Selected quad for the lemma: book_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
book_n	account_n	george_n	great_a	42	3	2.1254	3	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A74866	The geometrical sea-man: or, the art of navigation performed by geometry. Shewing how all the three kinds of sayling, viz. by the plain chart, by Mercators chart, by a great circle. may be easily and exactly performed by a plain ruler and a pair of compasses, without arithmeticall calculation. / By Henry Phillippes.	Phillippes, Henry, d. 1677?	1652 (1652)	Thomason E652_10; ESTC R205892	65,784	93

THE GEOMETRICAL SEA-MAN OR THE ART OF NAVIGATION Performed by GEOMETRY SHEWING How all the three kinds of Sayling viz. By the Plain Chart By Mercators Chart By a Great Circle May be easily and exactly performed by a Plain Ruler and a pair of Compasses without Arithmeticall Calculation By HENRY PHILLIPPES LONDON Printed by ROBERT and WILLIAM LEYBOURN for GEORGE HURLOCK and are to be sold at his Shop at Magnus Church-corner 1652. TO The INGENIOUS INDUSTRIOUS and Yonger SEA-MEN AS it is chiefely for your profit that I write so I hope that though I shall be condemned of others yet I shall gain your pardon I confesse my labour may seeme needlesse after so many learned Authots to set forth any thing of this subject And it may be accounted a presumptious folly for any to goe about to teach Sea-men in their Art especially in these times wherein there were never more nor more skilfull Seamen But in answer hereto take notice of these considerations First That many Books of this subject though they are plain and easie for all Sea-men to understand yet they are not so exact and perfect in all things as they ought to be Secondly That though Mr. Wright Mr. Gunter and Mr. Norwood have very fully shewed the errours of the foresaid Books and have very perfectly reformed them yet their Books are not plain and usefull for all men because they require much knowledge in Arithmetick Thirdly Though there be many skilfull Sea-men which are able to make use of these Authors yet there are many others who would willingly attain to a more perfect knowledge in this Art and yet cannot for want of Arithmetick Now for the helpe of such as these especially have I published this Book wherein you shall finde how all that which is to be performed by Arithmetick in the foresaid Authors may be sufficiently exactly perform'd by Geometry with the Ruler and Compasses so that any one that can but read and write a little though he have no skill in Arithmetick may hereby attain a true and perfect knowledge of the Art of Navigation so that he shall be able to keepe as true and certain an account of his Voyage in any part of the World as one that works by the most exact rules of Arithmetick Nay I dare say that one that can neither write nor read yet being of an ingenious capacity and having one to teach him according to this way may attain sufficient skill in this Art Fourthly This may also be usefull to those who can performe these things by Arithmetick and the Doctrine of plain Triangles For by this way they may perform them far more easily and readily and almost as exactly And though such men may know many of these things already yet perhaps they may gain some knowledge hereby Lastly As by this way the knowledge of the Art is most easily and speedily attained so it is more certainly and constantly retained and preserved both in respect of the knowledge and practice thereof First the knowledge hereof is more certainly retained in your memory for this is the reason why all Authors are forced to make use of some Geometricall figures partly to explain their Rules and partly to fixe them in the memory by making them visible to the eye for we more surely remember any thing which we see done then what we only hear Now in this way every thing is made much more visible to the eye and therefore more easie both to learn and remember Secondly the practice of this knowledge will be more surely and constantly preserved for Arithmeticall calculations require many Tables viz. of Sines Tangents Secants Meridian which cannot possibly be kept in memory so that if by any cross accident a Sea-man be deprived of his Books he can make no use of his skill in Arithmetick But if a man knowes how to performe these things by Geometry though all his Books and Writings be lost yet having but a plain Ruler and a pair of Compasses he may quickly recover his loss and fall to his work as before Upon these considerations I have adventured to publish this little Book wherein I have briefely and plainly laid down the whole Art as to the Geometricall part thereof beginning at the first principles and proceeding by degrees to the highest conclusions I have used the more figures to make every thing the plainer And I have provided such figures as serve not only for demonstration of the thing but may serve for Instruments to work upon or you may easily by the directions given make the like To conclude I have studyed to make those things plainest which have at any time most troubled my selfe to understand So that I question not but that any one that is industrious may here of easily and speedily