CHAP. I.

BEing intended in this Treatise of the playne Scale, to declare the manner of projection of the Sphear, in plano, I have thought fitting first, to shew unto you some terms of Geome­try which are necessary for the unlearned to know (for whose sake chiefly I write this Treatise) before they enter [Page 2] into the definition of the Spheare. First, therfore I in­tend to relate unto you, what a point or prick is, and afterward a Line both right and crooked, and such sorts thereof as are appertinent unto the operations and use of this Scale.

Punctum, or a Point, is the beginning of things, or a prick supposed indivisible, void of length, breadth, and depth; as in the figure following is noted by the Point or Prick A.

Linea, or a Line, is a supposed length, or a thing extending it selfe in length, not having breadth nor thicknesse, as is set forth unto you by the Line B AD.

Parallela, or a Parallell Line, is a Line drawne by the side of another Line, in such sort that they may [Page 3] be equidistant in all places. And of such Parallels two only belong unto this work of the plain Scale, that is to say, the right lined parallell, and the circu­lar Parallell.

Right lined Parallells, are two right lines equidi­stant one from another, which being drawn forth in­finitely, would never touch or meete one another, as you may see in the figure where the line H. I. is Paral­lell unto the line C. E. and the line G. F. is Parallell unto them both.

A circular Parallell is a Circle drawn eyther within or without another Circle upon the same Centre, as you may plainly see by the two Circles B. C. D. E. and X. V. Y. W. These Circles are both drawne upon the Centre A. and therefore are Parallell the one unto the other. There is another kinde of Parallell also, which is called a serpentine Parallell, but because it is not belonging unto the use of this Scale, I will omit it and so proceede unto the rest.

Perpendiculum, or Perpendicular is a Line raysed from, or let fall upon another Line, making equall an­gles on both sides, as you may see declared in the fi­gure, wherin the Line A. C. is perpendicular unto the line B. A. D. making equall angles in the point A.

Diameter Circuli, or the Diameter of a Circle, is a right Line drawne thorow the Centre of any circle, in such sort that it may divide the Circle into two equall parts, as you may see the line B. A. D. is the Diameter of the Circle B. C. D. E. because it passeth thorow the Centre A. and the two ends therof do divide the Cir­cle into two equall parts, in the two extrems B. & D making the semicircle B. C. D. equall unto the semi­circle D. E. B.

Semidiameter circuli, or the Semidiameter of a Cir­cle, [Page 4] is halfe of the Diameter, and is contayned betwixt the Centre, and the one side of the Circle, as the Line A D, in the Semidiameter of the Circle B C D E.

Semi-circulus, or a Semi-circle, is the one halfe of a Circle, drawne upon his Diameter, and is contained upon the Superficies, or Surface of the Diameter, as the Semicircle B C D, which is halfe of the Circle B C D E, and is contayned above the Diameter B A D.

Quadrans circuli, is the fourth part of a Circle, and is contayned betwixt the Semidiameter of the Circle, and a line drawn Perpendicular, unto the Diameter of the same Circle, from the Centre thereof, dividing the Semicircle into two equall parts, of the which parts, the one is the quadrant, or fourth part of the same Cir­cle. As for example, the Diameter of the Circle B C D E, is the line B A D, dividing the Circle into two equall parts: then from the Centre A, raise the Per­pendicular A C, dividing the Semicircle likewise, in­to two equall parts, so as A B C, or A C D, the qua­sired.

CHAP. II.

DRaw first a ground line whereupon you would have a Perpendicular raised, then open your Compasses unto any distance (so it exceed not the end of your line,) placing one foot of the said Compasses, in the point from whence the Perpendicular is to be raised, and with the other foot make a mark in the line on both sides, then removing your Compasses, unto any other distance that is greater, and set one foot therof, in one of the marks, and with the other foot make a mark over the middle point, then with the same di­stance of your compasse, set one foot in the other mark upon the Line, and with the other foot make another arch of a Circle over the middle point, so that it may crosse the first arch, and from the meeting of these two arches, draw a right Line unto the middle point, from which the Perpendicular was to be rai­sed, which Line shall be the Perpendicular desired.

Example, suppose your Base or ground Line wher­upon a Perpendicular is to be raised by the Line F L K, and from L, the Perpendicular is to be raised, set one foot of your Compasses in the point L, and with the other, make the marks G, and M, on both sides of the point L, then opening your Compasses wider, set one foot in the point M, and with the other draw the arch S, over the point L, then with the same di­stance of your Compasses, set one foot in G, and with [Page 6] the other make the arch R. crossing the arch S. in the point T. then from T. draw the Line T. L. which Line is Perpendicular unto the Line F. L. K. from the point L, which is the Perpendicular desired.

CHAP. III.

LEt the line whereupon you would have a Perpendicular let fall, be the Line L F K, and the Point assigned, to be the point T, from whence you would have a Perpendicular let fall upon the Line F L K, first set one foote of your Compasses in T, and open your Com­passes unto any distance, so that it be more than the distance T L, which here wee suppose to bee the di­stance T M, then make in the Line F L K, the marks G, and M, then with your Compasses, take the one halfe of G M, which is in the point L, then from L, draw a Line unto the point T, so the Line T L, shall be the Perpendicular, which was desired to be let fall from the assigned point T, unto the middle of the Line F L K.

[Page 7]

CHAP. IV.

SUppose the Line whereupon you would have a Perpendicular raysed, be the Line F L K, and from the point F, a Perpendicular is to be ray­sed: first open your Compasses unto any distance, which here we put to be the distance F G, & set one foot of your compasses in the point F, and with the other draw the arch D E G, then set one foote of your Compasses in the point G, and with the other draw the arch E, then placing one point of your Compasses in F, with the other draw the arch D B, then place your Compas­ses in D, and with the same distance, draw the arch A, cutting the arch D B, in C, then draw a Line from C, unto the end of the Line F L K, unto the assi­gned point F, so shall the Line G F, be a Perpendicu­lar, raysed from the end of the Line F L K, and from the assigned point F.

CHAP. V.

LEt the Line F L K, bee the Base or ground Line, and from the point I, a Perpendicular is to bee let fall up­on the end of the Line K, first from the assigned point I, draw a Line unto any part of the Base, which shall be the Line IHM, then finde the middle of the Line IM, which is at H, place therefore one foote of your Compasses in the point H, and extend the other unto I, with which distance draw the arch INK, up­on the Centre H, cutting the Base or ground-line in the point K, then draw the Line KI, which Line shall be the Perpendicular desired.

