HOW TO FIND OUT BY THE SAIDE TABLES , THE DISTANCE BETWIXT TWO PLACES DIFFERING BOTH-2 IN LONGITUDE AND LATITUDE , MAKING THE TOTALL SINE TO BE NO MORE BUT (BLUNDEV-E2-P1,51V.3) This is done by finding out two numbers , whereof the one is called in Latine Primum inuentum , that is to say , the first found number , and the other is called Secundum inuentum , that is the second found number in such order as followeth . (BLUNDEV-E2-P1,51V.5) First then knowing the Longitude of either place , take the differe~ce of their Longitudes by subtracting the lesser Longitude out of the greater , (BLUNDEV-E2-P1,51V.6) that done , multiply the right Sine of that difference into the Sine of the complement of the lesser Latitude , (BLUNDEV-E2-P1,51V.7) and diuide the product of that Mutiplycation by the totall Sine , (BLUNDEV-E2-P1,51V.8) and then seeke out the arch of that quotient according to the rule before taught , (BLUNDEV-E2-P1,51V.9) so shall you haue the first found number : (BLUNDEV-E2-P1,51V.10) That done , multiply the right Sine of the lesser Latitude by the totall Sine , (BLUNDEV-E2-P1,51V.11) and hauing diuided the product thereof by the right Sine of the complement of the first found number , subtract the arch of that quotient out of the greater Latitude , (BLUNDEV-E2-P1,51V.12) and you shall haue the second found number : (BLUNDEV-E2-P1,51V.13) Then multiply the right Sine of the complement of the first found number into the right Sine of the complement of the second found number , (BLUNDEV-E2-P1,51V.14) and hauing diuided the product of that Multiplycation by the totall Sine , seeke the Arke of that quotient in the tables , (BLUNDEV-E2-P1,51V.15) and take that Arke out of the whole Quadrant , (BLUNDEV-E2-P1,51V.16) and the degrees that doe remaine , are degrees of the great Circle , which if you multiply by the product of y=t= Multiplycation will shew you how many Italian miles the one place is distant from the other , (BLUNDEV-E2-P1,51V.17) or if you would haue Germane miles , the~ multiply the foresaid degrees of the great Circle by 15. (BLUNDEV-E2-P1,51V.18) or else diuide the product of the Itailian miles by 4. (BLUNDEV-E2-P1,52R.19) and you shall haue your desire . (BLUNDEV-E2-P1,52R.20) As for example , you would know what distance is betwixt Hierusalem and Noremberg a famous towne in Germanie , (BLUNDEV-E2-P1,52R.21) Hierusalem according to Appian his tables , hath in Longitude 66. degrees , , and in Latitude 31. degrees , . (BLUNDEV-E2-P1,52R.22) Againe Noremberg hath in Longitude 28. degrees , . and in Latitude 49. degrees , 2'4 . (BLUNDEV-E2-P1,52R.23) the difference of their Longitudes is 37. degrees , . the right Sine whereof is 36$$664 (BLUNDEV-E2-P1,52R.24) for in this example Appian maketh to be the total Sine , (BLUNDEV-E2-P1,52R.25) and therefore he reiecteth the two last figures on the right hand found in the first tables of Monte Regio (BLUNDEV-E2-P1,52R.26) Now you must multiply 36$$664 into the right Sine of the complement of the lesser Latitude which Sine is , the product of which two Sines being multiplyed the one by the other , amounteth to which if you diuide by the totall Sine . , you shall find in the quotient whose arch is 31. degrees , . (BLUNDEV-E2-P1,52R.27) and this shal be your first found number . (BLUNDEV-E2-P1,52R.28) This done , multiply the right Sine of the lesser Latitude which is 31$$498. by the totall Sine (BLUNDEV-E2-P1,52R.29) and the product thereof will be which summe if you diuide by the Sine of the complement of the first found number which Sine is 51$$249. you shall find in the quotient 36876. the Arke whereof is 37. degrees 5'5 . which arch being subtracted out of the greater Latitude , there will remaine 11. degreees , 2'9 . (BLUNDEV-E2-P1,52R.30) and that shall be your second found number , (BLUNDEV-E2-P1,52R.31) then multiply the foresaid Sine of the complement of the first found number which is 51$$249. by the Sine of the complement of the second found number which is 58$$798. (BLUNDEV-E2-P1,52R.32) and the product therof will amount to which if you diuide by the totall Sine , you shall find in the quotient the arch whereof is 56. degrees , . which being subtracted out of the whole Quadrant which is degrees , there will remaine 33. degrees , of the the greater Circle , which 33. degrees , if you multiply by it will make miles , whereunto you must adde for y=e= miles , (BLUNDEV-E2-P1,52R.33) so shall you find the distance betwixt the two foresaid places to be Italian miles , which if you would reduce into Germaine miles , then diuide that number by 4. (BLUNDEV-E2-P1,52R.34) for 4. Italian miles doe make but one Germaine mile , (BLUNDEV-E2-P1,52R.35) so shall you haue 497. Germaine miles , and two Italian miles remaining , which is halfe a Germaine mile , which summe agreeth with that which Appian setteth downe in his Geographie , $where $as {TEXT:whereas} hee vseth the selfe same example , and worketh it in like manner Per tabulas sinuum . (BLUNDEV-E2-P1,52V.36) THE ALTITUDE OF THE SUNNE BEING KNOWNE , HOW TO FIND OUT THE LONGITUDE OF THE SHADOW BOTH RIGHT AND VERSE OF ANY BODY YEELDING SHADOW BY HELPE OF THE FORESAID TABLES . (BLUNDEV-E2-P1,52V.38) First you haue to vnderstand that euery bodily thing yeelding shadow , is diuided into 12. equall partes , and euery such part into minutes , and every minute into seconds , and so forth : (BLUNDEV-E2-P1,52V.40) Againe , of shadowes there bee 2. kindes , that is , Vmbra recta , and Vmbra versa : (BLUNDEV-E2-P1,52V.41) Vmbra recta is that which proceedeth from some body rightly erected vpon the vpper face of the Horizon , as from some tower or post standing right vp vpon a leauel ground : (BLUNDEV-E2-P1,52V.42) And that shadowe is called Vmbra versa which proceedeth from some right style or pearch being thrust into a wall or post standing