attain such a competent measure by knowledge in this Art that by Gods blessing upon his study and labour therein he may obtain much credit and profit Which is all the desire of Your well meaning Friend Henry Phillippes THE CONTENTS AND order of the whole BOOK IN the two first Chapters is shewed how to perform some Geometricall Principles which are necessary to be known because most of the following work is done thereby The third Chapter shews the making and use of the plain Chart being the common way of sayling The fourth Chapter shews the making and use of the true Sea-Chart being in many respects more perfect then the former The fifth Chapter shews the way of sayling by a great Circle being the most exact and best way of sayling that can be The sixth Chapter shews many usefull observations in all these kinds of sayling The seventh Chapter shews another way of sayling by the arch of a great Circle he last Chapter shews how to keepe a perfect account of any Voyage by a little common Arithmetick viz. Addition and Substraction The names of such Books as are printed and sold by George Hurlock at Magnus Church corner THe Seamans Kalendar The enemie of Idlenesse teaching how to endite Epistles Letters in 4 Books 83. Normans Art of Tens or Decimall Arithmetick 4o. The Art of Navigation by Martin Curtis Safeguard of Saylors or great Rutter by Robert Norman A Table of Gauging all manner of Vessels by John Goodwin 8o. Path way to perfect sayling by Richard Polter 4o. Pitiscus his Doctrine of Triangles with a Canon of naturall Sines Tangents and Secants Norwood's Doctrine of Triangles with Logarithmes Norwood's Epitomie applyed to plain and Mercators sayling Norwoods sea-mans practice The Navigator by Captain Charles Saltonstall 4o. Dary's description and use of a Vniversall Quadrant 8o. Errata Page 16. A is wanting in the figure page 33 line last read A F page 56 line 25. for 28 read 58 page 62 67 69. some words doubled may b● left out page 70 line last read thereby know whether c. page 80. last line of the Table for 22 deg read 33. page 88. in the Table Col. 3. line 3. for 1 80 read

places but it is onely their distance in the rumbe So that if the tvvo places are not both under the Equinoctiall or both in one meridian then there is somewhat a neerer cut betvven the tvvo places then the rumbe points out vvhich sometimes especially neere the Poles is very considerable But this is not all the benefit vvhich comes by this vvay of sayling Secondly it is the most convenient way but many times vvhen your course lies neer the East and West this vvay is farre more convenient For if you should sail full East or West you must altogether depend upon your dead reckoning having no vvay to help your self by the observation of the latitude but novv if you sail by the arch of a great circle betvveen tvvo such places you not onely go the neerer vvay but also may alter your latitude many degrees vvhereby your account may be often rectified * So in the example of the Summer Ilands the distance by the rumbe is 3299 miles The distance by the arch is 3204 miles that is 95 miles lesse as for example suppose you vvere to sail from Spain to Virginia both vvhich lye neer the parallel of 40 degrees and suppose the difference of longitude betvveen tvvo such places in the parallel of 40 to be 70 degrees the distance of these tvvo places measured in the parallel of 40 vvhich is the rumbe that leads betvveen the tvvo places being East and West is 53 degrees 62 100 but their distance in the arch of a great circle is but 52 degrees 08 100 that is 1 degree 54 100 less But this as said is but the least part of the benefit that comes by this vvay of sayling the chiefest is this that in sayling between two such places by the arch of a great circle you wil first in the one half of the way raise the Pole 5 degrees 69 100 and then in the other half depress the Pole as much so that in your whole Voyage you wil alter the latitude 11 degrees 38 ●0 so by the observation of the latitude you may rectifie your dead reckoning very wel which you cannot do sayling in the parallel Thus you see this way of sayling is not only the neerest but the best way Now concerning this way of sayling there hath been but little written by any Few have written of this subject and therefore I shal be the more large in this Captain Saltonstall in his Booke called the Navigator hath said somwhat how to direct a parallel course but for any other course he hath said nothing and what hee sheweth is to be performed by Arithmetick Master Norwood in his Book of Trigonometry hath added as an appendix many Problemes of Sayling by the arch of a great circle whereby those who both can and wil take the pains may by calculation finde out all things necessary in this way of Sayling But those ways of calculation as they are very difficult to the unlearned so they are tedious to those that have the best skil and therefore I hope it will be wel accepted if I here shew you how the same may be performed by Geometry both plainly and speedily and yet with as much exactnesse as need be required The chiefe things to be known And in the pursuance hereof I shal keep as close to Master Norwood as