NOW I doubt not but you understand the way to let fall, or to rayse, any manner of Perpendi­cular Line, eyther from, or upon any part of a Line: therefore now I intend to proceede unto the maine point here aymed at, which is, to declare, and make known unto you the several operations performed by the plain Scale, which though it be in use with very few, yet it is most necessary with Sea-men, because all questions in Navigation are thereby easily and plainly wrought. And also all questions in Astronomy (be­longing unto the expert and industrious Sea-men) may both speedily and easily be wrought by the same Scale: in regard whereof I have declared in this little Book, that knowledge (which God hath beene plea­sed [Page 9] to bestow upon me) concerning the necessary use and practice therof; hoping that you will as kindly accept it, as it is freely offered unto your courteous considerations.

CHAP. VI.

THis Scale usually is divided into three parts, the first wherof is a Scale of equall Leagues, divided into De­grees, or Leagues from 1 unto 100. and upwards, at your pleasure, and numbred with 10 20 30 40, and so forth unto the end. All these divisions are equall one unto another, and is in use for to measure the leagues that any ship hath run upon any course, or the leagues that she hath raised or depressed the Pole, or departed the Meridian, as in the worke hereafter shall be more fully declared.

The second part of the Scale, is the single Corde [Page 10] of a Circle, or the Cord of 90, and in dividing into 90, unequall divisions, representing the 90, deg. of the Quadrant: and are numbred with 10, 20, 30, 40, &c. unto 90. This Cord is in use to measure any part, or arch of a Circle not surmounting 90 degrees: The number of these degrees from 1 unto 60, is called the Radius of the Scale, upon which distance, all Circles are to be drawne, whereupon 60 of these degrees are the Semidiameter of any Circle, that is drawn upon that Radius.

The third part of the Scale is divided into 8 parts, representing the 8 points of the Mariners Compasse, contained in one quarter of a Circle, if the Circle bee drawn upon the same Radius, and every one of the aforesaid points, is (for exactnesse sake) subdivided into 8 smaller parts.

I have likewise caused two other lines to be placed upon the back side of the Scale, which I doe call the first and second Lines of Longitudes: the first is divi­ded into 20 unequall parts, or leagues, which 20 Leagues are equall unto the Cord of 90. The use of this first Line of Longitude, is to shew how many Leagues and Miles in any Parallell, doe answere unto one degree of the Equinoctiall.

The second Line of Longitude is divided into 100 proportionable parts, or into 100 unequall Leagues; and every league is subdivided into miles, and halfe miles. The use of this Line is thus, when you have found by the first Line of Longitudes, how many Leagues and Miles doe answere unto a degree of the Equinoctial in any latitude you desire: this second line will shew you how many degrees any number of leagues in that Parallell, will answere unto a degree in the Equinoctiall Circle.

[Page 11] Thus having shewed you the parts of the Scale, and unto what use they doe generally serve, I will pro­ceede to declare the particular use thereof, in the Art of Navigation, as followeth.

CHAP. VII.

THe Course is Southwest and by South, the Leagues sayled are 100, the difference of Latitude is demanded.

In the first Demonstratiou, draw first the Line A B, and upon the Centre A, raise a Perpen­dicular A F. Then opening your Compasses unto the Radius of your Scale, and set one Foot therof in the Center A. and with the other draw the Arch K C B, then in regard your course is Southwest & by South, that is three points from the South, take three of the eight points of the Compasse with your Compasses, and place them from K, unto C, then draw the Line A C D, and place the distance of the Leagues you have sayled (which) are 100. upon the Line A C D, from A, unto D. Then from D, draw the Line D F. Parallell unto A B, cutting the Meridian A K F, in the point F, then take the distance of F A, and apply it unto the Scale of equall Leagues, and you shall find it just 83 Leagues, or 4 Deg. 9, Min. which are the degrees you have altered the Latitude, which degrees and minutes (if the Latitude from whence you de­parted, be South) must bee added unto the Latitude [Page 12] from whence you departed, and you shall have the Latitude that you are in: contrariwise, substract them (if the Latitude from whence you departed, be North) and you have likewise the Latitude that you are in.

CHAP. VIII.

IN the first demon­stration draw the Quadrant A K C B, as is taught in the last Chapter. Then reduce your degrees of Latitude into Leagues, which is done by mul­tiplying of them by 20 the product will be 83 leagues, which leagues being applied unto the Meridian Line A K F, they will end in the point F, Then from F, draw the Line D F, Parallell unto A B, Then open your Compasses unto the di­stance of 100. leagues of your Se [...]lt of equall parts, [Page 13] and set one foote of your Compasses in the point A, and with the other draw the arch G H, cutting the Line FD, in D, so shall the distance D F, bee the di­stance of the Meridian, from the Meridian, from whence you departed, which (being applyed unto the Scale) is 56 leagues. Then in regard you sayled from the North Parallell of 56 deg. and 5 min. untill you had depressed the Pole 4 deg. 5. min. Substract there­fore 4 deg. 9. min. from 56 deg. 5 min. and there re­mayneth 51 deg. 56 min. which is the latitude of the place you are in, and in that Parallell have you depar­ted the first Meridian 56 leagues. Then opening your Compasses unto 51 deg. 56 min. of your Cord, and apply it unto the first Line of Longitudes, and you shall finde that 12 leagues and one mile (in that Pa­rallell) doe alter one degree of Longitude. Then set one foote of your Compasses in the second Line of Longitude, at 12 Leagues, one Mile, and extend the other unto one degree of that Line; then with that distance set one foot of your Compasses in 56 leagues of the aforesaid Line, and the other will extend unto 4 degrees 33 min. which is the distance Meridionall desired.

CHAP. IX.

SAyling from the North Paralell 69 degrees 20 min. untill the Pole be depressed four degrees and 9 min. and the distance Meridionall, or difference of Longitude, six degrees to finde the Rhombe is required. By the first Demonstration, draw the Quadrant A K C B, then turne your four degrees nine minutes into Leagues, it maketh eighty three Leagues; which place upon the line A K F, from A, unto E, then substract the difference of the two La­titudes, from the number of the first Latitude, and it leaves the second Latitude 62 deg. 11 min. Then o­pening the Compasses unto the middle Latitude, which is sixty four degrees, and fifteen minutes of the Cord, applying it unto the first Line of Longitudes, and you shall finde eight Leagues, two miles, and four seconds to answere unto one degree: then set your Compasses in one degree, in your second Line of Longitudes, and extend the other foote unto eight Leagues, and two miles, and four seconds: then with that distance of the Compasses, place the one foot at six degrees of that line, and turne the other up­ward, and it will extend unto fifty six leagues, there­fore open your Compasses to the distance of fifty six Leagues, in the line of equall leagues, and apply them from the point P, upon the line F D, parallell unto A B, from F, unto D, then from the point D, draw the [Page 15] line D A. cutting the Quadrant K C B, in C, so shall K C, be the distance of the Rhombe from the South Westward, which is just thirty three degrees, forty five minutes from the South, which is Southwest and by South, the Rhombe desired.