right vp and not leaning , in such sort as the sayde style or pearch may bee a iust paralell to the vpper face of the Horizon . (BLUNDEV-E2-P1,52V.43) Now to find out the length of either the foresaide shadowes , you must doe thus . (BLUNDEV-E2-P1,52V.44) Multiply the right Sine of the complement of the giuen Solar altitude , by 12. (BLUNDEV-E2-P1,52V.45) and diuide the product by the right Sine of the said Solar altitude , (BLUNDEV-E2-P1,52V.46) and you shall haue the Longitude of the right shadow of the said body . (BLUNDEV-E2-P1,52V.47) Againe if you multiply the right Sine of the foresaid altitude by 12. and diuide the product by the Sine of the complement of the said altitude , you shall haue the Longitude of Vmbra versa , of the saide body . (BLUNDEV-E2-P1,52V.48) As for example , suppose the giuen Solar altitude to be 25. degrees , the complement whereof is 65. (BLUNDEV-E2-P1,52V.49) and the right Sine of that complement is 54$$378 if you make the total Sine to be (BLUNDEV-E2-P1,52V.50) Then in multiplying the foresaid right Sine by 12. the product will be 652$$536. which if you diuide by the Sine of the altitude which is 25$$357. you shall find the longitude of Vmbra recta to be 25. parts 4'4 4" 2.'''6' . (BLUNDEV-E2-P1,52V.51) Now if you multiply the Sine of the altitude which is 25$$357. by 12. and diuide the product by the Sine of the complement which is 54$$378. you shall finde the Longitude of Vmbra versa to bee 5. parts , 3'5 . (BLUNDEV-E2-P1,52V.52) and in saying here parts , I meane alwaies such parts as are the 12. parts , whereinto the body yeelding shawdow is diuided : (BLUNDEV-E2-P1,53R.53) but if you worke this example by the first tables of Sines making the totall Sine of though you finde it true in the parts and minutes , yet shall you not finde it so in the seconds and thirds , (BLUNDEV-E2-P1,53R.54) and if you worke the same by the second tables making the total Sine you shal find it to agree only in the parts , but neither-1 in minutes nor secondes , which maketh me to suspect that the Printer hath committed some error therein , (BLUNDEV-E2-P1,53R.55) for both the tables were made by one selfe rule . (BLUNDEV-E2-P1,53R.56) A BRIEFE DESCRIPTION OF THE TABLES OF SINES PRINTED IN QUARTO LIKE VNTO THOSE WHICH CLAUIUS SETTETH DOWNE IN HIS COMMENTARIES VPON THEODOSIUS HIS SPHERIQUES . (BLUNDEV-E2-P1,53R.58) Hauing heere before plainely described vnto you the tables of Sines made by Monte Regio , which are Printed in folio , & how to vse the same , I wil now briefly describe the said tables lately corrected by Clauius , (BLUNDEV-E2-P1,53R.60) and were Printed in quarto at Rome Anno 1586 , the totall Sine of which tables according to the last table of Monte Regio , is , by which Tables are to be wrought all the conclusions hereafter following . (BLUNDEV-E2-P1,53R.61) First then you haue to vnderstand that these table {COM:sic} are contained in 36. Pages , in the front whereof are set downe the degrees of the Quadrant proceeding from 1 to 89. (BLUNDEV-E2-P1,53R.62) but because the whole number of minutes belonging to the saide degree , which is can not be all placed in one selfe Page , but only in the left outermost collum of the left hand Page : and other in the left outermost collum of the right hand Page : therefore the degrees or arches of the Quadrant are faine to be twice repeated in the front of euery two Pages , as you may plainely see by viewing the said tables , (BLUNDEV-E2-P1,53R.63) and euery Page containeth seauen collums , whereof the first on the left hand containeth the minutes belonging to the degrees or arches of the Quadrant , which minutes do proceed downward from 1. to (BLUNDEV-E2-P1,53R.64) and the seauenth collum on the right hand in euery Page containeth the minutes belonging to the complement of euery arch , which minutes doe proceede backward , that is to say from 1. see downe at the lowest end of the last collum of the second Page , (BLUNDEV-E2-P1,53R.65) and so proceeding vpwarde to . which is also set downe at the lowest end of the last collum of the left hand Page , and so proceedeth vpward to which minutes doe helpe to make vp the complement that is answerable to euery arch wherevnto no minutes be annexed , (BLUNDEV-E2-P1,53V.66) for if the arch hath no minutes , then you must adde to the complement thereof minutes , which is one whole degree , to make vp the complement . (BLUNDEV-E2-P1,53V.67) As for example , suppose the Arke to be 46. degrees , without any minutes ioyned thereunto , the complement whereof set downe at the foote of the said arch , is but 43. degrees , wherefore you must adde thereunto which is one degree , (BLUNDEV-E2-P1,53V.68) so shall the complement be 44. degrees , which is the true complement indeede , (BLUNDEV-E2-P1,53V.69) but if you suppose the foresaid Arke to haue 1'3 ioyned thereunto you shall find the complement to be 43. degrees , 4'7. which is answerable to the foresaide Arke 46. degrees , and 1'3. (BLUNDEV-E2-P1,53V.70) for if you take 46. degrees , 1'3. out of degrees , the remainder will be 43. degrees , 4'7. which is the complement , so as you neede not to make any Subtraction out of to find the complement of any arch , that hath any minutes annexed thereunto : (BLUNDEV-E2-P1,53V.71) but when so euer you haue to finde out the right Sine of any complement in these tables , you must then make the complement an arch , seeking for the same in the front and not at the foote of the tables , (BLUNDEV-E2-P1,53V.72) & if the said complement haue any minutes annexed thereunto , you must seeke those minutes in the left outermost collum of euery Page , and not in the outermost right collum belonging to complements , (BLUNDEV-E2-P1,53V.73) for in this case the complement is an arch and not a complement . (BLUNDEV-E2-P1,53V.74) The order of working by these tables