I can both in his Propositions and Examples that thereby you may see how neerly my plain lines wil approach to the exactnesse of his calculations Now if you observe him there are these three things which must be found out in every Example First the distance of the two places in the arch of a great Circle Secondly the angle of position from the one place to the other Thirdly to finde out what longitudes and latitudes the arch of the great circle doth passe through between the two places To finde the distance of two places For the first of these knowing the longitude and latitude of two places to finde their distance in the arch of a great circle which is always the neerest distance I might shew you how to perform this in the first place but I here passe it by for these reasons First because Master Wright Master Blundevile and Captain Saltonstall have all of them demonstrated it in their Books already And secondly because the chief benefit in this way of sailing doth not so much consist in saving of a litle way as in sayling the most convenient way that is so as you may alter your latitude most and so your reckoning may be the more certain For though neer the Poles the difference of the distance of two places in the arch of a great circle and in their rumbe may be considerable yet in most Voyages it is not as in the forenamed Example of two places in the parallel of 40 degrees the difference by calculation is found to be but one degree 54 100 which is scarce considerable in the whole Voyage being 52 degrees Thirdly it wil be somewhat difficult it requires great curiosity in drawing of those lines prescribed by them so exactly that you may come to the knowledge of the distance any thing neer Lastly all that trouble is needlesse For though in calculation this distance must be found out first that so you may find out the rest of the Propositions following yet in this way I am about to shew that which follows no way depends upon the true knowledge of this distance it shal be sufficient therefore for the present to tel you that this way is always somewhat the neerest way For the second of these Propositions which is to know the angle of position from the one place to the other The angle of position is needless in this operation Though this must be found out in calculation before you can proceed any further yet in this work it is more needlesse then the former proposition and therefore may be very well omitted But now for the third Proposition To finde out the longitudes and latitudes by which the great circle doth pass which is the finding out by what Longitudes and Latitudes the great circle must passe between the two places this being the very end aimed at in all the work may be thus attained First draw the following Quadrant A D B and divide it into degrees then consider of what length your Tangent line must be and accordingly set off your Radius from A toward D the larger * You may make your tangent larger either by making your Quadrant larger or by setting your Radius further from the Center Thus in the Quadrant the line D K is a larger tangent line which though it reach but to 45 degrees yet by lengthening of the line you may set on the rest the better but in this Quadrant the Radius is A R and this Radius is always a tangent of 45 degrees Then from the point R draw the line R T parallel to the side of the

of latitude and the degrees of longitude truly you shal not need to use any calculation though you are wel skil'd therin for the thing hereby may be much more exactly known then the course of a ship can be steered For the further explaining of this take another example An example of two places in one parallel which shal be of a parallel course Suppose two places to be scituate in the parallel of 40 degrees of North latitude and their difference of longitude to be 70 degrees the one being in 300 the other in 10 degrees of longitude and it is desired to know what longitudes and latitudes the arch of a great circle being drawn between these two places will passe through To perform this first in the line A B marke out the latitude of the one place which is 40 degrees at E. Then in that same arch count 70 degrees of longitude from E to F and there make a mark for the other place thus the two places being set down upon the blanke map according to their latitudes and longitudes draw a straight line from E to F and this will represent the great circle which is to be drawn between the two places and the intersections which it maketh with the arches of latitude and the lines of longitude will shew the true longitudes and latitudes by which this great circle ought to passe Proofe of the worke by its agreement with calculation Now for the proof hereof though Mr. Norwood in his Book hath not calculated the longitudes and latitudes of the arch of a great circle in such an example as this yet his rules shew how to do it and according to them I have calculated this table so that you might see the exactnesse of this way by its agreement with the table Longitude Latitude Deg.   