpendicular which is ouer the Center of the Instrument intersect the same houre in the Parallel of the day of the Moneth that the Axis doth amongst the Common houres so that houre shall be the houre of the day for that instant and the shadow of the said perpendicular cutting the Limbe or extended unto it doth there shew the Suns Azimuth and so the Meridian of the Instrument at that position shal be in the Meridian of the world required Sixtly to finde the variation Pro. 32 of the needle By the twentie nineth Pro. vpon an even Plaine parallel to the Horizon draw the Meridian line Constru ¦ ctio 42 place the North South line of the Card directly over the said Meridian line so the Number of degrees that the Needle cutteth in the Card from the North and South line of the Card that shall be the variation of the Needle required otherwise it may be found thus Neere unto the Center of the Index upon the Index may a small Brosse pinne be so placed that it may be erected perpendicular to the Center of the Instrument and halfe an inch above it Let a Needle by placed upon this pinne then lay the East and West edge of the Instrument to the Meridian line when the Needle resteth move the Index untill the edge of it be directly under the Needle so the edge of the Index in the Limbe of the Instrument shall point out or shew the Needles variation required Pro. 33 Seventhly to finde the Latitude of a place or the Poles hight above the Horizon Constru ¦ ctio 43 First draw the Meridian line upon some plaine by helpe of the 38. Construction then erect the prependicular at the end of the Index and place the North and South edge of the Instrument to the Meridian line so drawne upon the plaine and move also the Index untill the edge thereof touch the houre of 12. let the Instrument rest at this position then marke diligently about noone or 12. of the Clocke when the shadow of the perpendicular doth fall by the edge of the Index for then the sun is in the Meridian at which time according to the 27. Pro. obserue or take the suns height which is his Meridian Altitude for that day and by the 3. Pro. finde the Suns declination agreeable to that day and adde it to the Suns Meridionall Altitude observe if it be South declination otherwise subtract it from the former Meridionall Altitude so have you the height of the Aequinoctial above the Horizon that taken from 90. gives the depression of
of them to be divided into 100 or 1000 diuisions with a Quadrantall Arke or more divided and fastned also at the end of one of the leggs but so that the Quadrantall Arke have also an edge to lie flat upon the Paper and to slide in at the other leg so shall it be accommodated and made a fit apt Instrument to finde the Quantitie of Angles in a Plot or to protract Angles for service as followeth So to search out the distance of O P Q R Exam. the one from the other or all the distances from Y as was required by the helpe of the former Angles of observations and Protracter it may be done thus Thirdly how to take the Circuite Pro. 46 of a figure or the surueigh of a Place Let ABCD Exam. be a plaine to be raised as Fortifiers have it or a field to be ploted as surveyers account it or a Figure whose Perimeter is required as Geometritiās treate of it The Plaine Table Notatio may be held best for this service as such would have it whose learning is altogether versed therein But any Instrument shall be able to doe this Service that can but accuratly take or measure any Angle not that we reject that but make use of this for the present and therefore in this action it were no losse of time to make a preambulation about the field to view the severall windings and turnings thereof and what Angles with greatest Conveniency and expedition are to be observed and what might be omitted and at the Angles of consequence there to set up some marke and upon those Angles to fabricate the whole worke for here especially is to be noted that the more Angles that are obserued in any practise by way of Circumscribing a Field or Campaigne the greater and more evident shall the error be in the Conclusion So in the Figure A B C D Exam. there is eleven Angles and as many sides now if at every Angle an observation should be made it would be more subiect to error as before then if lesse Angles were observed therfore in this Diagramme fewer Angles of observation may be fully sufficient to raise that Plaine Take the Plot of the Field or give the Perimeter of that Figure Therefore suppose the noted Angles of Consequence to be A B C D Q the worke may be then thus Place the Instrument upon his rest at A and obserue the Angle Q AB which suppose 32. gr 10 m then measure Q A with a Decimall Chaine or such like which suppose to be 5. Chaines note this in a peece of paper then take the Instrument up and measure the line A B but first onely A E which suppose to be 11. Chaines and 60 Linkes which is written down thus 11. 60. Then measure the distance from E to the Angle F which admit to be 2. 20 Lastly go one with the measure A B which suppose to be 15. 00 the Angle of obseruation and measures thus taken may be noted downe one against another as in the Table following then place the Instrument Constru ¦ ctio 63 upon his rest at B and obserue the Angle ABC which note downe also and measure the distance B G and G H and then going on with G B to G I and marke and measure B I and then measure also I K and so goe on with B C which measures are all placed down as appeares in the Table of Angles and measures following In like matter performe the rest of the worke untill you come to Q and so all the Angles and measures will be according to the Table here under specified The Table of Angles The Table of measures G.M. 5. 00. 32.10 11. 60.  2.20  15. 00. 80.10 6. 00. 1.00 9. 20. 2.00 16. 40. 79.30 6. 90. 1. 29. 8. 00. 74. 45. 3. 70. 1. 15. 5. 40. But it had beene fully sufficient by helpe of this Protractor to have plotted the aforesaid Plaine by knowing the former Measures and two Angles of obseruation only Pro. 47 Fourthly how to finde the Inclination of a Plaine or to Elevate a Plaine unto an Angle assigned and to Place a Plaine Horizontall Constru ¦ ctio 65 For the first Set the East and West edge of the Instrument unto the Plaine then if the edge of the Index in the Limbe of the Instrument cut the point of East or West the Plaine is verticall and doth not Incline but if the Index fall from the points looke how many degrees it is from the points of East or West in the Limbe of the Instrument so much is that Inclination of the Plaine For the Second to Elevate a Plaine to an Angle assigned This is onely the same with the former but may be applyed to severall uses as to trie the mount or to mount a Peece of Ordinance at any Randon or to place Burning glasses or others at severall Angles to receive each others Reflexon and that the point of concurse or inflammation in such Glasses may be in the Radius or beame of the Sunne or that the point of inflamation the representative Image or the extensive Elumination may be proiected to a point assigned For the Third to rectifie a Plaine Horizontall Constru ¦ ctio 66 Place the North and South edge of the Instrument unto the under face of the Plaine and then marke if the edge of the Index cut the points of East or West in the Limbe of the Instrument for then the Plaine is Horizontall but if it swarne from that point then it is not Horizontal but the Plaine is to be raised or depressed untill by severall tryalls in sundry parts of the Plaine you see the edge of the Index fall upon the points of East or West for then shall it be truly Horizontall Otherwise you may rectifie the Plaine Horizontall by operating upon the upper face of it if you set a Cube upon the plaine and then placing the East and West edge of the Instrument unto the side of the Cube for then the obseruation will be as the former and therefore accommodated concluded accordingly Pro. 48 Fiftly to finde whether an Altitude be in the Point of libration or above or below the levell of the eye and how much Declara ∣ tion Let C B and X be three severall obiects and let their severall situations be required Constru ¦ ctio 67 First let the Instrument hang upon a rest perpendicular and let it be held stedfast that the Index may be verticall and play easily by the side of the Instrument then looking through the sights of it lift the Instrument up and downe untill you see your marke which suppose first C and admit the Index should cut 5. in the line of shadowes which sheweth that C is higher then the eye by the 5th part of the distance of the bassis of the obiect from the eye supposed at A. Secondly if through the sights of the Instrument you see the second obiect B and the Index falling upon