to bee ABC from the extreame Angles of this Triangle we will suppose certaine Rayes to bee drawne through the hole D into a darke place wherein shall bee opposed to the hole D a white Table or paper which shall be NM Here will a Ray from the point designing out the Angle at A bee carried through the hole that it will point out in the Table K because all such beames according to the Opticks are right lines Likewise the Angle B will in the Table designe out the Point I also C will fall into the point H Let KH IK HI be ioyned together by right lines there will appeare the Triangle IKH wherein the top of the Triangle A will bee seene in the lowest place K Likewise the Angles of the Basis B and C will appeare in the points of the highest place HI and the right side A C will shew it selfe in the left HK as the left side will be the right in IH wherefore the side of the whole Triangle ABC will shew it selfe in the Table NM although inuersely placed according to the sides and Angles and of a various greatnesse in respect of the distance of the Table from the hole The inuention hath great vse in Astronomy in obseruing Eclipses the beginning and continuance without any hurt at all to the sight No lesse vse may it challenge in Topography in describing of Territories Citties Borrowes Castles and such like in their due symmetry and proportion To practise which the better Reusner would haue a little house built of light Timber with a Muliangle Basis in euery one of whose sides a hole should be made looking inwardly at the vertex or top but outwardly at the Basis through which the species or Image of all such things a◠are visible may haue free passage 2 The manner of translation of a Region into the chart depends from the knowledge of the Longitude and Latitude 3 The parts to bee described whereof the chart consists are either Essentiall or Accidentall The Essentiall are either the Lines as are the Meridians and Parallels or the Places to bee delineated out by Pictures The declination of both which shall be taught in these rules 1 To set downe the Meridians and Parallels in a particular chart To shew the practise hereof wee will take for instance the Region of France an example familiar with our later Topographers and therefore can better warrant the description France is supposed to haue in latitude 10. degrees in longitude 16 This knowne you must proceede in this manner First through the middle of your table from head to foote let there bee drawne a perpendicular line expressing the Meridian of the world which shall bee marked with the letters EF let this line bee diuided into 10. equall parts then draw two Parallell lines whereof the one must crosse the said line about the point E with right Angles and the other Parallell must crosse it againe beneath in the point F with like Angles let the vppermost Parallell bee expressed by AB The neathermost with CD Then with your compasse take one of the 10 parts of the line EF which is one degree and set that downe apart by it selfe diuiding the same into 60 Minutes as the short line GH in the table here inserted will shew on the right hand Now you may learne by some Table or Mappe that the farthest part of France toward the North through which is drawne the Parallell AB is 52. degrees distant from the Equatour And that the South Parallell CD is distant 42 degrees Also certaine Tables in our former booke will informe you that to euery degree of the Parallell 42. delineated by AB doe answer 37 miles and that to euery degree of the Parallell CD answer 45 miles wherefore with your compasse take from the short line GH 37 partes or Minutes and with your compasse kept at the same largenesse let the Parallell AB bee diuided into 16 equall spaces correspondent to that widenesse that is to say on each side of the Meridian 8 parts at which Meridian EF you must begine your measure towards either hand both right and left marking the end of euery such space with a certaine point Moreouer for the South Parallell CD let 45 parts likewise bee taken from the short line GH and let that Parallell bee diuided into 16 spaces correspondent to that widenesse of the compasse eight spaces being set downe on each side of the Meridian EF So that wee must beginne from the Meridian EF and marke the end of euery such space with a point Then from those points wherewith each of those two Parallells AB and CD is marked Let there bee drawne a right line from point to point and those shall serue for Meridians expressing as well the longitude of the whole Region as of euery particular place therein seated In like sort as you haue diuided the Meridian EF into 10 equall parts so againe into the like number of equall parts must bee diuided each of the two vttermost Meridians on the left hand and the right marking with a point the end of euery such space and so from point to point let there bee drawne right lines cutting all the Meridians and those shall serue for Parallells and in the vttermost spaces let there bee written the numbers of Longîtude and Latitude The Longitude is supposed to beginne at the vttermost Meridian at the left hand which in both Parallells is the farthest Meridian Westward Now for as much as the most Westerly Meridian is foureteene degrees distant from the Meridian passing by the Canary Ilands from which