in all other things differeth not one iotte from that which we haue obserued in working the two former conclusions by the tables of Monte Regio Printed in folio , as you shall easily perceiue by the examples here following . (BLUNDEV-E2-P1,53V.75) 1 (BLUNDEV-E2-P1,53V.77) HOW TO FIND OUT THE DECLINATION OF THE SUNNE AT ANY TIME HIS PLACE IN THE ZODIAQUE BEING GIUEN , PER TABULAS SINUUM . (BLUNDEV-E2-P1,53V.78) Knowing the place of the Sun for the day , consider how much the said place is distant from the first point of Aries if y=e= place of the Sunne be nigher to Aries then to Libra . (BLUNDEV-E2-P1,53V.80) But if it be nigher to Libra , then take his distance from the first point of Libra , which distance must not exceede degrees , (BLUNDEV-E2-P1,53V.81) and seeke that distaunce amongst the Arkes in the front of the Tables if they be degrees , (BLUNDEV-E2-P1,54R.82) if minutes , you shall finde them in the first collum on the left hand , (BLUNDEV-E2-P1,54R.83) then multiply the Sine of that distance by the Sine of the greatest declination which is 23. degrees , 2'8 . (BLUNDEV-E2-P1,54R.84) and diuide the product therof by the total Sine , (BLUNDEV-E2-P1,54R.85) and the quotient wil shew you the Sine of the declination for that day , the arch wherof , is the very number of the declination it selfe . (BLUNDEV-E2-P1,54R.86) As for example , you would know the declination of the Sunne the eleauenth of Aprill 1591. when as the Sunne was entred 3'3 into Taurus vnto which you must adde according to the rule before giuen degrees , (BLUNDEV-E2-P1,54R.87) for that is his distance from the first point of Aries , (BLUNDEV-E2-P1,54R.88) then seeke out the said degrees , in the front of the last Tables among the Arkes and the 3'3. in the first collum on the left hand right against which you shall find the sine of the saide distance to bee which being multiplyed by 3$$982$$155 which is the Sine of the greatest declination the product thereof will be which if you diuide by the totall Sine which is you shall find the quotient to be which quotient must be sought out in the said Tables , (BLUNDEV-E2-P1,54R.89) and if you find no such number , then take the nearest number thereunto , which is (BLUNDEV-E2-P1,54R.90) and the Arke thereof together with the minutes that stand right against the said quotient in the first collum on the left hand , is the declination of the Sunne for that day wich is 11. degrees , 4'1 . (BLUNDEV-E2-P1,54R.91) 2 (BLUNDEV-E2-P1,54R.93) HOW TO KNOW THE RIGHT ASCENTION OF THE SUNNE , PER TABULAS SINUUM . (BLUNDEV-E2-P1,54R.94) First knowing the Sunnes place , you shall learne the right ascention therof thus . (BLUNDEV-E2-P1,54R.96) First consider how farre his place is from the Equinoctiall point , as is saide before in the last proposition , (BLUNDEV-E2-P1,54R.97) and multiply the Sine of the complement of that distance by the totall Sine , (BLUNDEV-E2-P1,54R.98) then knowing the declination of the Sunne for that day by the last rule , diuide the former product by the Sine of the complement of the said declination , (BLUNDEV-E2-P1,54R.99) and the quotient will shew the Sine of that Arke whereof the complement is the right ascention . (BLUNDEV-E2-P1,54R.100) As for example , the Sunne being in the 3'3. of Taurus and his declination 11. degrees , 4'1. as you found by the last proposition & his distance fro~ the first point of Aries to be in all degrees 3'3. the complement whereof is 59. degrees , 2'7. the Sine of which complement is which being multiplyed by the totall Sine which is the product will be which being diuided by the Sine of the complement of the Sunnes declination which is 78. degrees , 1'9. whose Sine is 9792818. by which Sine if you diuide the former product , the quotient will bee the Arke of which quotient is 61. degrees , and 1'9 . (BLUNDEV-E2-P1,54V.101) and the complement of that is 28. degrees , and 45'1 . which is the right ascention of the place of the Sunne for the foresaid day . (BLUNDEV-E2-P1,54V.102) And here note that if the Arke from Aries to the giuen pointe , doe containe iust degrees , the right ascention thereof is also degrees , (BLUNDEV-E2-P1,54V.103) but if the said Arke bee more then degrees , and lesser then degrees , then subtract the same out of (BLUNDEV-E2-P1,54V.104) and seeke out the right ascention of the remainder as before , whose right ascention if you take out of the remainder shall bee the ascention of the propounded Arke . (BLUNDEV-E2-P1,54V.105) But if the said Arch which is comprehended betwixt Aries and the giuen pointe bee greater then degrees , or 6. signes , and lesser then degrees , or 9. signes , then hauing subtracted degrees from the same arch , calculate the right ascention of the arch from the beginning of Libra , as before , (BLUNDEV-E2-P1,54V.106) and the right ascention thereof being added to degrees , shall be the ascention desired . (BLUNDEV-E2-P1,54V.107) Lastly if the arch comprehended betwixt Aries and the pointe giuen , be greater then degrees , or 9 signes , then subtract that same out of degrees , (BLUNDEV-E2-P1,54V.108) and seeke out the right ascention of that remainder as before , which if you subtract out of degrees , the remainder shall be the right ascention desired . (BLUNDEV-E2-P1,54V.109) 3 (BLUNDEV-E2-P1,54V.111) HOW TO FINDE OUT THE ASCENTIONALL DIFFERENCE , PER TABULAS SINUUM . (BLUNDEV-E2-P1,54V.112) Multiply the Sine of the Latitude giuen by the total Sine , (BLUNDEV-E2-P1,54V.114) and diuide the product by the complement of y=e= said Latitude (BLUNDEV-E2-P1,54V.115) that done , multiply the quotient by the Sine of the sunnes declination , (BLUNDEV-E2-P1,54V.116) and diuide the product by the Sine of the complement of the declination , (BLUNDEV-E2-P1,54V.117) and the quotient thereof will shew the signe of the ascentionall difference : (BLUNDEV-E2-P1,54V.118) and by working according to this rule $you $shall {TEXT:youshal} find that when the Sunne is entred 3'3. into Taurus , at which time his declination is 11. degrees , 4'1. as haue {COM:sic} been said before the ascentionall difference will be 15. degrees , 2'1 . (BLUNDEV-E2-P1,55R.119) And heere note that the ascentionall differences for one quarter of the Circle serueth also for all the rest , so that the Latitude bee not altered , and that the declination of the points in the later quarters be equall to the declination of the points in the first quarter . (BLUNDEV-E2-P1,55R.120) 4 (BLUNDEV-E2-P1,55R.122) HOW TO FINDE OUT THE OBLIQUE ASCENTION OF ANY POINTE OF THE ECLIPTIQUE IN ANY LATITUDE ASSIGNED . (BLUNDEV-E2-P1,55R.123) First finde the right ascention of the giuen pointe by the second proposition , & also the ascentional difference therof by the third proposition : (BLUNDEV-E2-P1,55R.125) the~ consider whether the declination of the said point be Northward or Southward , (BLUNDEV-E2-P1,55R.126) for if it be northward , then subtract the ascentionall difference out of the right ascention , (BLUNDEV-E2-P1,55R.127) and the remainder shall be the oblique ascention desired : (BLUNDEV-E2-P1,55R.128) but if the declination be Southward , then adde the ascentionall difference vnto the right ascention , (BLUNDEV-E2-P1,55R.129) and the summe shall be the oblique ascention . (BLUNDEV-E2-P1,55R.130) In working thus for the Latitude 52. and suppose the Sunne to bee in the 3'3. of Taurus , and hauing found by the former proposition his right ascention to be 23. degrees , 4'1. and the ascentional difference to be 15. degrees , 2'1. you shall find his oblique asention in the foresaid Latitude to be 13. degrees , (BLUNDEV-E2-P1,55R.131) 5 (BLUNDEV-E2-P1,55R.133) HOW TO FINDE OUT THE TIME OF THE SUNNES RISING AND SETTING , AND THEREBY THE LENGTH OF THE ARTIFICIALL DAY . (BLUNDEV-E2-P1,55R.134) First you must know the ascentional difference , and conuert the same into howers & minutes , (BLUNDEV-E2-P1,55R.136) then if the Sunne be in any of the northern signes , adde those howers to 6. howers which is the one halfe of an Equinoctiall day , (BLUNDEV-E2-P1,55R.137) and the summe of such Addition shall be the one halfe of the artificial day , which being subtracted out of 12. howers , the remainder shal be the hower of the Sunnes rising : (BLUNDEV-E2-P1,55R.138) As for example , the Sunne being in the 3'3. of Taurus you found the ascentionall difference to be 15. degrees , and 2'1. which being turned into howers maketh one hower 1'.2". and somewhat more , which being added to 6. maketh 7. howers 1'. 2". and a little more : which is the one half of the artificiall day which being doubled , maketh in all 14. howers 2'. and 4". (BLUNDEV-E2-P1,55V.139) but if the Sunne be in any of the Southerne signes , you must remember to subtract y=e= howers of the ascentionall difference out of 6. howers , (BLUNDEV-E2-P1,55V.140) and the remainder shall be the one halfe of the artificiall day , (BLUNDEV-E2-P1,55V.141) and by subtracting the halfe length of the artificiall day out of of 12. you shall know the hower of the Sunnes rising , (BLUNDEV-E2-P1,55V.142) and hauing the time of his rising , you must needs know the time of his setting . (BLUNDEV-E2-P1,55V.143) 6 (BLUNDEV-E2-P1,55V.145) HOW TO FIND OUT THE MERIDIAN ALTITUDE OF THE SUNNE IN ANY DAY THOUGH HE DOTH NOT SHINE AT ALL , THE ELEUATION OF THE POLE BEING GIUEN . (BLUNDEV-E2-P1,55V.146) Subtract the eleuation of the pole from (BLUNDEV-E2-P1,55V.148) and the remainder shall be the eleuation of the Equinoctiall , (BLUNDEV-E2-P1,55V.149) then if the Sunne be in any of the Northern signes , adde the declination of the Sunne , vnto the altitude of the Equinoctiall , (BLUNDEV-E2-P1,55V.150) or else if he bee in any of the Southern signes , subtract the declination , (BLUNDEV-E2-P1,55V.151) and the summe of the Addition , or remainder of the Subtraction , shall shew the Meridian altitude . (BLUNDEV-E2-P1,55V.152) As for example , the second of May 1591. the sunne being in the degrees , 4'2. of Taurus , and his declination northward 17. degrees , 5'6. 2"1 heere by subtracting 52. degrees , which is our Latitude from you shall find the remainder to be 38. which is the altitude of the Equinoctiall , whereunto if you adde the Sunnes declination for that day which is 17. degrees , 5'6 and 2"1 the summe will bee 55. degrees , 5'6. and 2"1 . (BLUNDEV-E2-P1,55V.153) and that is the Meridian altitude of the Suune for that day . (BLUNDEV-E2-P1,55V.154) Let these few conclusions serue to shew you the vse of the Tables of Sines , (BLUNDEV-E2-P1,55V.155) for it would make a long booke to set downe so many conclusions as are to bee wrought by these Tables , (BLUNDEV-E2-P1,55V.156) and therefore I leaue to trouble you any further therewith , minding now briefly to declare vnto you the vse of the Tables of lines Tangent and Secant by one example or two as followeth . (BLUNDEV-E2-P1,55V.157) But first I thinke it necessarie to shew you what those lines bee , and where to they serue . (BLUNDEV-E2-P1,55V.158) CAP. 11 . (BLUNDEV-E2-P1,144V.161) WHAT IS THE ZODIAQUE ? (BLUNDEV-E2-P1,144V.162) It is a broad , oblique , or slope Circle , hauing a circular line in the midst thereof , called the Ecliptique line , (BLUNDEV-E2-P1,144V.164) and deuideth the Spheare into two equall partes , by crossing the Equinoctiall with oblique Angles in two points , that is in the beginning of Aries , and in the beginning of Libra , so as the one halfe of this broad Circle declineth towardes the North , and the other halfe towardes the South : in which Circle many thinges are to bee considered , (BLUNDEV-E2-P1,144V.165) first the name , (BLUNDEV-E2-P1,144V.166) then what breadth it hath , and why it hath such breadth , and into what parts it