CHAP. X.

IN the second Demonstration draw the line A E, then from A, raise the Perpendicular A C, then opening the Compasses to the distance of the Radius, placing one foot thereof in the Centre A, and with the other draw the Quadrant B D E, Then reduce your three degrees, thirty minutes into leagues, counting for e­very degree twentie Leagues, and for thirty minutes ten Leagues, so they make seventy Leagues; then open your Compasses unto seventy degrees in the line of equall parts, and place them upon the line A B C, from A, unto C, then from C, draw the line C F, Parallell unto A E. Then in regard your Rhombe was the fourth from the South, take foure of the eight points of the Compasse, and place them upon [Page 16] the Quadrant from B, unto D, then from A, by the point D, draw the line A D F, cutting the line C F, in F. So shall the distance betwixt A, and F, bee the number of leagues (upon the fourth Rhombe) before you can either raise or depresse the Pole three degrees thirty minutes, which is here found to be ninety nine Leagues.

CHAP. XI.

IN the second Demonstration let A, be the first Station, and upon the Centre A, draw the quadrant A B D E, then in regard you found the Island to beare South-west from you, therfore take four of your eight points of Com­passe, and place them upon your Quadrant from E, unto D, then from the Centre A, [Page 17] by the point D, draw the Line A D F, representing the visuall Line passing betwixt your sight and the Island, being in the first Station. Then sayling seventy leagues South, which is from A, your first Station, unto C, the second Station: then observing the Is­land to beare West of you, therefore from the point C, the second Station, draw the Line

C F, parallell unto A E, cutting the Line A D E, in point F, so shall the point F, be the place of the Island desired, and the distance A F, is the distance of the Island from the first Station, which is just ninety nine Leagues off the Line of equall parts. And likewise the distance from C, unto F, is the distance of the Is­land from the second Station, which is here found to be just seventy Leagues: and by this manner of worke you may finde the distance of any Island from you, which you may discerne either by Sea or Land.

CHAP. XII.

IN the second Demonstration, draw the Quadrant A B C D E, as is formerly taught: then in regard you sail South-west, take foure points of the Compasse from your Scale, & place them from B, unto D, then by the point D, draw the line A D F, then place your ninety nine Leagues up­on the Line A D F, from A, unto F, so shall E, be the place of your Ship. Then from F, draw the Line F C, parallell unto A E, cutting the line A B C, in C, so let the distance C A, be Leagues that you have run South, which is 70 Leagues. or 3 deg. 30 min. which being added to the latitude from whence you depar­ted, makes sixty foure degrees and twenty one mi­nutes for the Latitude of the second place: then take the distance C F, and apply it unto the Line of equall parts, and you shall finde it likewise seventy Leagues: then opening your Compasses unto the middle Lati­tude 62 degrees, 36 minutes in the Line of Cordes, and apply it unto the first Line of Longitudes, you shall finde that nine leagues and 0 miles, and 38 se­conds, doe alter a degree of longitude, then placing one foot of your Compasses in the second line of lon­gitudes, [Page 19] at 9 leagues and thirty eight seconds, and ex­tend the other to one, then keeping the distance of the Compasses, set one foot in the seventy leagues of the same line, and the other foot will extend unto 7 degrees 37 min. which being substracted from the longitude from whence you departed, leaves seven­teen degrees, and forty seven minutes for the Longi­tude of the second place.

CHAP. XIII.

IN the third Demonstration, draw the Line A D, and from the point A, raise the perpen­dicular A B, then open your Compasses unto the Radius of your Scale, and place one foot therof in the centre A, & with the other draw the Quadrant B C D, then take three points of the Compasses, and [Page 20] and place them upon the Quadrant from D, unto C, then from the Centre A, by the point C, draw the line ACL, 100 Leagues in length, which is the true course you are to saile. Then in regard you sayled 30 leagues direct, take thirty degrees from your Scale of equall parts, and place them upon the line AEC, extending from A, unto E, then in regard you turned your Course, West, Northwest, from the Centre E, draw the Line EG, parallel unto AD, and againe from the Centre E, draw the Line EH, Perpendicular to EG, and parallell to AB, then with the distance of the Ra­dius, set one foot of your compasses in the Centre E, and with the other draw the quadrant G MH, and in regard you sayled West, Northwest, which is 2 points from the West,

Northward, take from your Scale two points of the Compasse, and place them upon the Quadrant GM, H, from G, unto M, then from the Centre E, unto the point M, draw the line EFM, then take twenty leagues with your Compasses from the Scale of equal parts, and place them upon the line EFM, from E, unto F, then is your Ship in the point F. Lastly, in re­gard [Page 21] you run South sixty Leagues, from F, draw a Line Parallell unto the Meridian AB, which is the line FI, then take from your Scale of equall parts 60 Leagues, and place them from F, unto I, then is your Ship in the point I, then last of all is to be found how far it is to the place whereunto you were bound, the distance of the Rhombe that is betwixt you, the de­grees and minutes you have raised the Pole, the di­stance of departure from the first Meridian, and there­by the difference of Longitude, and that you may so doe, first draw the Line OIK. Perpendicular unto the line IF, in the point I, and with your Compasses o­pened unto the distance of the Radius, set one foot of your Compasses in the Centre I, and with the o­ther draw the Quadrant KNF, then in regard your ship is in the point I, and the place whereunto you are bound in the point L, therefore from I, thorow the point L, draw the Line ILN, cutting the Arch KNF, in the point N, therefore let IL, be the Leagues you have unto the place whereunto you are bound, which is forty one Leagues and a halfe, and the Rhombe the distance KN, which is West, and by North, and three degrees unto the Northward, so likewise is the line AO, the number of Leagues you have run due South, which is 68 Leagues and one Mile, or 3 degrees and 25 minutes, which being taken from 50 degrees, the parallell from which you departed, leaves 46 degrees and 35 minutes for the Parallell you ate in. Last of all, shall the line IO, be the Leagues that you have departed your first Meridian, which are 42 leagues and one mile: then open your Compasses unto 48 degrees 17 minutes and 30 seconds of the line of Cords, which is the middle Latitude, and apply it un­to the first line of Longitudes, you shall finde that [Page 22] 13 Leagues 0, miles, fifty six seconds do answer unto a degree of Longitude in that Parallell, then setting one foot of your Compasses in 13 Leagues, and 56 seconds in your second line of Longitudes, extending the other unto one degree, then with the same di­stance of your Compasses, set one foot in 42 Leagues and one mile of the same line, and the other will shew you 3 degrees and 13 minutes, which is the difference of the Longitude desired.