as the first Meridian the auncients beganne their accompts you must set downe in the first place on the left hand as well ouer as vnder in the first space 15 in the second 16 in the third 17 and so orderly proceed through all the spaces till you come to 30 For the difference betwixt 14 and 30 is 16 So you haue the whole Longitude of France expressed in your Table which is 16 degrees In the like sort to expresse the Latitude hauing the degrees of Latitude marked out you must beginne at each end of the South Parallell CD and so proceed vpward in the two vttermost Meridians writing downe in the first space at the foot of the Table 43 degrees on the right hand and the left in the second space 44 in the third 45 and so vpwards along to 52 so haue you expressed the whole Latitude of France from North to South for betwixt 42 and 52 are comprehended iust 10 degrees These degrees may againe be diuided at pleasure into lesser parts as minutes according to the largenesse of your chart 2 To set downe Citties Castles Mountaines Riuers and such like speciall places in the chart The platforme of your chart being once drawne out as wee haue formerly taught in the precedent rule you may very easily set downe speciall places by obseruation of the Longitudes or Latitudes of such places either by
as meere points in respect of their Orbs because they sensibly are seene as parts of these Orbs. But the Earth is greater then some of the lower Starres as the Moone Whence we may with good grounds auerre that if a man were placed in the Moone hee might behold the Earth far greater then the Moone being obserued by vs in the Earth Wherefore no man can deny but the Earth in it selfe hath a great vastnesse But if wee consider this greatnesse in respect of the Heauens we shall find this vast greatnesse to shrinke almost into nothing and become as a meere point without sensible magnitude But this is not altogether generall without limitation because the heauenly bodies are distinguished into the higher and greater such as are the Firmament with the foure higher Planets such as are Saturne Iupiter Mars and the Sunne or the lower and lesser such as are Venus Mercurius and the Moone which difference in place and greatnesse admits a great diuersity in this proportion as wee shall shew in these two Theoremes 1. The Earthly Globe compared in quantity with the Firmament and superiour Orbes of the planets hath no sensible magnitude This Proposition is supported not only by the authority of many and graue Authors as Aristotle Ptolomy Pliny Alphragan and others but by diuers strong reasons drawne from experience and obseruation of Astronomers The first argument shall be this which is most popular The Sunne and many other Starres in the Firmament are found out by Astronomicall Instruments to bee manifold greater then the Globe of the Earth yet appeare they in respect of the heauens but as a little point or portion Then must the Earth being in comparison far lesser be deuoyd of all sensible magnitude or proportion Secondly if the Earth had any notable quantity in respect of the Heauen then must the Diameter of the earth haue as great a quantity in respect of the Diameter of the Sky for there is the same proportion of the Diameters which the circumferences haue one to the other as is demonstrated in Geometry Now if the Diameter of the Earth hath any notable magnitude in coÌ„parison of the Diameter of the Skye then the Starres which be ouer our heads be neerer vnto vs by a notable quantity then when they bee either in the East or West For it must needs follow that the Starres placed in the verticall point are neerer by the Semidiameter of the Earth then when they are either in the Easterne or Westerne point as we see in â—his figure here set downe ACDB wherein I make E to be the Center of the Earth AEB the true Horizon and EF the Semidiameter of the earth Now if the Semidiameter FE haue any sensible proportion then must G the verticall point be neerer to F. then either A or B. supposed to bee the East west points because EA or EB are the whole Semidiameter of the Celestiall circle whereof FG is only a part But contrarywise there is no such diuersity perceiued in the magnitude of the Starres but that they appeare still to bee of one and the same greatnesse except by accidentall interposition of vapours and grosse bodies wherefore it must of necessity follow that their distance is all one in all parts of the Skye and by consequence the Semidiameter of the earth hath no sensible diuersity in distance Thirdly hence would arise another reason no lesse forcible then this that if the Semidiameter of the Earth had any comparison or proportion to the Semidiameter of the Skye the Horizon that we haue on the vpper part of the earth should not diuide the Skye into two equall parts for as much as the part which is couched vnder the Horizon would alwayes be greater and the other lesser as in our former Diagramme if EF haue a notable quantity in compaâ—ison of EA then will the line CFD being the Horizon on the top of the earth differ notably from the line AEB being the Diameter of the World and the Horizon to the Center of the Earth and so shall not the Horizon CFD diuide the world into two equall parts but the vpper part shall alwayes be lesser then the lower which crosses