the Course A 56 deg 15 min. 9,824897 To the Difference of Latitude in parts 1968 parts 3,293977 This done I look in the Tables against the Latitude that is given me 23 deg 9 min. and the Meridional part answering to it is 1428 To which I add the parts here found 1968 because the Latitude is increased  And there comes forth 3396 I look for that in the Tables and I find answering to it the Latitude of 49 deg 9 min. which is the Latitude of the unknown place B. For the Distance between these Places I subtract the Latitude of A 23 deg 9 min. from the Latitude of B now found 49 deg 9 min. and the Remainder is the Difference of Latitude between them 26 deg 0 min. which converted into miles is 1560 miles then say As Sine comp 56 deg 15 min. A comp arith 0,255260 Is to A B 1560 miles 3,193124 So is Radius  To the Distance run A C 2808 miles 3,448384 I had thoughts to have shewed the Difference between Plano and Mercator in an Example but my Father hath done it in page 170 of his Book If you are desirous to know Great Circle Sailing you may learn it from his Book for he hath treated of it largely and indeed it is the most necessary way of Sailing that is for a man cuts his way much shorter in many runs than the usual way that men go doth If you desire to know in any Latitude the number of miles contained in any number of degrees of Longitude convert your degrees and minutes of Longitude into minutes and say As Radius To Sine comp that Latitude So is the Difference of Longitude in minutes To the Difference of Longitude in miles If you desire to convert miles of Departure in any Parallel into degrees say As Sine comp the Latitude or the Parallels dist from the Pole Is to Radius So is the Departure in miles To the Difference of Longitude in minutes Divide that by 60 and the Quotient with the Remainder is the degrees and minutes contained in that Departure Of the Longitude and Latitude of Places BEfore I come to shew how to keep a Reckoning by Mercator's way I will set down a Catalogue of the Latitude and Longitude of some Places in degrees and minutes the Longitude taken from Floures and Corves Places Names Latitude Longitude D. M. D. M. The Tassel North 53 00 35 10 The Maze North 52 00 34 29 The Willing 51 30 33 53 Isle of Wight 50 24 29 16 Dover 51 05 32 04 Portland 50 24 28 16 The Start 50 07 27 07 The Lizard 50 00 25 20 Silly 50 04 24 00 Vshin 48 30 25 30 Cape Finistre 43 08 20 30 The Rock of Lisbon 38 52 20 47 Cape St. Vincent 37 00 21 29 Gilbraltar 36 01 24 39 Cape Blanco 20 32 13 09 Cape de Verde 14 31 13 10 Serrat Lion 08 00 17 53 South side of St. Ann 06 42 17 32 Cape de Palmose 04 00 24 30 Cape Terras Pantas 04 06 30 30 Cape Formosa 04 04 39 15 River Comrans 03 19 42 32 Nethermost of the Isle Farmandosa 03 26 41 56 Middle of the Isle of Thoma 00 00 40 00 Cape de Lopez 10 00 42 01 Cape Negro South 16 00 4 521 Cape Bonesperanza South 34 25 52 30 North end of Martinass 23 02 17 16 Isle of Picos 23 01 17 16 Isle Terrestinam 37 15 23 31 Y Digon Aluarum 38 54 26 45 Ascension 08 21 20 16 St. Ellna 16 00 28 21 Cape Agulhas 35 00 54 00 Pomte Primere 32 25 63 06 Cape Corentas 24 00 69 50 Mosambique 15 10 75 32 Pemba 04 41 77 02 Cape Derfue 10 20 87 40 Cape Guardafa 12 01 87 41 Cape de Raffas 22 10 97 29 Serrat 21 01 108 35 Goa 15 40 109 22 Cape Cormoram 07 53 112 20 Point Gada 06 02 115 00 Northwest Point of Sumatra 05 30 129 02 The Flat Point 05 51 137 26 Crequeta in Sinda 06 02 137 21 East end of St. Brandon 17 15 102 05 East end of Diego Roderigos 19 24 99 22 Southeast Harbor of Maurice 20 11 92 54 Southeast end of Mastorbos 20 16 90 22 Cape de Roman 25 02 83 24 Isle St. Paulo 38 30 108 40 Isle St. Maria Dogusto 19 02 13 00 Assemaon 20 01 02 42 East end of the Foul Ground 18 21 00 00 Isle de Lobas at Rio de Plato 35 25 343 02 Cape St. Thoma 22 21 358 01 Bay Todas Sanctos 13 15 357 41 Cape St. Augustin 08 41 001 12 Isle Fernando 03 45 005 14 Vizia 03 30 003 01 Venedo St. Paulo 01 52 006 25 The West-Indies Barbadoes North 13 12 327 42 