CHAP. IV.

IN the fourth Demonstration, draw the Quadrant ABC DE, then in regard the first Shippe hath raised the Pole two degrees, which is forty leagues, take forty leagues of your Scale, and apply them unto the Meridian line AG L, from A, unto G, then from the point G, draw the line GF, parallell unto AB, then opening your com­passes unto 80 Leagues set one foot in the Centre A, [Page 23] with the other, make a marke in the line GF, which will bee at F, so shall F, bee the place of the first shippe: the second shippe hath raised the Pole foure degrees, which is eighty Leagues, therefore place eightie Leagues upon the Meridian line AGL, from A, unto L, and from the point L, draw the line LM, parallell unto GHF, then open your Compasses unto the distance of a hundred Leagues, which are the Leagues the second shippe did runne, and set the foot of your Compasses in the Centre A, and with the other make a marke in the line LM, which will be at M, then draw the line MA, which is the course of the second Ship, and the line FA, is the course of the first shippe, then from F, let a Perpendicular fall, being Perpendicular to the line GF, which is the line FK, then opening your Compasses unto the Ra­dius of your Scale, set one foot in the Centre F, and with the other draw the Quadrant HIK, likewise from F, the place of the first ship, draw a line by the point M, the place of the second ship: cutting the quadrāt KHI, in I, so let IK, be the course that is be­twixt them, that is, if you will saile from the first ship unto the second, you must saile North, and by East, and 41 minutes to the Eastward, likewise let FM, be the distance that is betwixt them, which in this Demon­stration is 40 Leagues, two miles, so shall BC, be the course of the first shippe from the West Northward, which here is found to be 30 degrees and one minute frō the West Northward, or Northwest, by West & 3 deg. and 44 min. to the Westward. Lastly, the Arch E D, is in the distance of the course that the second ship made from the North Westward, which is found by this Demonstration to be Northwest, and by North, and three degrees five minutes to the Westward.

CHAP. XV.

IN the fourth Demonstration draw the Quadrant ABCD E, then multiply your two de­grees, you have altered your latitude by twenty, and it ma­keth forty Leagues; which forty Leagues set upon the line AEL, from A, unto G, then from the point G, draw the line GF, parallel unto AB, then open your Compasses unto the distance of 80 Leagues, which are the leagues your first ship did run, and place one foot of your Compasses in the Centre A, and with the other make a marke in the line GF, which will be at the point F, then from the Centre A, unto the point F, draw the line AF, representing the distance of the course of the first ship 80 Leagues: Then from F, let fall a perpendicular FK, and upon the Centre F, upon the Radices of the Scale draw the Arch HIK. Then in regard you must bring the second shippe [Page 25]

North and by East, and 41 minuts East­ward of the first ship, take 11 de­grees, 56 minutes from your Scale of Coards, and place them from K, unto I upon the Qua­drant KIH, Then from F, draw the line IF, and upon the line FI, place the distance that you must bring the se­cond ship from the first (which is 40 leagues and two miles) from F, unto M, So is M, the place of your second ship. Then from M, draw the line ML, parallell unto FG, cut­ting the line AGL, in L, then draw the line MA, cutting the Quadrant BDE, in D, So shall the arch DE, be the course that the second ship must run, to bring her selfe 40 leagues, and two miles North and by East, and 41 minuts East of the first ship. Then to know what you have altered the Latitude, first take the distance LA, and apply it unto the Scale of e­quall parts, and you shall finde it to be 80 leagues, which is just 4 degrees, which you have altered your latitude, or Poles elevation: which 4 degrees added unto the Latitude you departed from it, makes 51 degrees, 56 minutes for the Latitude that your se­cond Ship is in, then take the distance LM, and ap­ply it to the Scale, it gives 60 leagues; then open your Compasses unto the distance of the middle Latitude, [Page 26] which is 39 degrees, 51 minuts of the Coard, and apply it unto the first line of Longitudes, and it gives 12 Leagues, and two miles and a halfe, to alter one degree of Longitude in that Parallell: Then set one foot of your Compasses in 12 Leagues, two miles and an halfe in the second line of Longitudes, extending the other foot unto one degree, and with the same distance upon the same Line, set one foot of the Com­passes in 60 leagues (the leagues that you are from the Meridian) and the other foot will extend unto foure degrees forty minuts, which is the difference of the Longitude.

CHAP. XVI.

LEt the Latitude given be 58 degrees 54 minuts, therefore having drawne the Quadrant ABC, from B, upon the Coard BEC, set the Latitude of the place 58 degrees 54 minuts un­to the point D. Then from the point D, draw the line DF, parallell unto BA, So shall the length of the line DF, be the num­ber of miles which an­swer unto one degree of Longitude in the Pa­rallell of 58 degrees 5 minuts, which being

[Page 27] applyed unto your Scale of equall parts, gives thirty one miles. So likewise the Arke BE, being the Lati­tude of 52 degrees, ending in the point E, give the lines EG. For the miles that answere unto one de­gree of Longitude in the parallell of 52 degrees were found by the Scale to be 36 miles, and 56 seconds, or 56/60 of a mile.

CHAP. I.

A Spheare according to the de­scription of Theodosius, is a cer­tain solid Superficies, in whose middle is a Point, from which all lines drawne unto the Cir­cumference are equall; which Point is called the Centre of the Sphear, by which Centre a right Line being drawn, and extending himselfe on ei­ther [Page 30] side unto that part of the Circumference wher­upon the Sphear is turned, is called Axis Sphaera, or the Axletree of the World.

A Sphear accidentally is divided into two parts, that is to say, in Sphaeram rectam, & Spharam obli­quam.

Sphera recta, or a right Sphear, is onely unto those that dwell under the Equinoctiall, Quibus neuter Po­lorum magis altero elevatur: that is, to whom neither of the Poles of the World are seen, that lie hid in the Horizon.

Sphaera obliqua, or an oblique Sphear, is unto those that inhabit on either side of the Equinoctiall, unto whom one of the Poles is ever seen, and the other hid under the Horizon.

