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ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A26045 Speculum nauticum a looking glasse for sea-men : wherein they may behold a small instrument called the plain scale whereby all questions nautical and propositions astronomical are very easily and demonstratively wrought ... / by Iohn Aspley. Aspley, John. 1647 (1647) Wing A4011; ESTC R27669 26,980 68

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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 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. The manner how to raise a Perpendicular from the midle of a Line given 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 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. To let a Perpendicular fall from any Point assigned unto the middle of a Line 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. CHAP. IV. To rayse a Perpendicular upon the end of a Line 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. To let a Perpendicular fall from any point assigned unto the end of a Line 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 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 The figure of the plaine Scale CHAP. VI Of the description of the Scale 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 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 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 To finde how much any Ship hath raised or depressed the Pole knowing the course she hath made and the leagues she hath sayled 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 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 The distance of Latitude and Leagues sayled being given to finde the distance Meridionall and consequently the difference of Longitude Sayling from the North Parallell of 56. deg. and 5. min. 100 Leagues betwixt South and West untill the Pole be depressed 4 deg. 9 min. the difference of Langitude is demanded dem. prim 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 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 distance of Latitude and distance Meridionall given to finde the Rhombe 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