is deuided aswell touching the breadth or Latitude , as circuit or Longitude thereof , also into how many parts the firmament is diuided by the spaces described in the Zodiaque , and appointed to the 12. signes . Also how much it declineth from the Equinoctiall towards the South or North , and vpon what poles it turneth about , and why the line in the midst is called the Ecliptique line , (BLUNDEV-E2-P1,144V.167) and many other necessarie points , which I minde here briefely to touch . (BLUNDEV-E2-P1,144V.168) Why is this Circle named the Zodiaque ? (BLUNDEV-E2-P1,144V.169) It is named the Zodiaque either of this Greeke worde zoe , which is as much to say as life , because the Sunne being mooued vnder this Circle , giueth life to the inferiour bodies , or else of this Greeke word Zodion , which is as much to say as a beast , because that 12. Images of stars , otherwise called the 12. signes , named by the name of certaine beasts , are formed in this Circle : (BLUNDEV-E2-P1,144V.170) and therfore the Latines do call this Circle Signifer because it beareth the 12. signes . (BLUNDEV-E2-P1,144V.171) How are these signes called , (BLUNDEV-E2-P1,144V.172) and with what Characters are they marked . (BLUNDEV-E2-P1,144V.173) Their names and Characters this table here following doth shew , and also which be opposite one to another , as Aries to Libra Taurus to Scorpio , and so foorth . (BLUNDEV-E2-P1,144V.174) {COM:zodiac_signs_omitted} The sixe Northerne signes : Aries , Taurus , Gemini , Cancer , Leo , Virgo (BLUNDEV-E2-P1,145R.177) The sixe Southerne signes : Libra , Scorpio , Sagittarius , Capricornus , Aquarius , Pisces Of which signes the first sixe on y=e= left hand are called the Northerne signes , because they are contained in that halfe of the Zodiaque , which declineth towards the North . (BLUNDEV-E2-P1,145R.178) And the other sixe on the right hand being right opposite to the first 6. are called the Southern signes , because they are contained in the other halfe of the Zodiaque , declining towards the South : (BLUNDEV-E2-P1,145R.179) And against euerie sign is set his proper Character . (BLUNDEV-E2-P1,145R.180) What diuision doe Astronomers make of the 12. signes . (BLUNDEV-E2-P1,145R.181) Diuerse , as followeth : (BLUNDEV-E2-P1,145R.182) for some are said to be ascendent , and some descendent . (BLUNDEV-E2-P1,145R.183) Ascendent are those that rise from the South towards our Zenith , tending Northward , which be these , Capricornus , Aquarius , Pisces , Aries , Taurus , and Gemini . (BLUNDEV-E2-P1,145R.184) The descendent are these , Cancer , Leo , Virgo , Libra , Scorpio and Sagitarius . (BLUNDEV-E2-P1,145R.185) Againe some are saide to bee vernall , as Aries , Taurus and Gemini . Some Estiuall as Cancer , Leo , Virgo . Some Autumnall as Libra , Scorpio , and Sagitarius . And some Hiemall or Brumall , as Capricornus , Aquarius , and Pisces , signifying the foure seasons of the yeare , that is to say , the Spring , Sommer , Autumne , and Winter . (BLUNDEV-E2-P1,145R.186) And some doe make diuerse other diuisions , which because they appertaine to Astrologie rather then to the Treatise of a Spheare I willingly omit them . (BLUNDEV-E2-P1,145R.187) Now tell what breadth the Zodiaque hath , and why it is imagined to haue such breadth ? (BLUNDEV-E2-P1,145R.188) It hath according to the ancient writers 12. degrees in the bredth , that is to say , 6 degrees on the one side of the Ecliptique line , & 6. degrees on the other side of the Ecliptique line , (BLUNDEV-E2-P1,145R.189) but according to the moderne writers , it hath 16. degrees in breadth , that is , eight degrees on ech side of the Ecliptique line , which breadth was necessarily imagined , first to the intent that by the measure and degrees thereof it might bee knowne , how much the Planets otherwise called the wandring starres , whose course is to pass continually vnder this broade Circle doe wander at any time on either side of the Ecliptique line , (BLUNDEV-E2-P1,145V.190) for they all wander , but some more , some lesse , the Sunne onely excepted , which neuer swarued from that line , but alwayes goeth right under the same , (BLUNDEV-E2-P1,145V.191) and therefore the saide line is called by some writers the way of the Sunne : (BLUNDEV-E2-P1,145V.192) And secondly it hath such breadth to the intent it maye containe within the same , the 12. signes aforesaid , by meanes of which signes the whole circuit or longitude of the saide Circle is deuided into 12. equall parts , (BLUNDEV-E2-P1,145V.193) and euery such part is deuided into degrees , and euery degree into minutes , and euery minute into seconds , &c. so as the whole Longitude thereof contayneth degrees , according vnto which diuision , all the rest of the Circles both greater and lesser described in the Spheare , are made to containe the like number of degrees , and euerye halfe Circle to containe degrees , and euery quarter of a Circle to containe degrees , (BLUNDEV-E2-P1,145V.194) and by this diuision as well of the breadth as of the length of the Zodiaque , it appeareth that euery one of the 12. Signes hath degrees in length , and 12. degrees , in bredth , (BLUNDEV-E2-P1,145V.195) and thereof the Planets , Starres , and all other Celestiall bodies are said to haue both Longitude and Latitude , the Sunne onely excepted . (BLUNDEV-E2-P1,145V.196) How is such Longitude and Latitude to be vnderstood ? (BLUNDEV-E2-P1,145V.197) The Longitude of any Planet or Starre is to bee counted in the Ecliptique line containing in circuit degrees , reckoning from the first point of Aries , and so to Taurus , Gemini , and Cancer , & so foorth according to the succession of the signe , vntill you come againe vnto the first point of Aries , at which point such Longitude both endeth and beginneth . (BLUNDEV-E2-P1,145V.198) The Latitude is