De. De. m. 100 parts 300 or difference of longit 00 40 00 these minutes are in 00 305 05 41 34 57 310 10 42 53 88 315 15 43 55 92 320 20 44 42 70 325 25 45 15 25 330 30 45 35 58 335 35 45 41 68 335 35 45 41 68 340 40 45 35 58 345 45 45 15 25 350 50 44 42 70 355 55 43 55 92 360 60 42 53 88 005 65 41 34 57 010 70 40 00 00 Note if you draw lines by every degree of longitude in the blanck Map as there is by every degree of latitude you may then finde out the latitude of the great circle for every degree of longitude But this paines wil be needlesse yet the lines may be for some use for if your two places differ more in latitude then they do in longitude then it will be your better way to set down by what longitudes the great circle doth pass at every fourth or fift degree of latitude Now that the longitudes and latitudes of a great circle thus found out will be exact enough for the Seamans use The longitudes latitudes of the arch thus found out wil be exact enough if you be any thing carefull and handsome in drawing of the lines of latitude and longitude true observe what Mr. * See Master Norwood in his Problemes of saling by a great circle Prob. 9. latter end Norwood saith to this purpose his words are these Having spoken before the calculation hereof but notwithstanding all that hath hitherto been said it may seem hard to direct a ship and to keep such a rekoning as may be agreeable to this method of sailing And indeed as it is in a manner impossible so neither is it necessary that a ship should alwayes persevere exactly in the arch of a great circle It may suffice and it is almost the same in effect if a ship be so directed that shee go neer this arch Which how to do he sheweth in the next probleme wherein I shall follow him onely whereas he directs you to finde out the longitudes and latitudes of the arch of the great circle by calculation I have shewed you how to save that labour and yet finde it out sufficiently exactly for your use Having therefore found but the longitudes and latitudes by which the great circle must passe as is before shewed How to use the longitude and latitude being found out you must likewise provide you a blank Sea-chart drawing it either by the lesser or larger Meridian line as is before shewed Then prick down in this chart the latitudes through which the arch of the great circle doth passe at every tenth degree of longitude Then if your chart be of the lesser size you may with your compasses draw an arch of a circle through those pricks and this arch will represent the great circle between the two places But if your chart be of the larger size and so your compasses be not large enough to draw this circle or else you are forced in regard of the length of the voyage to make two or three charts for it then you may prick down the longitudes and latitudes of the great circle for every fift degree of longitude and with your ruler draw little straight lines from one prick to another and yet these lines wil represent the great circle wel enough And thus the great circle being drawn upon the chart you may easily by the former directions in the use of the chart see what point you must steer upon at the beginning of your voyage and afterward altering your course by halfe a point at a time It is not good to steere upon quarter points because they are not so visible in the Compass neither is it good to alter your course too often you may keep as neer to the arch of the great circle as either you need or can expect to do Now because Mr. Norwood hath sufficiently explained this in the example of the Summer-Ilands and the Lizard I shall passe by that example onely setting it down upon the chart and referre you to his directions and shew you the like in a parallel course Suppose you were to sail from the coast of Virginia to the coast of Portugal between two places lying in the parallel of 40 degrees north latitude and the difference of longitude between them is 70 degrees the first place being in * These places are not set down according to their true Longitudes it is only the difference of Long. which I respect 300 degrees of longitude and the second place in 10 degrees of longitude and you would sail by the arch of a great circle between these two places The severall places where you alter your course The course you steere The dist or way sailed The Longitude The Latitude     Deg. P. Deg. m. Deg. m. P. 1 from N to a E N E 4 09 305 0 41 34 57 2 from a to c ½ 7 69 315 0 43 48 80 3 from c to e E b N 7 26 325 0 45 13 22 4 from e to f ½ 4 93 332 0 45 42 70 5 from f to g East 2