Ditiatha North 16 18 326 32 St. Christophers 17 20 324 52 Tobago 11 16 327 41 East side of Trinidado 11 37 326 41 Mattinino 14 48 325 30 St. Vincent 13 10 326 00 New point of Portorica 19 02 319 22 Altanalla near Hispaniola 17 26 313 52 Cape Tibarune in Hispaniola 18 14 310 22 West end of Margareta 11 11 321 51 Cartagena 10 49 310 41 Island Guanatho 16 51 297 11 West end of Cuba 22 00 298 44 Cape Florida 25 20 302 35 Bermuda Island the body of it 32 20 325 15 Island of Sable 43 40 334 02 Cape Race at New-found-land 46 32 339 32 Cape Sable 43 41 327 21 Cape Cod 41 20 322 01 Cape Hattarass 35 40 314 11 Cape Henry 37 00 344 00 Cape Charles 37 20 313 55 West side of CORVES 40 00 000 00 East side of FLOVRES 37 20 000 00 The Rode of Fial 38 50 002 17 West end of Fial 38 41 002 48 West end of St. George 39 00 003 00 Gratiosa 39 15 003 20 West end of Tercera North 39 00 03 40 East end of Michael North 38 05 06 10 East end of Maria 37 00 06 01 East point of Porto Santo 33 05 15 26 West end of Madera 32 20 13 48 East side of Palma 28 45 12 48 North point of Gomera 28 10 13 20 North side of Ferro 27 40 12 30 Northeast side of Gammest 28 36 14 31 Northeast point of grand Canaria 28 20 15 10 East end of Fortaventure 20 21 17 18 East end of Lausareta 28 53 17 21 East end of Gratiosa 29 00 17 29 East end of St. Antonio 17 21 04 20 East end of St. Vincent 17 12 05 00 East point of St. Lucia 16 54 05 25 East point of Sal 16 54 07 30 East side of Bonavista 16 10 08 00 East side of the Isle of May 15 00 07 30 East side of St. Jago 15 10 07 02 Fogo 14 36 06 00 Bramma Island 14 24 05 38 The Longitudes and Latitudess of these places here inserted are some of them my own Experiences and the rest Accounts of able men Concerning the foregoing Tables HE that is bound to any place the first thing that he ought to consider is the Latitude of each place and the
6 is equal to the Sine of S ♈ when you have measured it convert it into time and set it down I find it to be 1 hour 44 min. The Meridian Altitude of the Sun being given and the Latitude to find the Suns Declination as also all the other things before found Latitude 51 deg Northerly Meridian Altitude 52 deg 30 min. I demand the Suns Declination or any other thing that I found before FOR the doing of this project your Sphere as before was shewed that done I consider the Meridian Altitude of the Sun is given to be 52 deg 30 min. I will take 52 deg 30 min. from the Scale of Chords and fix one foot of my Compasses in the South point of the Horizon at A and extend the other foot upwards upon the Meridian which falls at B then I conclude the Sun is upon the Meridian in the point B Take the Distance between B and the Aequinoctial which is B C and apply it to the Scale of Chords and so much as it is so much is the Declination of the Sun and you see it is Northerly for the Sun is to the Northwards of the Aequinoctial If you have a desire to find any thing else in this Sphere draw the Parallel of the Suns Declination thus found and work with it as before in other Examples also draw the Ecliptick and Tropick Many other things might be done but for Brevities sake I omit them judging this to be as much as we have occasion for in Navigation which is the thing I aim at If I have committed a fault in being too tedious in these things pardon me and remember it was my Beginnings riper years which may bring more ability it is probable will bring forth something more new and admirable Be charitable Terms of Art used in Navigation LAtitude as I have cited before is the Distance between the Aequinoctial and the Zenith what is meant by Longitude and Difference of Latitude I have shewed before also the difference between Longitude and Departure from the Meridian in this Book before Now in every Distance that is sailed upon any Course that makes an Angle from the Meridian either of North or South or the Parallels of East and West that is to say any Distance that is sailed upon a point that is between those Courses we have