ordinary experience for we may see in long winter nights that those Starres which are in the East Horizon in the beginning of the night will be in the West at the end of twelue houres and contrarywise those Stars which did set in the West when those others did rise in the East shall rise agayne when the other shall set Fourthly if the earth had any sensible greatnesse in respect of the Heauens then were it vnpossible for any Sunne Diall to bee regular and obserue due proportion For we see the shaddowes to moue as duely and orderly about the Center of Dials and such instruments as if their Center were the very Center of the world which could neuer happen if these two Centers should differ notably in respect of the Spheare of the Sunne to expresse it the better we will set this Figure which represents the three notable circles in a Diall which are described by the course of the Sunne in three notable places of the Zodiacke to wit the two Tropicks and the Equinoctiall Herein the vttermost arch BLC represents the Tropicke of Capricorne and is described no greater then the quarter of a circle because the Sun placed in the Signe shines vnto vs but six houres The Equinoctiall is set as halfe a circle because the Sun being in it appeares vnto vs 12 houres is here noted out by EIF The Tropicke of Cancer containes 3 quarters of a Circle because when the Sun is in it there are eighteen houres from Sun-rising to Sun-set and that circle is GHK The Center of the Diall is A and the Style which giues the shadow DA whose top being D doth describe those portions of circles with such exactnesse as if the Diall were set in the very Center of the Earth and the distinction of the houres shewes it selfe no otherwise then if the Center of the Diall were the same with the Center of the world To these arguments I may adde that if there should bee a sensible greatnesse of the earth in respect of these superiour Orbes either all or most of these absurdities would arise which follow their opinions who place the Earth out of the CeÌ„ter of the World which we haue before treated of 2 The Terrestriall Globe compared with the inferiour Orbs hath a sensible magnitude Although the whole Earth compared with the Firmament and superiour Orbs of the Planets seeme no otherwise then a point yet from this wee must except the Orbes of the lower Planets Venus Mercury but especially the Moone Who are found by obseruations of diuerse skilfull Astronomers to haue a sensible and notable greatnesse in respect of the earth whereof a manifest argument may bee drawne from the Parallax or variation of the sight wherein our obseruations of the same Starre at diuerse places are
GEOGRAPHIE DELINEATED FORTH IN TWO BOOKES CONTAINING The Sphericall and Topicall parts thereof By NATHANAEL CARPENTER Fellow of Exceter Colledge in Oxford THE SECOND EDITION CORRECTED ECCLESIAST 1. One generation commeth and another goeth but the Earth remayneth for euer OXFORD Printed by Iohn Lichfield for Henry Cripps and are to be sold by Henry Curteyne Anno Domini M. DC XXXV TO THE RIGHT HONOVRABLE WILLIAM EARLE OF PEMBROKE LORD CHAMBERLAINE to the Kings most excellent Maiesty Knight of the most Noble Order of the Garter and Chancellour of the Vniuersity of Oxford Right Honourable THis poore Infant of mine which I now offer to Your Honourable acceptance was consecrated Yours in the first conception If the hasty desire I had to present it makes it as an abortiue brat seeme vnworthy my first wishes and Your fauourable Patronage impute it I beseech You not to Selfe-will but Duty which would rather shew herselfe too officious then negligent What I now dedicate rather to Your Honour then mine owne Ambition I desire no farther to bee accompted Mine then Your generous approbation wishing it no other fate then either to dye with Your Dislike or liue with Your Name and Memory The generall Acclamation of the Learned of this Age acknowledging with all thankefull Duty as well Your Loue to Learning as Zeale to Religion hath long since stampt me Yours This arrogant Desire of mine grounded more on Your Heroicke vertues then my priuate ends promised mee more in Your Honourable Estimation then some others in Your Greatnesse The expression of my selfe in these faculties beside my profession indebted more to Loue then Ability setts my Ambition a pinch higher then my Nature But such is the Magnificent splendour of Your Countenance which may easily lend Your poore Seruant so much light as to lead him out of Darknesse and as the Sunne reflecting on the baser earth at once both view and guild his Imperfections My language and formality I owe not to the Court but Vniuersity whereof I cannot but expect Your Honour to be an impartiall Vmpier being a most vigorous Member of the one and the Head of the other Corporation If these fruites of my Labours purchase so much as Your Honours least Approbabation I shall hold my wishes euen accomplished in their ends and desire only to be thought so worthy in Your Honourable esteeme as to liue and dye Your Honours in all duty and seruice to bee commanded NATHANAEL CARPENTER The Analysis of the first Booke Geography whose obiect is the whole earth is either Sphericall which is two-fold either Primary which considers the Terrestriall Spheare either as it is Naturall wherein are to