counted from the said Ecliptique line towards any of y=e= poles of the Zodiaque . (BLUNDEV-E2-P1,145V.199) And hereof looke how many degrees any fixed starre or Planet is distant from the Ecliptique line towards any of the said poles , (BLUNDEV-E2-P1,145V.200) so much Latitude it is said to haue either Northerne or Southerne : (BLUNDEV-E2-P1,145V.201) moreouer , by this diuision of the signes the whole firmament is deuided into 12. parts by reason of 6. Circles called the circles of position , imagined to passe through the poles of the Zodiaque , and also through y=e= beginning of euery signe , wherby we know vnder what signe euery star is situated though it be cleane out of the Zodiaque as this figure here plainely sheweth , marked with these letters A. B. C. D. (BLUNDEV-E2-P1,146R.202) {COM:figure_omitted} A. signifieth the North pole of the worlde , B. the North pole of the Zodiaque , C. the South pole of y=e= world , D. the South pole of the Zodiaque . (BLUNDEV-E2-P1,146R.203) HOW MUCH THE ZODIAQUE DECLINETH FROM THE EQUINOCTIALL TOWARDS EITHER OF THE POLES , AND THE GREATEST DECLINATION OF THE SUNNE , WHAT IT IS AT THIS PRESENT , AND WHAT IT HATH BEENE IN TIMES PAST . (BLUNDEV-E2-P1,146R.205) CAP. 12 (BLUNDEV-E2-P1,146R.206) You have to vnderstande that the Zodiaque or rather the Ecliptique line , declineth from the Equinoctiall towards eyther of the poles , 23. degrees 2'8 . (BLUNDEV-E2-P1,146R.208) and that is saide in these dayes to be the greatest declination of the Sunne , which declination is twofold , that is Northerne and Southerne , (BLUNDEV-E2-P1,146R.209) for like as the Sunne entring into the First pointe of Aries , beginneth then to decline from the Equinoctiall Northward , to the quantitie of 23. degrees , and 2'8. so entring into the first point of Libra , he declineth againe from the Equinoctiall as much Southward . (BLUNDEV-E2-P1,146R.210) And note by the way that by reason of this slowe motion , when he is in the Northerne signes , he spendeth 7. dayes , and 3$$5 of a daye more in making his North declination then in making his South declination , because hee is then in his swift motion , (BLUNDEV-E2-P1,146V.211) and the time hath beene that he hath spent aboue ten dayes more in making his North declination , then in making his South declination : (BLUNDEV-E2-P1,146V.212) neither is the greatest declination of the Sunne in all ages of like quantitie . (BLUNDEV-E2-P1,146V.213) For in Ptolemies time it was 23. degrees , 5'1. and euer since whose time it hath alwaies continually decreased vntill this present , so as now the greatest declination is no more but 23 degrees and 2'8. (BLUNDEV-E2-P1,146V.214) And Copernicus maketh the declination of the Sunne in respect of quantitie to bee twofold , that is greatest and least , affirming the greatest to be 23. degrees and 5'2. and the least to be 23. degrees and 2'8. as it is now counted , the difference wherof is 2'4 (BLUNDEV-E2-P1,146V.215) and whilst the Ecliptique departeth from the Equinoctiall , and turneth againe towards the Equinoctiall , there doe run as he saith 3434. yeares . (BLUNDEV-E2-P1,146V.216) HOW TO KNOW THE QUANTITIE OF THE SUNNES DECLINATION BEE IT NORTHWARD OR SOUTHWARD , EUERY DAY THROUGHOUT THE YERE , AS WELL BY A TABLE AS BY HELPE OF THE SPHEARE . (BLUNDEV-E2-P1,146V.218) CAP. 13 (BLUNDEV-E2-P1,146V.219) This is cheifely to bee knowne by Tables calculated of purpose , which Tables most commonly are eyther-2 made to aunswere euerie day of the moneth , or else to the degree of the signe wherein the sunne is euery day , which kind of Table is contained in lesser roome then the other , (BLUNDEV-E2-P1,146V.221) but to worke by such a Table , you must first knowe in what signe and degree the sunne is euery day . (BLUNDEV-E2-P1,146V.222) How is that to be done ? (BLUNDEV-E2-P1,146V.223) It is to bee knowne most truely by the Ephemerides or such like Table calculated of purpose , shewing not onely the degree of the signe , but also the verie minute wherein the Sunne is euerie day , (BLUNDEV-E2-P1,146V.224) and for want of such a Table , you may without consideration of the minutes , know it by such an instrument or figure as this following , which consisteth of diuerse Circles , whereof the outermost contayneth the degrees of the 12. signes , together with the names of the said signes , and the next the daies of ech moneth , together with the names of the said moneths , much like the backside of an Astrolabe , in the center or midst of which instrument or figure is a thred , which if you lay vpon the day of the month which you seek , it will straight direct you to the degree of the signe wherein the Sun is that day , (BLUNDEV-E2-P1,147R.225) as for example , if you would know in what signe and degree the Sun is the 4. of May , then by drawing the thred right vpon the said day ouer and beyond the outermost cicle , you shall finde that it will fall right vpon the 23. degree of Taurus . (BLUNDEV-E2-P1,147R.226) An instrument to know thereby in What signe and degree the Sunne . is euery day throughout the yeare . (BLUNDEV-E2-P1,147R.227) {COM:figure_omitted} Then hauing found the degree of the Sun you must resort therewith to this Table following , made for the declination of the sun . (BLUNDEV-E2-P1,147V.230) A table shewing the declination of the sun euery day throughout the yeare (BLUNDEV-E2-P1,147V.231) THE DESCRIPTION AND VSE OF THE TABLE . (BLUNDEV-E2-P1,148R.234) This Table consisteth of fiue collums , whereof the first on the left hand , and the last on the right hand doe containe the degrees of the 12. signes of the Zodiaque , counting from one to (BLUNDEV-E2-P1,148R.236) And the three middle collums doe containe the degrees minutes , and seconds of declination , ouer the head of which three middle collums are set downe the Characters of these 6. opposite