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Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
book_n	line_n	page_n	read_v	9,933	5	9.6901	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A75737	Speculum nauticum A looking-glasse for sea-men. Wherein they may behold, how by a small instrument, called the plain-scale, all nautical questions, and astronomical propositions, are very easily and demonstratively performed. First set down by John Aspley, student in physick, and practitioner of the mathematicks in London. The sixth edition. Whereunto are added, many new propositions in navigation and astronomy, and also a third book, shewing a new way of dialling. By H.P. and W.L.	Aspley, John.; H. P.; W. L., 17th cent.	1662 (1662)	Wing A4013; ESTC R229501	35,709	72

Speculum Nauticum A Looking-Glasse FOR SEA-MEN Wherein they may behold how by a small Instrument called the PLAIN SCALE all Nautical Questions and Astronomical Propositions are very easily and demonstratively performed First set forth by John Aspley Student in Physick and Practitioner of the Mathematicks in London The Sixth Edition Whereunto are added many new Propositions in Navigation and Astronomy and also a third Book shewing a new way of Dialling By H. P. and W. L. LONDON Printed by W. Leybourn for George Hurlock and are to be sold at his Shop at Magnus Church-Corner in Thames-Street near London-Bridge 1662. TO THE WORSHIPFVLL THE MASTER WARDENS ASSISTANTS OF THE TRINITY HOVSE JOHN ASPLEY IN TESTIMONY OF THE HONOUR HE BEARS TO THE GOVERNOURS PRACTISERS OF THE ART OF NAVIGATION DEDICATES THESE HIS FIRST LABOURS The Printer to the Reader THis little book having been well accepted of among Sea-men being the first fruites of Mr. Aspley's Mathematical Studies hath passed five Impressions without any alteration and so I doubt not might have done still But because since that time there have been severall bookes put out of this nature I have procured this to be revised and severall alterations and additions to be made therein So that here you have both the old and a new booke intermingled all in one with a third part added thereto concerning Dialling by a way not formerly published by any All which I doubt not you will kindly accept of and receive much delight and profit thereby Your G. H. ERRATA PAge 34 line 26 read 360. Page 45. l. 8. r. Distance I M. Page 50. line 13. for 14 c. 〈…〉 which is just the length of the Gnomon Page 50 line 28. for increase read decrease Page 52 line 4. r. H A I. line 18. r. point O. Page 57 line 11 r. point L. Also for some lite●all faults we shall desire your Pardon Speculum Nauticum OR THE SEA-MANS GLASSE The First Book CHAP. I. The Explanation of certain Terms of Geometry BEing intended in this Treatise of the plain Scale to declare the manner of projection of the Sphere in plano I have thought fitting first to shew unto you some tearms of Geometry which are necessary for the unlearned to know for whose sake chiefly I write this Treatise before they enter into the definition of the Sphere First therefore 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 self in length not having breadth nor thickness as is set forth unto you by the Line BAD Parallela or a Parallel Line is a line drawn by the side of another line in such sort that they may 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 Parallel and the circular Parallel Right lined Parallels are two right lines equidistant one from another which being drawn forth infinitely would never touch or meet one another as you may see in the Figure where the line H I is Parallel unto the line CE and the line GF is Parallel unto them both A circular Parallel is a circle drawn either within or without another circle upon the same center as you may plainly see by the two circles BCDE and XVYW These circles are both drawn upon the center A and therefore are parallel the one unto the other There is another kind of Parallel also which is called a Serpentine Parallel but because it is not belonging unto the use of this Scale I will omit it and so proceed unto the rest Perpendiculum or a Perpendicular is a line raised from or let fall upon another line making equal Angles on both sides as you may see declared in the figure where in the line AC is perpendicular unto the line BAD making equal ●ngles in the point A. Diameter circuli or the Diameter of a Circle is a right line drawn thorow the center of any circle in such sort that it may divide the circle into two equal parts as you may see the line BAD is the Diameter of the circle BCDE because it passeth thorow the center A and the two ends thereof do divide the circle into two equal parts in the two extreams B and D making the semicircle BCD equal unto the semicircle DEB Semidiameter circuli or the semidiameter of a circle is half of the Diameter and is contained betwixt the center and the one side of the circle as the line AD is the Semidiameter of the circle BCDE This Semidiameter contains 60 degrees of the line of Chords which we sometimes call the Radius Semicirculus or a Semicircle is the one half of a circle drawn upon his Diameter and is contained upon the Superficies or Surface of the Diameter as the Semicircle BCD which is half of the circle BCDE and is contained above the Diameter BAD Quadrans circuli is the fourth part of a circle and is contained betwixt the Semidiameter of the circle and a line drawn Perpendicular unto the Diameter of the same circle from the Center thereof dividing the Semicircle into two equal 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 BCDE is the line BAD dividing the circle into two equal parts then from the center A raise the Perpendicular AC dividing the Semicircle likewise into two equal parts so is ABC or ACD the Quadrant of the circle BCDE which was desired CHAP. II. The manner how to raise a Perpendicular from the middle of a line given 〈◊〉 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 ●o be raised and with the other foot make a mark in the line on 〈…〉 removing your Compasses unto any other distance that 〈…〉 set one foot thereof in one of the marks and with the 〈◊〉 foot make an Arch over the middle point then with the same distance of your Compasses 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 cross 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 whereupon a Perpendicular is to be raised be the line FLK and from