bee considered two things the Principles whereof it consists to wit Matter and Forme Chapter 1. Proprieties arising out of them which againe are either Reall such as are assigned in respect of the Earth it selfe which are either Elementary as the conformity of all the parts concurring to the constitution of the Spheare Chapter 2. Magneticall which are either Partiall as the Coition Direction Variation Declination Chap. 3. Totall as the Verticity and Reuolution Chap. 4. Heauens wherein we treate of the Site Stability and proportion of the Earth in respect of the Heauens Chap. 5. Imaginary such as are the Circles and Lineaments of the Globe of whose Inuention and Expression Chap. 6. Artificiall in the Artificiall Spheare representing the Naturall vnto vs which is either Common or Magneticall Chap. 7. Secondary which handles such matters in the Spheare as secondarily arise out of the first Such are Measure of the Earth with the diuerse manner of Inuention Chap. 8. Distinction which are either Spaces considered Simply in themselues in which sort they are diuided into Zones Climates and Parallels Chap. 9. In respect of the Inhabitants which suffer manifold Distinction Chap. 10. Distances which are either Simple wherein is considered the Longitude Latitude of places Chap. 11. Comparatiue wherein two places differing either in Longitude or Latitude or both are considered Chap. 12. Topicall Libro 2o. OF THE SPECIALL Contents of each Chapter of the first Booke according to the seuerall Theoremes CHAP. I. Of the Terrestriall Globe the Matter and Forme 1 IN the Terrestriall spheare is more Earth then Water pag. 8 2 The Earth and Water together make one Spheare pag. 10 CHAP. II. Of the Conformity of parts in the constitution of the Terrestriall Spheare 1 The parts of the terrestriall spheare doe naturally conforme and dispose themselues as well to the Production and Generation as to the continuance and preseruation of it pag. 14 2 All Earthly bodyes incline and approach to the center as neere as they can 16 3 Of two heauy Bodies striuing for the same place that alwayes preuaileth which is heauiest 22 4 Hence it comes to passe that the Earth enioyes the lowest place the next the Water and the last the Aire ibid. 5 The Center of the Earth is not an Attractiue but a meere Respectiue point 25. 6 The same point is the center of Magnitude and weight in the Terrestriall spheare 26 7 Euery point or center of a weighty body is moued towards the center of the terrestriall Globe by a right line 27 8 A heauy point mouing toward the center will moue faster in the end then in the beginning 28 9 The motion of a magnitude towards the center is not meerely naturall but mixt with a violent motion 29 10 The lines wherein the centers of two heauy bodyes are moued downewardly being continued will meete in the center of the Earth 31 11 Two heauy bodie of the same figure and matter whether equall or vnequall will in an equall time moue in an equall space 32 12 The Terrestriall Globe is round and sphericall 33 13 The Rugged and vnequall parts of the Earth hinder not the sphericall roundnesse of it 36 14 The Water concurring with the Earth in the Globe is also sphericall 38 CHAP. III. Of the Partiall Magneticall affections in the spheare of the Earth 1 The Terrestriall spheare is of a magneticall Nature and disposition pag. 46 2 The magneticall motion is excited in a small and vnperceiuable difference of time 49 3 The motiue quality is spread spherically through euery part of the magneticall body 49 4 The motiue quality of the magneticall body is strongest of all in the poles in other parts so much the stronger by how much they are situated neere the poles 50 5 Magneticall bodies moue not vncertainly but haue their motions directed and conformed to certaine bounds 52 6 The Magnet communicates his vertue to iron or steele if it be touched with it 55 7 The Magneticall Coition is strongest of all in the poles 56 8 The South part of the Loadstone turnes to the North and the North to the South 57 9 The contrary motion in magnets is the iust Confluxe and Conformity of such bodies to magneticall vnion 59 10 If any part southward of the magneticall body be torne away or diminished so much
magnitude for as the Philosopher hath taught vs continuate and diuisible things cannot bee made out of such things as are meerely discontinuate and indiuisible but because it is the first Mathematicall principle or beginning of termination and figuration This point although it haue euery-where an vse in Geometrie yet no-where more remarkeable then when it becomes the center of a circle which center wee ought not to imagine a meere Geometricall conceit but such as findes ground in the Naturall constitution of the Terrestriall Spheare For seeing all terrene bodies are carried in a right line as by a Radius to one point from euery part of the circumference we may obserue a center as it were designed and pointed out by Nature it selfe in the Globe Some haue here distinguished betwixt a point Physicall and a point Mathematicall as allotting the former Latitude and sensible existence but making the other meerely Indiuisible But if the matter bee rightly vnderstood they are not two points but all one distinguished only by a diuers name of conceit or consideration For wee consider