The Circles wherupon the Sphear is composed are divided into two sorts: that is to say, in Circulos ma­jores & minores.

Circuli majores, or the greater Circles, are those that divide the Sphear into two equall parts and they are in number six: viz. the Equinoctiall, the midle of the Zodiacke, or the Ecliptique Line, the two Colures, the Meridian and the Horizon.

Minores vero Circuli, or the lesser Circles, are such as divide the Sphear into two parts, unequally: and they are foure in number; as the Tropick of Cancer, the Tropick of Capricorn: the Circle Artike, and the Circle Antartike.

CHAP. II.

THe Equinoctiall is a Circle that cros­seth the Poles of the World at right angles, and divideth the Sphear into two equall parts, and is called the E­quinoctiall, because when the Sunne commeth unto it, which is twice in the yeer, viz. In principio Arietus & Libra, that is, March and Septem­ber) the dayes and nights are equall throughout the whole World, whereupon it is called, Equator dici & noctis, the equall proportioner of the day and night ar­tificiall: and in the figure is described by the Line CAE.

The Meridian is a great Circle, passing thorow the Poles of the World, and the Poles of the Horizon, or Zenith point over our heads, and is so called, because that in any time of the yeare, or in any place of the World, when the Sunne (by the motion of the Hea­vens) cometh unto that Circle, it is noone or 12 of the Clock. And it is to be understood, that all townes and places that lie East and West one of another, have every one a severall Meridian: but all places that lie North and South one of another, have one and the same Meridian. This Circle is declared in the figure following by the Circle BCDE.

The Horizon is a Circle, dividing the superiour Hemisphere from the inferiour, wherupon it is called Horizon. that is to say, the bonds of sight, or the far­thest distance that the eye can see, and therefore it is also called Circulus Hemispheri. The Horizons are di­vided into two sorts, viz. Rectus & obliquus, a right [Page 32] and an obliqne, or a declining Horizon: whereof those have a right Horizon which have the Equi­noctiall for their Zenith, and the Poles of the World in their Horizon: Because the Horizon (hiding both the Poles of the World) is a Circle supposed to be drawne by the Poles of the World, di­viding the Equinoctiall at right angles, as in the fi­gure following you may plainly see. First, imagining the Circle XVYW, to be the earth, and those that inhabit at the Point V, have the line BD, for their Horizon, cutting the Equinoctiall CAE, at right angles in A, and therefore is called Horizon rectus & Sphaerarecta, a right Horizon, and a right Spheare. Those have an oblique Spheare, or an oblique Horizon to whom one of the Poles are visuall, or elevated a­bove the Horizon, and have the other hid under the Horizon, and in regard such a Horizon doth crosse the Equinoctiall at oblique angles, it is called Horizon obliquns, or a declining Horizon, as for example: Those that inhabit at the point S, have T, for their Zenith, and KAL, for their Horizon, dividing the Equinoctiall CAE, at oblique angles, making the angle contained betwixt the Horizon AK, and the Equinoctiall A C, an angle of thirty eight degrees, and 28 minutes, and the angle contained betwixt the Horizon AL, and the Pole AD, an angle of 51 deg. 32 minutes, which is the elevation of the Pole for those that inhabit at S, those and all other have an oblique Spheare, except they inhabit just under the Equinoctiall Circle, unto whom onely doth a right Sphear belong.

Colurus Solstitiorum, or the Summer Colure is a Circle passing by the Poles of the World, and by the Poles of the Ecliptique, and by the head of Cancer [Page 33] and Capricorn, whereupon the first scruple of Can­cer where the Colure crosseth the Ecliptique Line, is called Punctus Solstitiae aestivalis, or the point of the Summer Solstice: to which place when the Sun com­meth: he can approch no neerer unto our Zenith, but returneth unto the Equator again. Arcus vero Colu­ri, The Arke of the Colure contained betwixt the Summer Solstice and the Equator, is called the grea­test declination of the Sun, which Ptolemie found to be 23 degrees, 31 minutes: but by the observation of Copernicus it was found to vary, for he found the de­clination sometimes to be 23 degrees 52 minutes, and in the processe of time, to be but 23 degrees, 28 mi­nutes. And in these our daies (by the observation of Ticho de Brake, and that late famous Mathematician, Master Edward Right) it is found distant from the Equinoctiall 23 degrees 31 minutes 30 seconds.

The other Colure passeth by the Poles of the World, and by the first point of Aries and Libra, whereupon it is called, Colurus distinguens Equinoxia. These two Colures doe crosse each other at right angles in the Poles of the world, whereupon these Verses were made.

The Zodiack is another of the greater Circles, di­viding the Equinoctiall into two equall parts, by the head of Aries and Libra, the one halfe of it doth de­cline unto the North, the other into the South, the greatest of which declination is 23 degrees, 31 mi­nutes, and 30 seconds. Note also, this Circle is divi­ded into 12 equall parts, which parts are attributed [Page 34]

unto the 12 Signes, Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagitarius, Capricornus, Aquarius, & Pisces. And everyone of these Signes are divided into 30 equall parts, which are called degrees, so the whole Zodiake containeth 160 degrees. Like­wise every degree is divided into 60 equall parts, which parts are called minutes, and are in number 21600 minutes, and as 21600 minutes is the whole circumference of the Heavens, so is 21600 miles the whole circuit of the Earth.

CHAP. III.

THe Sun having ascended unto his highest Solstitiall Point doth describe a Circle, which is the neerest that he can approach unto the North Pole, wherupon it is cal­led, Circulus Solstitii aestivalis, the Circle of the Summer Solstice, or the Tropick of Cancer, and is no­ted in the figure before, by the line H. Y. I.

The Sun also approching unto the first scruple of Capricornus, or the Winter Solstice, describeth ano­ther Circle, which is the utmost bounds that the Sun can depart from the Equinoctiall Line towards the Antartike Pole, whereupon it is called, Circulus Sol­stitii hyemalis, sive Tropicus hyemalis, vel Caepricorni: the Circle of the Winter Solstice, the Winter Tro­pick, or the Tropick of Caepricorn, and is described in the figure by the Line G. X. F.

So much as the Ecliptick declineth from the Equino­ctiall, so much doth the Poles of the Ecliptick decline frō the Poles of the World, wherupon the Pole of the Ecliptick, which is by the North Pole of the World, describeth a certain circle as it passeth about the Pole of the World, being just so farre from the Pole as the Tropick of Cancer, is from the Equator, and it is the third of the lesser Circles, and is called, Circulus Ar­cticus, or the Circle of the North Pole, and is descri­bed in the Diagram, in the second Chapter by the Line P. O.

