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)