signes , Aries and Libra , Taurus and Scorpio , Gemini and Sagittarius , (BLUNDEV-E2-P1,148R.237) and at the foote of the said middle colums are set downe the characters of the other 6. opposite signes , that is , Virgo and Pisces , Leo and Aquarius , Cancer and Capricornus , for euery 2. opposit signes , as well aboue as beneath , haue like declination the vse of which Table is thus : (BLUNDEV-E2-P1,148R.238) first hauing found out the degree of the Sun by the instrument before described , or rather by some true Ephemerides , you must seeke out the number of y=e= said degree , either-1 in the first or last collum , according as the character of the signe is placed . (BLUNDEV-E2-P1,148R.239) For if the sineg or character be aboue , then you must seek for the said number in the first collum on the left hand , which numbers do discend from 1. to (BLUNDEV-E2-P1,148R.240) but if the signe bee beneath , then you must find it out in the outermost collum on the right hand , the numbers whereof doe ascend from 1. to and the common Angle or square , standing right against the saide number will shew you the degree , minutes and seconds of the declination , (BLUNDEV-E2-P1,148R.241) as for example , hauing found by the former instrument that the 4. day of May the Sunne is in the 23. degree of Taurus , I seeing the Character of Taurus to stand aboue , do seeke my foresaid number of 23. degrees in the first collum on the left hand , (BLUNDEV-E2-P1,148R.242) and in the common angle or square right against that number , and vnder the signe Taurus , I finde the declination of the Sun to be 18. degrees 32.' and 37" . (BLUNDEV-E2-P1,148R.243) But this Table $can $not {TEXT:cannot} serue alwaies : (BLUNDEV-E2-P1,148R.244) yea rather such tables are to bee renewed as our Astronomers say euery yeres . (BLUNDEV-E2-P1,148R.245) Also you may know the dayly declination of the Sun , by helpe of the materiall Spheare or globe : (BLUNDEV-E2-P1,148R.246) thus hauing set the Spheare at your Latitude , bring the degree of the signe wherein the Sunne is that present day vnto the mooueable Meridian , (BLUNDEV-E2-P1,148R.247) and staying it there , marke whether it falleth on the South side or on the North side of the Equinoctiall : (BLUNDEV-E2-P1,148R.248) for if it be in any of the Northern signes , it will fall on the North line of the Equinoctial , (BLUNDEV-E2-P1,148V.250) and if it be in any of the Southern signes , it will fall on the south side of the Equinoctiall , (BLUNDEV-E2-P1,148V.251) and by counting the degrees vppon the Meridian , contained betwixt the degree of the Sun and the Equinoctiall , you shall know what declination the Sun hath that day , (BLUNDEV-E2-P1,148V.252) as for example in the latitude 52. in the yeare , the fift day of May , I find the Sunne by the Ephemerides to be in the 23. degree and 48'. of Taurus , which point I bring to the moouable Meridian , (BLUNDEV-E2-P1,148V.253) and there staying it , I find that point to be distant from the Equinoctial Northward 18. degrees , and certaine minutes , (BLUNDEV-E2-P1,148V.254) and so much of North declination I conclude the Sun to haue that day . (BLUNDEV-E2-P1,148V.255) VPON WHAT POLES THE ZODIAQUE TURNETH ABOUT , (BLUNDEV-E2-P1,148V.257) ALSO OF THE ECLIPTIQUE LINE AND OF THE DIUERS VSES THEREOF . (BLUNDEV-E2-P1,148V.258) CAP. 14 (BLUNDEV-E2-P1,148V.259) The Zodiaque turneth about vpon his owne proper Poles from West to East , wherof the one being placed in the Colure of the Solstices towards the North , is distant from the Pole Arctique 23. degrees , & 28' . (BLUNDEV-E2-P1,148V.261) and the other is placed in the saide Colure towards the South , being of like distance from the pole Antarctique , whereof the Astronomers haue a generall rule , affirming that the distance of the two Poles of the world from the Poles of the Zodiaque , is alwaies equall to the greatest declination of the Sunne , which as hath been said before , is 23. degrees and 28'. as you may plainly see by the Spheare . (BLUNDEV-E2-P1,148V.262) And note that these 2. Poles are otherwise called the Poles of the Ecliptique , (BLUNDEV-E2-P1,148V.263) for in considering the declination of the Sunne or of the Zodiaque from the Equinoctiall , you must haue respect onely to the Ecliptique line , which is in the midst of the Zodiaque , and not to any other parte of the Zodiaque . (BLUNDEV-E2-P1,148V.264) And as the Equinoctiall line sheweth the moouing of the first moouveable , which is from East to West , so the Ecliptique line sheweth the moouing of the second mooueable , which is from West to East , cleane contrary to the first mooueable , the causes whereof haue beene before declared . (BLUNDEV-E2-P1,148V.265) What other vses hath this line more than you haue already declared . (BLUNDEV-E2-P1,148V.266) It hath diuers , (BLUNDEV-E2-P1,149R.268) for in this line or Circle are noted the degrees , wherewith any starre riseth or goeth downe , either rightly or obliquely , (BLUNDEV-E2-P1,149R.269) for all the appearances of the heauens are chiefly referred to this Circle . (BLUNDEV-E2-P1,149R.270) Againe by this circle the chiefest distinctions and parts of times , as yeares and moneths are knowne , and also the foure seasons of the yeare , as Spring , Summer , Autumne , and Winter . (BLUNDEV-E2-P1,149R.271) Moreouer , the obliquitie of this circle vnder which the Sunne continually walketh , is cause that the dayes both naturall and artificiall are vnequall . (BLUNDEV-E2-P1,149R.272) Finally , this circle doth shew the places and times of the Eclipses both Solar and Lunar from whence this line taketh his name , of which Eclipses we mind here briefely to treate . (BLUNDEV-E2-P1,149R.273) OF THE ECLIPSES BOTH SOLAR AND LUNAR , AND OF THE HEAD AND TAILE OF THE DRAGON , WITH CERTAINE FIGURES SHEWING THE SAME . (BLUNDEV-E2-P1,149R.275) CAP. 