these things considerable namely The Distance run which must be the longest side the Difference of Latitude and Difference of Longitude or Departure from the Meridian and the Course the Course is the Point of the Compass or Rumb you steer on A Dead Reckoning is when a man cannot observe but is forced to judge of the Course and Distance to find the Difference of Latitude and Departure A Reckoning is an Account of the Difference of Latitude and Departure from the Meridian that is made in the time a Ship hath been out Read Tan. for Tangent Sine com for Sine Complement Tan. com for Tangent Complement comp arith for Complement Arithmetical PROPOSITIONS of SAILING BY THE PLAIN SCALE Difference of Latitude and Course given to find the Distance run and the Departure from the Meridian QUESTION I. Admit I set from the Lizard lying in the Latitude of 50 deg and sail S W b W till I alter my Latitude 1 degree or 60 miles I demand my Distance run and Departure from the Meridian IN this Question we have the Course 5 points from the Meridian towards the West which is 5 times 11 deg 15 min. or 56 deg 15 min. for 5 times 15 min. is 75 min. or 1 deg 15 min. and 5 times 11 deg is 55 deg to which add the 1 deg and 15 min. and the whole is 56 deg 15 min. To protract this Question or any other of this nature I wish you to observe the end of your Book that lies from you to be the North part of your Book then that to the right hand will be the East part that to the left hand the West and that right to you the South part The Reason why I wish you to observe this Method is that so in any Travis you may set every Angle the right way which must be observed then and is good to be always used But besides this Geometrical way of resolving Triangles there is an exacter way by the Tables of Sines Tangents and Logarithms which is done thus A General Rule Note that in all right lined Triangles the Sine of every Angle is proportional to its opposite side or every side is proportional to the Sine of its opposite Angle The greatest side will have the greatest Angle opposite to it the last side will have the least Angle opposite to it As here in this Question A B is the longest side and opposite to it is the right Angle B D A which is the greatest Angle A D is the next and hath A B D to it D B is the least side and hath D A B for its opposite Angle which is the least Angle Now as the Sine of A is to B D so is the Sine of D to A B or the Sine of B to A D and the contrary To find the Distance run As Sine com B 56 deg 15 min. comp arith 0,25526 To B D 60 min.  1,77815 So is Radius or Sine D 90 deg   To A B 108 miles  2,03341 If Radius be not in the first place you must take the Complement arithmetical of the first number as here I have done but if Radius be in the first place take no Complement arithmetical at all The Complement arithmetical of a number is what every single figure wants of 9 take them in their due places as here the Sine in the Tables answering to A 33 deg 45 min. which is the Sine Complement of B 56 deg 15 min. is 9,74473 whereas I have set it down 0,25526 now if you compare them the number that I have taken is what the figures in the other want of 9 as 9 wants 0 and 7 wants 2 and 4 wants 5 and so forward after the Complement arithmetical of the first number is taken take the others as they be in the Tables and add them together casting away Radius always and look for what comes out either in the Sines Tangents or Logarithms according as the order requires into which the proportion runs You see here I took no notice of Radius which is a casting of him away in like manner if the things added up come to above Radius always cast Radius away and set down what is above Radius as here the last came out to be 11 and I cast away the 10 and set down 1. For the Departure from the Meridian As Sine comp B 56 deg 15 min. comp arith 0,25526 Is to B D 60 miles  1,77815 So is Sine B 56 deg 15 mim  9,91984 To A D almost 90 miles  1,95325 But I have been often asked