The fourth and last of the lesser Circles, is descri­bed in like manner, by the other Pole of the Ecliptick, about the South Pole of the World, and therefore [Page 36] called Circulus Antarcticus, the Antartick Circle, or the Circle of the Antartick or South Pole, and is de­monstrated in the former figure, by the line N. M.

CHAP. IV.

THe Sun being in the head of Taurus, his declination is desired: by the se­venth Demonstration, draw the line A. D. then upon the Centre A. raise the Perpendicular A. B. thē opening your Compasses to the Radius of your Scale, and place one foot in the Centre A. and with the other draw the Quadrant B. C. D. then ope­ning your Compasses unto the greatest declination of the Sun, and place it upon the Quadrant from D. un­to K. then from the point K. draw the Line K. H. cut­ting the line A. B. in H. then with the di­stance A. H. draw the small Quadrant G. E. H. and in regard the Sun is in the head of Taurus, which is thir­ty degrees from the beginning of Aries, let A. D. be the Equator,

[Page 37] and D the beginning of Aries, D. C. 30 degrees, or longitude of the Sunne, then from the point C. draw the line C. A. cutting the Quadrant G. E. H. in E. then from E. draw the line E. L. parallell to A. D. cutting the Quadrant B. C. D. in L. so shall the arch L. D. be the declination of the Sun desired, which in this de­monstration is found to be 11 deg. and 31 minutes.

CHAP. V.

FIrst by the seventh Demonstration draw the Quadrant A. B. C. D. as is taught in the former Chapter, then set the greatest declination of the Sun upon the Cord from D. unto K. which is 23 deg. and 31 minutes, then from K. draw the line K. H. parallell unto the Equator D. A. cutting the line B. A. in the point H. So shall H. A. be the signe of the Suns greatest decli­nation, then with the distance A. H. draw the Circle, G. E. H. then from D. upon the Cord D. B. C. set the declination of the Sun, which is 11 degrees, 31 min. from D. unto L. then draw the line L. E. parallell unto A. D. cutting the Quadrant G. E. H. in E. Then from the Centre A. by the point E. draw the line A. E. C. cutting the Quadrant B. C. D. in C. So shall the arke [Page 38] C. D. be the distances of the Sunne from the head of Aries, which is here found to be just 30 deg. which is in the beginning of Taurus.

CHAP. VI.

BY the eight Demonstration, first draw the line B. D. then upon the Center A. draw the Circle B. C. D. E. then from A. raise the perpendi­cular C. A. E. then is your Circle di­vided into foure equall parts: then suppose the elevation of the Pole to be 51 deg. 32 min. which must be placed upon the Circle, from D. unto F. then from the point F. by the Center A. draw the line F. A. G. representing the Pole of the World F. being the North Pole, and G. the South Pole, then substract 51 deg. 32 min. from 90. deg. and the re­mainder is the height of the Equinoctiall, which, is 38 deg. 28 min. which must be placed upon the Circle from the Horizon B. unto the point I: [...] then from I. by the Centre A. draw the line I. A. H. representing the Equinoctiall Circle. Then from I. unto M. set the declination of the Sun, being here supposed 14 deg. 52. min. North, then from the point M. draw the line, or Parallell of declination M. I. N. parallell unto the Equator I. A. H. cutting the Horizon B. D. in T. then from T. raise the perpendicular T. V. cutting the Cir­cle B. C. D. E. in V, so shall the distance C. V. be the true amplitude of the Sunne desired, which here is found to be 24 deg. 21 min. North.

CHAP. VII.

HAving found the amplitude of the Sun by the last Chapter, first observe with a Compasse, or rather with a Semicircle upon what degree and minute the Sun riseth or setteth, be­ginning to reckon from the East or West, & ending at the North or South at 90 degrees: and when you have diligently observed the Magne­ticall rising or setting, by the Semicircle, or by some other like fitting Instrument: and also the true am­plitude found, as is declared in the last Chapter, the difference of these two amplitudes, is the variation of the Compasse: But when the Sunne riseth upon the same Degree of the Compasse, as is found by the Scale, the variation is nothing, but the Needle poin­teth directly unto the Poles of the World, which by Master Mulinux was affirmed to be at the Western­most part of Saint Michaels, one of the Islands of the Azores, from whence hee will have the Longitude reckoned. Secondly when the Sunne is in the Equi­noctiall Circle, where hee hath no amplitude, looke what distance the Compasse maketh the Sun to rise from the East or West of the Compasse, the same di­stance is the Compasses variation, from the North or South. Thirdly, if the Sunne rise more to the South of the Compasse, or setteth more to the North by the compasse, then is shewed by the Scale, the difference betwixt the amplitude given by the Scale, and the [Page 40] amplitude given by the Needle, is the Variation of the compasse from the North Westward. Fourthly, if the Compasse sheweth the Sun to rise more North­ward, of set more Southward, then is shewed by the Scale, the difference is the variation of the Compasse, from the North Eastward. Fiftly, if the Scale shew the amplitude of the Sunne rising Southerly, and the Compasse shew it to be Northerly, adde both the Amplitudes together, and they shew you the varia­tion Westerly.

CHAP. VIII.

ACcording unto the right Demon­stration, first draw the Circle B. C. D. E. then draw the Horizon B. A. D. and then the Equinoctiall I. A. H. as is before taught: and then the Tro­pick of Cancer K. L. 23 degrees and a halfe from the Equinoctiall: then draw the Tropick of Capricorn P. O. of like distance from the Equino­ctiall, and after from K. to O. draw the Ecliptique Line K. A O. And when you have thus laid downe the Spheare, suppose the Sun to be in the tenth degree of Taurus, at which time his declination is desired. And in regard the Sunne is more neere unto the Tropicall point Cancer, then unto Capricorn; first finde how [Page 41] many degrees he is from the Tropick of Cancer, and you shall finde him to be 50 degrees; therefore take with your Compasses 50 degrees from the Coard, and apply it from the Tropicall point Cancer at K. unto V. upon one side, and upon P. on the other side: then draw the Line V. P. cutting the Ecliptick K. O. in the point R. then from R. draw the Line M. R. N. paral­lell unto the Equinoctiall I. A. H. and cutting the Quadrant B. C. in the point M. So shall the Arke M. I. be the declination of the Sun desired, which being applied unto your Scale, gives you 14 degrees and 52 minutes.

CHAP. IX.