15 (BLUNDEV-E2-P1,149R.276) WHAT SIGNIFIETH THE ECLIPSE ? (BLUNDEV-E2-P1,149R.277) It is as much to say , as to want light , & to be darkened or hidden from our sight , as when the Sun & Moone are both at one selfe time right vnder the Ecliptique line , the one of these two lights most commonly is Eclipsed and darkned : (BLUNDEV-E2-P1,149R.279) for there bee two Eclipses , the one of the Sunne , and the other of the Moone , (BLUNDEV-E2-P1,149R.280) but sith that neither-2 the Eclipse of the Sun or of the Moone doth chance , but when they meete either-3 in the head or taile of the Dragon , I thinke it good to shew first what is ment by the head and tayle of the Dragon . (BLUNDEV-E2-P1,149R.281) The Dragon then signifieth none other thing but the intersection of 2. circles , that is to say , of the Ecliptique , & of the Circle that carieth the Moone , called her Defferent , cutting one another in 2. pointes , whereof that intersection which is westward when as the Moone goeth towards the North , is called the head , and that which is Eastwards when the Moone goeth towards the South is called the taile , marked with such Characters as you see in the figure following , (BLUNDEV-E2-P1,149R.282) and that parte towards the south is called of some the belly of the Dragon . (BLUNDEV-E2-P1,149R.283) And note that the Defferent of the Moone is at no time distant from the Ecliptique aboue 5. degrees at the most . (BLUNDEV-E2-P1,149R.284) {COM:figure_omitted} This being presupposed , I will speake first of the Eclipse of the Moone , and then of the Sunne , both which may be Eclipsed either totally or in part . (BLUNDEV-E2-P1,149V.286) When is the Moone said to be totally eclipsed ? (BLUNDEV-E2-P1,149V.287) When the Sunne and Moone are opposite one to the other diametrally , and the earth in the verie midst betweene them both , (BLUNDEV-E2-P1,149V.288) for the body of the earth being thicke and not transparent , casting his shadow to that point which is opposite to the place of the Sunne , will not suffer the Moone to receiue any light from the Sun , from whome she alwaies boroweth her light . (BLUNDEV-E2-P1,149V.289) At what time is the Moone said to be diametrally opposite to the Sunne ? (BLUNDEV-E2-P1,149V.290) When a right line drawne from the center of the Sunne to the center of the Moone , passeth through the center of the earth : (BLUNDEV-E2-P1,149V.291) & note that euery time that she is at the ful , she is opposite to the Sun , and yet the earth is not at euery such full diametrally betwixt her and the sun , (BLUNDEV-E2-P1,149V.292) for then she should be eclipsed at euery full , which indeede $can $not {TEXT:cannot} be but when she is either-2 in the head or taile of the Dragon . (BLUNDEV-E2-P1,149V.293) When is the Moone said to be eclipsed in part ? (BLUNDEV-E2-P1,149V.294) When the Sunne , the earth , and the Moone be met in one selfe Diametrall line , but the Moone is declining either on the one side or on the other , as you may plainely see by this figure following (BLUNDEV-E2-P1,149V.295) {COM:figure_omitted} But note that the Eclipses of the Moone may be vniuersal , because the Earth is farre biggger then the Moone , and thereby able to shadow her whole bodie . (BLUNDEV-E2-P1,150R.298) When is the Sunne saide to be eclipsed ? (BLUNDEV-E2-P1,150R.299) When the Moone is betwixt the Sunne and the Earth , which chanceth in a Coniunction , and yet not in euery coniunction , but when it falleth either-2 in the head or taile of the Dragon , which may chance , as I saide before , either totally or in part : (BLUNDEV-E2-P1,150R.300) totallie I say , in respect of those parts of the earth whereon the shadow directly falleth . (BLUNDEV-E2-P1,150R.301) For sith the Moone is farre lesser than the Earth , shee $can $not {TEXT:cannot} shadow all the Earth , (BLUNDEV-E2-P1,150R.302) and therefore the Eclipse of the Sunne $can $not {TEXT:cannot} be vniuersall , but yet to some parts of the Earth totally , and to some partly , and to other some nothing at all , as you may plainly see by this figure following . {COM:figure_omitted} (BLUNDEV-E2-P1,150R.303) Yet all the histories doe affirme that the Eclipse of the Sun was vniuersall at the death of Christ . (BLUNDEV-E2-P1,150R.304) Yea , that was miraculous , (BLUNDEV-E2-P1,150R.305) and also it was then at the full of the Moone which was also as miraculous : (BLUNDEV-E2-P1,150R.306) and therefore Dionisius {COM:"dioni"_in_a_different_font_than_"sius"} a Senator of Athens , beholding that Eclips cryed out , saying these words , Either God this day suffereth (BLUNDEV-E2-P1,150V.307) or else the world must needes perish for euer : (BLUNDEV-E2-P1,150V.308) which Dionisius was the first that conuerted the Frenchmen to the faith of Christ , doing there great miracles , (BLUNDEV-E2-P1,150V.309) in honour of whom was erected the rich Abbey of S. Denise , not farre from Paris , $where $as {TEXT:whereas} the Kings and Princes of France were woont to be buried . (BLUNDEV-E2-P1,150V.310) How is it to be prooued that the Eclipse at Christ his death was at the full of the Moone ? (BLUNDEV-E2-P1,150V.311) As well by ancient historye , as by S. Augustine , who saith that the Iewes were woont to keepe their feast of Passouer at which time Christ suffered alway at the full of the Moone . (BLUNDEV-E2-P1,150V.312) If the Sun and Moone be eclipsed but in part , how are such partes to be accounted ? (BLUNDEV-E2-P1,150V.313) By the parts of the Diameter of the bodies of those two Planets , (BLUNDEV-E2-P1,150V.314) for the Astronomers doe diuide the Diameter as well of the Sunne , as of the Moone into 12 , and some into 24 parts , which they call points , (BLUNDEV-E2-P1,150V.315) and therefore are woont to say , that the Sunne or Moone are darkned or eclipsed 7. points , 8. points , 9. points , &c. (BLUNDEV-E2-P1,150V.316)