first a point as it is existent in a sensible particular body and so we call it Physicall Secondly wee abstract it from this or that body sensible but alwayes conceit it withall to bee in some body and in this sort wee terme it Mathematicall for the Mathematician abstracts not a Quantity or Quantitatiue signe from all subiects for so being an accident hee should conceiue it abstracted from its owne nature but from this or that sensible body as wood or stone Such a point ought we to imagine the center of the Earth to be not participating of any latitude or magnitude albeit existent in some magnitude I am not ignorant that some Writers haue taken a Physicall point for a small and insensible magnitude in which sense the Globe of the Earth is called the center of all heauenly motions But this sense is very improper and besides in this example is to bee vnderstood a point Opticall as such as carries no sensible or proportionable quantity in regard of the sight Taking then the center of the Earth to bee a point fixt in the middest of the Earthly Spheare as we haue described wee will further describe the nature of it in two Theoremes 1 The center of the Earth is not an Attractiue but a meere Respectiue point An Attractiue point I terme that which hath in it a vertue or power to draw and attract the Terrestriall parts or bodies in such sort as the Loadstone hath a power to draw iron or steele But a Respectiue point is that which the Bodies in their motions doe respect and conforme themselues vnto as the bound or center to which their course is directed Which may bee illustrated by the directiue operations of the Load-stone which wee shall hereafter handle by which the Magneticall Indix or needle pointeth directly Northward not that in the North is fixed any Attractiue vertue or operation whicâ— might cause that effect but because the Magneticall Instrument is directed towards such a point or center That the Center of the earth hath no Attractiue force may bee proued 1 Because it cannot in any probability bee thought that an Imaginary point hauing only a priuatiue Being and subsistence should challenge to it selfe any such operation For all positiue effects proceed out of positiue causes neither can it be imagined that this Attraction should grow out of a meere priuation Secondly should this be granted that the motion of Earthly parts should be from the Attractiue vertue of the Center it would follow necessarily that this motion should not bee Naturall but violent as proceeding from an externall cause which all ancient and moderne Philosophers deny 2 The same point is the center of Magnitude and waight in the Terrestriall Spheare That the same point in the Terrene Globe should make the center both of Magnitude and Waight may seeme very plaine 1 Because we are not to multiply things and Entities in our conceit without any necessary consequence drawne from Nature or Reason enforcing vs thereunto But what reason could euer perswade any man that the Earth had two Centers the one of Waight the other of Magnitude but only a bare Imagination without proofe or demonstration Secondly if this were granted that the Center of magnitude were remoued some distance from the other then consequently would one part of the Earth ouer-poize the other in ponderosity and so the whole Spheare would either be shaken out of its place or dissolue it selfe into its first principles Both of which being by experience contradicted our assertion will stand sure and vndoubted In the meane space we deny not but that some little difference may be admitted in regard of the vnequall parts of the Earth but this must needs be so small and insensible as cannot bee cacullated or cause any alteration 8 The Terrene parts conforming themselues to this center may bee considered two wayes either Absolutely or Comparatiuely Absolutely as euery part is considered in it selfe 9 A terrestriall part considered in it selfe vndergoes the respect either of a Point of Magnitude as a point when any signe or point in it selfe is considered in regard of his conformity to the center A Point albeit existing still in some magnitude as we haue shewed may notwithstanding bee abstracted from this or that body as seruing for the center of any body whose naturall inclination and conformity to the vniuersall center of the Earth we may in the first place handle as the Rule by which the motion and inclination of the whole magnitude ought to bee squared 1 Euery point or center of waighty body is moued toward the center of the Terrestriall Spheare by a right line A Right line is the measure and rule almost of all Naturall actions which albeit it be familiar in almost euery operation yet most of all in the motion of the Earthly bodies tending to the center of the Earth Why Nature in this kind should chiefly affect a Right line sundry reasons may bee alleaged 1 From the End which Nature doth propose it selfe which is to produce the worke which shee intends the readiest and shortest way as Aristotle testifies of her in the 5 of his Metaphisickes Now it is manifest that a Right line drawne betwixt the same points is alwayes shortest as Euclide shewes in his Elements where hee demonstrates that two sides of any triangle being counted together are longer then the third The better to vnderstand the working of Nature wee shall obserue in the motion of a heauy part to the center a double scope or end first that the said part of a terrestriall body should bee moued or separated from the place to which it is by violence transposed Secondly that this body should bee restored home and vnited to the Sphericall substance of the Earth in which it must chiefly seeke its preseruation That these two ends are best and soonest compassed by a right line is most manifest For