FIrst according unto the for­mer Chapter draw the Circle B. C. D. E. then the Horizon B. A. D. and after the Verticall Line C. A. E. then the Pole of the World F. G. and likewise the Equator I. A. H. this being don, place the declination of the Sun 14 degrees, 52 mi­nutes, upon the Circle from I. unto M. and also from H. unto N. then draw the Line M. N. cutting the line [Page 42] C. A. E. in S. then from S. draw the Line S. W. Pa­rallell unto the Horizon B. A. D. cutting the Meridian Circle B. C. D. E. in W. So shall the distance D. W. be the height of the Sun in the verticall Circle, for the time demanded which by this proposition is found to be 19 degrees and 8 minutes.

CHAP. X.

[Page 43] FIrst upon the Center A. draw the Circle B. C. D. E. then draw the Line B. A. D. repre­senting the Horizon, dividing the Circle into two equall parts: then draw the Line C A E, perpendicular to B A D. representing the East & West point of the Compasse, then placing the elevation of the Pole 51 degrees, and 32 minutes, from D unto F, from F, by the Centre A, draw the Line F A G, which let be the Pole or Axel­tree of the World; then from B unto I, and from D unto H, set the complement of the Poles elevation: which shall represent the Equinoctiall, in regard it maketh right angles with the Pole of the World, in the Centre A. Then from C unto V, place the ampli­tude of the Sun, which is 24 degrees, and 21 minutes: then from V. let fall the perpendicular V T, cutting the Horizon B A D, in the point T: then from the point T, draw the Line M T N, parallell unto the E­quinoctiall I A H: and cutting the Circle B C D E, in the point M and N, so let the distance of I and M, or H and N, be the declination of the Sun, which was desired: which being applied unto your Scale, gives you 14 degrees, and 52 minutes.

CHAP. XI.

BY the ninth Demonstration, first upon the centre A, draw the circle BCDE, then draw the Line B. D. for the Horizon, then place your Poles elevati­on which is 30 degrees upon the circle from D, unto R, then from R by the Centre A, draw the Line RAS, representing the Pole of the World, then from B unto F, place the Complement of the Poles elevation, which is 60. degrees, and from the point F, by the Centre A, draw the line FAH, re­presenting the Equinoctiall Line, and then set the de­clination of the Sun from F, unto L, and from L, draw the Line LPO, parallell unto the Equator FAH, cutting the Pole of the world in the point P, then set one foot of your Compasses in the point P, and ex­tend the other either unto L, or unto O, and with the same distance of your Compasses, upon the centre P, draw the circle LNOQ, which is called the houre circle, so shall L, be the point of 12 a clock at noone, N, the place of six a clock afternoone, O the place of 12 a clock at midnight, and Q, the place of six a clock in the morning: Every one of the foure quarters, must [Page 45] be divided into six equall parts, or houres, making the whole circle to containe 24 parts, representing the 24 houres of the day and night, then in regard the houre of the day was 9 of the clock, which is 3 hours forenoone, take three of those 24 houres, and place them upon the circle LNOQ, from the Meridian point L, unto K, the nine a clock point in the mor­ning, and unto M, the point of three a clock after noon, then draw the line MK, cutting the parallell of the Sun LO, in the point I, then from I, draw the line IG, parallell unto the Horizon BAD, which shall cut the Meridian circle BCDE, in the point G, so let the distance of G and B, be the Almicanter of the Sun which was desired, which in this Demon­stration is found to be 48 degrees and 18 minutes.

CHAP. XII.

FIrst, upon the centre A. draw the circle B. C. D. E. then draw the Diameter B. D. re­presenting the Horizon, then from D. unto R. set 30 degrees, the elevation of the Pole, then from R. by the Point A. draw the line R. A. S. representing the Pole of the World, then draw the line F. A. H. crossing the Pole in A. at right Angles, cutting the Meredian Line in F. then from F. set 20 degrees, the declination of the Sun unto L. and then from the point L, draw the Line LPO, representing the parallell of the Sunne, and cutting the Pole of the World in P, then placing one foot of your Compas­ses in P, extend the other unto L, with which distance of your Compasses, draw the houre circle I, NOQ, then from the Horizon at B, place the Suns Almi­canter: (which is 48 degrees, and 18 minutes) upon the Quadrant BGL, from B, unto G, then from the point G, draw the line GI, parallell unto the Hori­zon BAD, cutting the line LO, in I, then from the point I, draw the line KIM, parallell to the Pole of the World QAN, cutting the circle LNO, in M, then let IN, be divided into 6 houres, whereof LM, are three: whereupon I conclude, that it is three houres from noon, that is, at nine a clock in the morning, or three in the afternoone.

CHAP. XIII.

ACcording unto the tenth Dia­gram, draw the Line AF, and upon the centre A, raise the perpendicular AC; then upon the centre A, draw the Quadrant CDF. then suppose the height of your Gnomon, or substance yiel­ding shadow be the Line AB, which is to be divided into 12 equall parts, which Gnomon I have heere made just 12 degrees of the e­quall League of the Scale: then from B to the top of the Gnomon, draw the Line BE, parallell unto AF, then set the Almicanter which is 45 degrees from F unto D, and from the point D, draw the Line DA, cutting the Line BE, in the point G, so shall BG be the length of the right shadow desired, which is heere found to be 14 degrees and 18 minutes, which is but just the length of your Gnomon, and 2/12 and ⅓ of a twelfth over: Note that the right shadow, is the shadow of any Post, Staffe, or Steeple, that standeth at right angles with the Horizon, the one end thereof respecting the Zenith of the place, and the other the Nadir.

CHAP. XIV.

BY the verse or contrary sha­dow, is understood the length of any shadow, that is made by a Staffe or Gnomon stand­ing against any perpendicular wall, in such a manner that it may lie parallell unto the Ho­rizon, the length of the con­trary shadow, doth increase as the Sunne riseth in height: whereas contrariwise

the right shadow doth decrease in length, as the Sun doth increase in height: the way to find the verse shadow is as followeth. First, draw your Quadrant as is taught in the last Chapter wherin let A, B, be the length of the Gnomon, likewise from B, draw the line B E, paral­lell unto A F, as before, then set your Almicanter from C, upon the Quadrant which is given to be 70 degrees, and it will extend from C, unto H, then from the point H, draw the line H A, cutting the line B E, in the point K, so shall K B, be the length of the contrary shadow, which here is found to be 34 degrees and 8 min. or twice so long as your Gnomon, and 10/12 and about ½ part of a twelfth more.

CHAP. XV.