09 335 0 45 42 70 6 from g to h East 2 09 338 0 45 42 70 7 from h to i ½ 4 93 345 0 45 13 22 8 from i to k E by S 7 26 355 0 43 48 80 9 from k to l ½ 7 69 005 0 41 34 57 10 from l to P E S E 4 09 010 0 40 0 0 The Summe   52 12     You must not thinke to finde these courses and distances which I have set down in this table How to work upon a larger Chart. can be so exactly found out by the former generall chart which is drawn by che lesser Meridian line but if you draw two or three blank charts by the larger meridian line in two or three sheets of paper you may then finde them out easily and as exactly as need be In these several charts you may set down your dayly courses and distances and then when you please you may prick down the summe of these reckonings upon the generall chart and thereby the better see whereabouts you are in respect of your whole voyage Thus you may easily know the severall parts and the total summe of your voyage at any time Or else you may keep account of such a voyage as this and finde out all your distances and courses upon one blank chart A way to avoid drawing of many Charts drawn in a sheet of paper or less if you please as in the figure following But I would not wish you to scant your self to so small a chart as this is this being so little onely in regard of the littlenesse of the book and so the lines are broken off oftner then otherwise you need to do Now in this following chart being fitted to the latitudes you must sail under first set down your first place N according to the latitude thereof which is 40 degrees then prick down the latitude of the great circle at the first fift degree of longitude which is 41 degrees 34 minutes at a then laying your ruler from N to a pricke out the line N a which will represent the arch of the circle from N to a. Then the latitude of the circle for the next 5 degrees is 42 degrees 53 minutes or 88 100 parts this must be set down at R and then draw the pricked line from a to R so you have the arch of the circle from N to R. Now if you would know what course you must steer by your scale of rumbes you shal finde that from N to a the course is E N E and the distance from N to a measured in the meridian line is 4 degrees 1 10 or 41 tenths of degrees And here now because the rumb line doth run above the arch of the circle at a I leave this course and alter my course halfe a point more towards the east Also in regard of the shortnesse of the chart I am forced to break off the arch of the great circle at a and set down the latitude thereof in the first meridian again at a and set down the latitude thereof in the first meridian again at a drawing a line from a to a then 5 degrees from this meridian that is 10 degrees Take these Latitudes out of the Table page 56. from the first place N I set down the latitude of the great circle which is 42 degrees 53 minutes or 88 parts at b and 5 degr from b that is 15 degrees from N I set down the latitude of the circle which is 43 degrees 55 minutes or 92 at c and prick out the lines a b and b c which represent the great circle then by a scale of rumbes I set off 6 rumbes and a half which is the black line a c which almost meets with the pricked circle at c and the distance from a to c is 7 degrees 7 10 as you may finde by measuring it in the meridian line And note though the rumbe line and the arch of the circle do not here close exactly yet it is no matter for I have drawn it thus to even 5 and 10 degrees that it might agree with what hath been before said Here again because of the shortnes of the chart I am forced to break off the circle the rumbe-line set them in the first meridian at c then 5 deg from the meridian at c that is 20 deg from N I prick down the latitude of the arch which is 44 deg 42 minutes or 70 parts at 20 and five degrees from this 20 I prick down the latitude of the arch in that longitude which is 45 degrees 15 minutes or 25 parts at c then I draw the pricked lines from c to 20 and from 20 to e which represent the arch and I likewise draw the rumble line N by E from c to e which doth very neerly concurre with the arch at e and the distance from c to e is 7 degrees and almost ● 10 or as in the the table 7 degrees 26 100. Here again by reason of the shortnesse of the chart I am forced to break off again and setting the latitude of this point e in the first meridian at e 5 degrees from this I set down the latitude of the arch of the great circle belonging to that longitude which is 45 degrees 35 minutes or 58 parts at 30 this meridian is 30 degrees distant from the first place at N. And then 5 degrees from this which is 35 degrees from the first meridian at N I set down the latitude of the arch which is 45 degrees 41 minutes or 68 parts at g then I draw the pricked lines from e to 30 and from 30 to g this represents the arch now at the point e I alter my course half a point more to the Eastward therefore by the scale of rumbes setting off 7 points and a half from the point e I draw the line e f which is N by E half a point to the East and having sayled upon this point from e to f the latitude wil be 45 degrees 42 minutes or 70 parts and the difference of longitude from e is 7 degrees and the distance from E is 4 degrees 9 10 but the difference of longitude from the first place at N is 32 degrees Lastly because now I am as farre to the Northward as the arch of the great circle will allow me I here at f alter my course halfe a point more and so sail from f to g full East so I have altered my longitude in all 35 degrees and am come just one halfe of the voyage Now to perform the other half you must continue to do as you did before first prick out the great circle and then finde out the rumbes you must sail upon from one point to another which you may alter now and then half a point and so you may lay the Pole in the same order and proportion that before you raised it as you may see by the table before page 61. CHAP. VI. Shewing