first a sepaparation from the place to which it is moued is more quicke expedient by a right line forasmuch as crooked and circular lines turne backe as it were into themselues againe Also the vnion and coniunction of a part with the Spheare of the Earth is most indebted to a right motion because as wee haue declared the way is shorter Secondly it may bee alleaged that Nature is an vniforme and necessary Agent restrained to one only bound or end and therefore can neither strengthen weaken remit or suspend the action but workes alwayes by the same meanes the same effects whence it is that she chuseth a right line being but one betwixt two points whereas crooked lines may bee drawne infinite and the motion directed by crooked lines would proue various and opposite to the prescript of Nature Moreouer should wee imagine that nature at any time wrought by a crooked or circular line it might be demanded from what Agent this obliquity should arise not from Nature it selfe because as wee said shee worketh alwayes to the vtmost of her strength hauing no power to remit or suspend her actioâ—s But a crooked motion ariseth from the remission or slacking of the Agents force and turning it away from the intended end which only findes place in Free and voluntary Agents Neither comes this Deflexion from the medium or Aire because it can haue no such power to resist Thirdly if the motion were not performed in a right line it could haue no opposite or contrary because as Aristotle teacheth To a circular or crooked motion no other motion can bee opposite or contrary in respect of the whole circle but only in regard of the Diameter which is alwayes a right line By this it is plaine that a waighty point considered in it selfe abstractly cannot but be carried to the center in a right line which right line really and Physically points out vnto vs a Radius or Beame drawne from the center to the circumference to shew that the God of Nature in composing the earthly globe both obserued and taught vs the vse of Geometrie 2 A point mouing toward the Center will moue swifter in the end then in the beginning This hath been plainely obserued by experience that a stone let fall from a towre or high place will in motion grow swifter and swifter till it approach the ground or place whereon it falls The reason may bee giuen from the Aire which resist so much the lesse by how much the body descendeth lower toward the Earth or center because when it is higher the distance being greater the parts of the Aire will make more Resistance The reason rendred by Aristotle of this Resistance is because in the beginning of the motion the stone or heauy body findes the Aire quiet and fixed but being once set on motion the higher parts of the Aire successiuely moue those which are vnder being driuen by the violence of the stone so falling and prepare as it were the way for his comming This reason may in some sort content an ingenious wit till a better bee found out 10 So much for the motion of a heauy point or center it remaines that we treate next of the motions and conformity of Magnitudes to the center of the Earth wherein we consider not only the Center or middle point but the whole masse of the magnitude whose motion and conformity shall bee expressed in this Theoreme 1 The motion of a magnitude toward the center is not meerely naturall but mixt with a violent motion This may easily bee demonstrated because no point of any magnitude is moued to the Center naturally but the middle point or center of the magnitude For although the Center bee moued in a perpendicular line which makes right angles with the Horizon yet the extreme parts are moued in lines parallell which cannot possibly make right angles with the Horizon or meet in the Center which may bee showne in this Figure Let there bee a Circle as ABL This done wee will imagine a certaine magnitude hanging in the Aire and tending to the Center C which is signified by the line PEN It is certaine that the Center of the magnitude E will moue and conforme it selfe downeward toward the center of the Earth by the line EC which motion will bee naturall as that which is deriued to a center from a circumference by the direct Radius which is the Rule of all naturall motions But the other parts without the center of this magnitude cannot moue but in so many lines which shall bee parallell the one to the other as for example the point N must needs moue in the line NG and the point P in the line PF which being of equall distance will neuer concurre in the Center and therefore cannot bee esteemed naturall rayes of the circle whence wee may collect that the motion of these parts is not naturall but violent for if any should imagine the motion of these parts to be naturall then should the point N moue to the center of the Earth by the line NC and the point P. by the