FIrst upon the Centre A­draw the Circle B C D E, then draw the Diame­ter B A D, and from D, unto F, set the elevation of the Pole which is 51 degrees, and 30 minutes whose complement is 38 degrees and 30 minutes, which must be placed from B, unto H, then from H, draw the line H A I, representing the Equinoctiall Line, and from F, draw the line F A G, representing the Pole of the World, then from H, unto P, and from I, unto Q, set the de­clination of the Sun, which is 20 degrees, and by those two points draw the line P Q, for the Parallell of the Suns declination; then upon the Circle from B, unto H, set the Suns Almicanter, 38 degrees, and 30 minutes, then from H, draw the line H R, paral­lell unto the Horizon, cutting the Suns Parallell P O, Q, in O, then draw the line T V A E, Perpendicu­lar unto the line B A D, in the Centre A, and cut­ting the line H V R, in V, then set one foot of your [Page 50] Compasses in the point V, extend the other unto R, and with the same distance draw the Semicircle H,

L R, then draw the Concentrick Circle upon the Radius of the Scale M T N, and where the line P O Q, and the line M O N, doe meet in the point V, raise the Perpendicular O L, cutting the Semicircle H L R, in L, then lay the Scale from the Centre N, to the point L, and draw the Line L K, cutting the Semicir­cle M T N, in K, so shall K T, be the true distance of the Sun, from the East, or West point Southward, or [Page 51] the Suns true Azimuth, which is here found to be 72 degrees, and 10 minutes from the South part of the Meridian.

CHAP. XVI.

FIrst draw the line B A F, for the Pole of the world, then upon the Centre A, draw the Circle B C D E, then from the Centre A, raise the Perpendicular C A E, for the Equator: then place your greatest decli­nation frō C, unto Q, and from E, unto P, then draw the line Q A P, which doth represent the Ecliptick line, then in regard the Sunne is in the 20 degree of Taurus, which is 40 degrees, from the head of Can­cer, which 40 degrees place from Q, unto L, and un­to K, then draw the line K L, cutting the Ecliptick in I, then from the point I, draw the line H I, paral­lell unto C A E, cutting the Pole of the World in O, then set one foot of your Compasses in O, and extend the other unto G, with which distance draw the Se­micircle H D G, then opening your Compasses un­to the Radius of the Scale, and upon the Centre O, likewise draw the Circle H N F G, then draw the [Page 52] line I M, parallell unto A O D, cutting the Semicir­cle H M D G, in M, then lay your Scale from the

Centre O, unto the point M, and draw the Line N M, cutting the Concentrick Circle in N, so shall the distance N F, be the right ascention, which is here found to be 42 degrees, 27 minutes.

CHAP. XVIII

FIrst draw the Line B A K, re­presenting the Horizon, then upon the Centre A, draw the Circle B C D E F, Then from K, unto D, set the elevation of the Pole which is 51 degrees, and 32 minutes: then from the point D, by the Centre A, draw the line D A F, representing the Pole of the world: [Page 54] then from R, unto C, set the complement of the Poles elevation which is 38 degrees, and 26 minutes, then from C, by the Centre A, draw the line C A E, representing the Equinoctiall Line; then from C, un­to G, and likewise from E, unto H, for the declinati­on of the Sun, which is 21 degrees, then from G, un­to H, draw the parallell of the Suns declination, cut­ting the Pole of the World in L, and the Horizon in I, then set one foot of your compasses in the point L, and extend the other unto G, then with that distance of your Compasses draw the Semicircle G M N H, then opening your Compasses unto the radius of your Scale, and upon the same centre draw a Concentrick circle, G X O H, then from I, where the declnation of the Sun doth cut the Horizon, draw the line I N, parallell unto the Pole of the World A M, cutting the circle G M H, in N, then lay your Ruler from the point I, unto the point N, and so draw the line N O, cutting the Concentrick circle G X O H, in O, so shall the distance of O, and X, be the difference of the ascentions, which is here found to be 28 degrees, and 54 minutes.

CHAP. XVIII.

THe right ascention of any point of the Heavens being knowne, the dif­ference of the ascention is either to be added thereunto or else to be sub­stracted from it, according as the Starre is situate in the Northerne or Southerne Signes: As for example, if the Sun be in a­ny of these six Signes, Aries, Taurus, Gemini, Can­cer, Leo, or Virgo, then the difference of the ascenti­ons is to be substracted from the right ascention, and the remainder is the oblique ascention. Suppose there­fore the Sunne to be in the fourth degree of Gemini, where the right ascention is found to be foure houres, and 8 minutes, or 62 degrees, and the difference of ascention where the Pole is elevated 51 degrees, is found to be one houre 53 minutes otherwise 28 de­grees 53 minutes, which being taken from the right ascention, leaves two houres, and 16 minutes, or 33 degrees, and 42 minutes, which is the oblique ascen­tion of the Sun in the fourth degree of Gemini. But if the Sun be upon the South side of the Equinoctiall, either in Libra, Scorpio, Sagitarius, Capricornus, A­quarius, or Pisces, then the difference of the ascenti­ons is to be added unto the right ascention, and the Product will be the oblique ascention. Suppose the fourth degree of Sagitarius, is given, for which signe and degree the oblique ascention of the Sun is desi­red, [Page 56] his right ascention being then found to be 242 degrees, or 16 houres, 8, minutes, the difference of the ascention is one houre, 53 minutes, or 28 degrees, 18 minutes, which being added unto the right ascen­tion, makes 18 houres, and one minute; or in degrees 270 degrees, and 18 minutes: which is the oblique ascention of the Sun, when he is in the fourth degree of Sagitarius. And if you would finde the oblique de­scention, you must adde the difference of the ascenti­ons unto the right ascention, when the Sun is in these six Signes, Aries, Taurus, Gemini, Cancer, Leo, Virgo: and contrariwise, when the Sunne is in the other six Signes, you must substract the difference from the right ascention, and you shal have the oblique descen­tion of the Sun, or any Starre, whose right ascention and difference of ascentions is knowne. But it is to be understood, that this manner of operations doth serve no longer then you are upon the North side of the Equinoctiall. For if the South Pole be elevated, the worke is contrary: for so long as the Sun is in any of the Northerne Signes, the difference of the ascenti­ons is to be added unto the right ascention, to finde the oblique ascention. And contrariwise, substracted to finde the oblique descention. Likewise if the Sun or Starre be in the Southerne Signes, then is the diffe­rence of ascentions, substracted from the right ascen­tion, to finde the oblique ascention, and added, to finde the oblique descention.