CA and cutting the Quadrant BE C in N so shall the arch CN be the height of the Pole above the plain and in this example contains 32 deg 37 min. 2. To finde the Deflexion or the distance of the Substile from the Meridian Out of this figure take the distance HS and set it in the line DE from D to K through which point K draw the line AKL cutting the Quad ant BC in L so shall the arch CL be the distance of the Substile from the Meridian and in thls Example will be found to be 21 degrees 42 minutes CHAP. VI. How to draw the houre-Houre-lines upon an upright Plain declining from the Meridian towards the East or West VVE will here take for Example a South erect plain declining Eastward 30 deg Having by the Fifth Chapter of this Book found the Defl●xion of such a plain to be 21 deg 42 min. And the height of ●he ●●ile by the same Chapter to be 32 deg 37 min. we may proceed to draw the Diall in manner following With the radius of your line of Chords on the Center C describe the Circle XNSW and in it draw SN through the Center C for the Meridian or line of 12. Then the deflexion being found to be 21 deg 42 min. set that from N to E and draw the line ●C through the center to G This line representeth the Substilar line of your Diall upon which line the Stile or Co●k must stand Also out from your line of Chords take 32 deg 37 min. the height of the S●ile and set that distance from E to H and draw the line CH for the Stile of your Diall so shall the Triangle ECH be the true pattern for the Cock of your Diall The Substilar line EG being 〈◊〉 ●●aw the line XW through the center C and perpendicular to EG This done take the distance EH which is equall to the Stiles height and set that distance from A to B and from W to D. Likewise take the distance from W to B and set it from B to I. These three points I B and D being found in the circumference of the Circle XNSW lay a ruler from X to I and it will cut the substilar line EC being extended in the point G which is the center upon which the equinoctiall Circle must be described Again a ruler laid from X to B will cut the substilar line in F and a ruler laid from X to D will cut the substilar in O. Now if you set one foot of your Compasses in G and extend the other to X or W you may describe the Equinoctial circle XOW which if you have not erred in your former worke will passe exactly through the point O in the substilar line before found In the next place if you lay a Ruler from F to N it will cut the Equinoctiall circle in P and a ruler laid from C to P will cut the Diall circle in V. These things being performed the next thing is to draw the hour lines which will be easily effected if you 〈◊〉 the former directions First from the point V last found begin to divide your houre circle into 24 equall parts or only one halfe of it into 12 parts which you may do by taking 15 deg out of your line of Chords and set that distance on both sides of V at the marks ⚹ ⚹ ⚹ c. so many times as the plain is capable of hours This done If you lay a ruler on the center C and every of these points **** c. you shall divide the equinoctiall Circle into 12 unequall parts in the points ●●●● c. Now a ruler laid from F to every of these unequall points ●●●● c. will divide the houre circle into 12 other unequall parts marked with 4. 5. 6. 7. 8. 9. 10. 11. 12. 1. on the one side of V and with 2. 3 ●n the other side of V. Lastly a ruler laid from C to the severall points 4. 5. 6. 7. 8. 9. 10. 11. 12. 1. 2. 3. and lines drawn by the side thereof they shall be the true houre lines belonging to such a declining plain of 30 deg in the Latitude of 51 deg 30 min. But if you desire more hours then 12 the equinoctiall may be divided into more unequall parts being continued beyond X and W and if you will quite round the whole Circle but that is needlesse without you would make 4 Dialls in the makeing of one as you may easily do For The hours that are on the West side of the Meridian of a South East diall being drawn through the Center will make a North West diall of the same declination And the hours on the east side of the Meridian of a South West diall being drawn through the center will produce a North East diall of the same declination And Again the reall houre lines of a South East diall being drawn on the other side of the paper and the hours named by their Complements to 12 that is 10 for 2 9 for 3 8 for 4 c. will make a South West diall of the same declination CHAP. VII How to place any upright diall truly ALL upright dialls in what oblique latitude soever have the Meridian perpendicular to the horizon wherefore to set your diall exact hang a line with a plummet at the end thereof and with a nail fixed in the line of 12 towards the top thereof to hang the plummet upon apply the diall to the place where it is to be fixed so that the line and plummet may hang just down upon the line of 12 neither inclining on one side or the other the diall thus fixed if the declination were truly taken and the dial rightly made by the former directions shall at all times the Sun shining upon it give you the true hour of the day CHAP. VIII How to insert the halve and Quarters of hours in all dialls THe halves and quarters of hours are drawn in all plaines by the same rules and the like reason that the hours are inserted Therefore take notice that if you would insert the halfe hours into any diall you must divide your Equinoctiall Circle into 24 equall parts instead of 12 and if you would insert the quarters then you must divide it into 48 parts and then proceed in all respect as you did for the whole hours CHAP. IX How to finde the declinatioon of any upright Wall THe declination of a plain is an arch of the horizon comprehended between the pole of the plains horizontall line and the meridian of the place To finde this declination two observations must be made the Sun shining and both at one instant of time as neer as may be The first is the horizontall distance of the Sun from the pole of the plain The second is the Suns Altitude First to finde the horizontall distance Apply the side of a Quadrant to your plain holding it as neer as may be horizontall that is to say levell Then holding