line PC and so by how much the more any waighty body should approach the Center of the Earth by so much it should bee diminished and curtailed in his quantity so that in the Center it selfe all the parts should concurre in an Indiuisible point which is absurd contradicts all reason 11 Hitherto haue we spoken of the conformity of all Earthly and waighty bodies to the Terrene center as they are taken Absolutely It now remaines that we speake of these bodies as they are taken comparatiuely being compared one with the other This discourse properly belongs to an art which is called Staticke and Mathematicall whose office is to demonstrate the affections of Heauinesse and Lightnesse of all Bodies out of their causes The chiefe sensible Instrument whereon these properties are demonstrated and shewne is the Bilanz or Ballance But these specialties wee leaue to such as haue purposely written of this subiect amongst which the most ancient and chiefe is Archimedes whose heauenly wit ouertooke all such as went before him and out-went all such as followed Enough it will seeme in this Treatise to insert a proposition or two Staticall to shew the Conformity of two magnitudes and their proper Center mouing downeward toward the Globe of the Earth and it's Center 1 The lines wherein the centers of two heauy bodies are moued downeward being continued will meet in the Center of the Earth A heauy point or Center as wee haue demonstrated heretofore in this Chapter is moued toward the Center of the world in a right line which is imagined to bee a Ray of the whole Spheare deriued from the circumference to the Center therfore it is impossible they should bee parallell or Equidistant but concurrent lines But because the whole distance betwixt vs and the Center is very great it must needs happen that in a small space the concurse of
retaine in it selfe the vertue of the Load-stone yet by reason of the liquefaction is altogether languishing and as it were buried but vpon touch of a Load-stone is stirred vp to his former vigour for the magnet insinuats his Incorporeall influence into the iron and so rectifies and animates that force which was almost dead 2 The magneticall Coiton is strongest of all in the Poles This may easily bee demonstrated by an experiment for if the iron needle which is proposed to bee Attracted and the Poles and Center be placed in the same right line then this Coition will be to a perpendicular as in A and B to wit the Poles in the Diagramme but in the middle space they will obliquely respect and point and by how much farther off from the Pole it is by so much is this vertue weaker but in the Equator it selfe it becomes meerely parallell without any inclination at all To know in what proportion this force is increased or weakened we must put another ground That the force of this coition is increased proportionally as the chords of a circle for by how much the least chorde in a circle differs from the Diameter so much the forces Attractiue differ from themselues For sith the Attraction is a Coition of one body with another and magneticall bodies are carried by a conuertible nature it comes to passe that a line drawne from one Pole to another in the diameter directly meetes with the body but in other places lesse so that the lesse it is conuerted to the body the lesse and weaker will bee the coition 3 So much bee spoken of the magneticall Coition It followes that wee speake of Magneticall Direction which is a naturall conuersion and conformity of the magneticall bodies to the Poles of the Earth It is manifest that a magneticall body so seated that it can moue without any impediment will turne it selfe in such wise that the one Pole of it will respect the North Pole of the Earth the other the South which motion wee call Direction This we may plainely see in a Marriners compasse whose Lilly alwayes respects the North point If a compasse bee wanting the same may bee shewed in a little corken-boate which being put in the water with a load-stone in it will so turne and conuert it selfe that the Poles of the Load-stone will at length point out the Poles of the Terrestriall Globe The manner how shall be disclosed in these Theoremes 1 The South part of the Load-stone turnes to the North and the North part to the South To confirme this assertion some haue produced this experiment Let there bee cut out of a rocke of Load-stone a Magnet of reasonable quantity Let the two poles both North and South bee marked out in the Load-stone the manner of which wee shall perhaps teach hereafter then let it be put in a corken little boat on the water so that it may freely float hither thither It will be euident that that part which in the rocke or Mine pointed Northward will respect the South and contrarywise the South part will respect the North as wee may see in this figure Let the Magnet as it is continuated with the Mine or Globe of the Earth be AB so that A shall be in the North pole B the South-Pole Let this Load-stone be cut out of this rocke or Mine placed on the water in a little timber boat which shall be CD we shall find that this little dish or boat will turne it selfe so long vntill the Northpart A be turned to the Southpart B and on the other part the Southpart B be conuerted to the Northpart A and this coÌ„formity would the whole rock of Load-stone claime if it were diuided and separated from the Globe of the Earth The reason why the magnet in the boat on the water turneth windeth and seateth it selfe to a contrary motion to that it primarily receiued whiles it was ioyned to the bowels of the Earth and vnited to the body of the great Magnet is because euery part of a Load-stone being separated from the whole whereof it is a part becomes of it selfe a perfect compleat magneticall body as we may say a little Earth hauing all the properties of the great Globe as Poles Meridians Aequators c. And therefore according to the nature of magneticall vnion spoken of in our next Theoreme will in no wise endure to settle it selfe as it did before but deemes it a thing more naturall and of more perfection to turne his aspect a contrary way to that which he inioyed at his first constitution Here may we note a great errour of Gemma Frisius who in his corollary vpon the 15 Chap. of his Cosmographicall Comment on P. Appian affirmes that the Needle magnetically effected would on this side the Aequator respect the North-pole but being past the Line would straight-way turne about and point to the Southpole An errour as Mr Hues saith vnworthy so great a Mathematician But Gemma Frisius in some â—ort may be excused for as much as the grounds of magneticall Philosophy were in his time either not discouered or most vnperfectly knowne and the vncertaine relations of Nauigators were reputed the best Arguments and how easie a matter it is for a Trauailer in this sort to deceiue a Scholler who out of his reading and experience can shew nothing to the contrary let euery man iudge 2 This contrary motion here spoken of is the iust confluxe and conformity of such bodies to magneticall vnion This is demonstrated by Gilbert in this manner Let the whole magneticall body be CD then C will turne to the North of the Earth B and D vnto the South part A. Let this magnet bee cut in twaine by the middle line or Aequator and the point E will tend to A and the part F will direct it selfe to B for as in the whole so in the parts diuided nature desires the vnion of these bodies The end E willingly accords with F but E will not willingly ioyne it selfe with D nor F with C for then it would haue C against its nature to moue toward A the South or D in B which is the South Separate the stone in the place of diuision and turne C to D and they will conueniently agree and accord For D will turne it selfe to the South as before and C to the North and E and F ioynt parts in the minerall or rocke will now bee most sundred For these magneticall parts concurre and meet together not by any affinity of matter but receiue all their motion and inclination from the forme so that the limits whether ioynt or diuided are directed magnetically to the Poles of the Earth in the same manner as in the diuided body 3 If any part Southward of the magneticall body bee torne away or diminished so much shall bee also diminished of the North-part and contrariwise if any part bee taken away in the North-part so much shall the vertue of the
360 by multiplication is produced hath exactly these parts 1.2.3.4.5.6.10.12.15.20.30 Likewise 360 hath exactly 1.2.3.4.5.6.8.9.10.12.15.18.20.24.30.36.40.46.60.72.90.120.180 Of all which parts there is so great vse in Astronomy and many times in Geography that without it there would be small exactnesse For as we see a yard measure would little steed the Mercer or Clothier except it were againe diuided into smaller parts so fals it out in the account of the Cosmographer 3 Of the Terrestriall Circles some are Absolute some Relatiue the Absolute are such as are assigned without any respect to our sight of which sort are the Meridians and Parallells 4. The Meridian is a circle drawne by the Poles of the world and the verticall point of the place The Meridian Circle is so called of Astronomers because when the Sun according to their suppositions by the motion of the first moueable comes into this Circle it makes mid-day and then hath been running his course from his rising to arriue there iust so long as he shall be mouing from thence to the place of his setting In this Meridian are placed the two Poles of the Equator which are the same with the Poles of the world in this also are the verticall point and the point opposite vnto it tearmed the Poles of the Horizon whereof we shall speake hereafter So that so many Meridians are imagined to be in the Earth as there are vertical points for howsoeuer we see not many Meridians painted on the face of the artificiall Globe yet must there be so many imagined in the reall Earth as Zenithes and Horizons so that it is impossible for a man to moue neuer so little from East to West without changing his Meridian yet for more order sake haue the Cosmographers reduced the number of Meridians to halfe the number of the degrees in a Circle to wit to 180 that euery Meridian cutting the Equator and other Parallels in two opposite places should answer to two degrees in the same Circle By which it appeares that euery Meridian diuides the Terrene Globe in two halfes whereof the one is respectiuely tearmed of the East the other of the West But to auoid all ambiguity of speech we ought to consider that a Meridian is twofold either the true Meridian or Magneticall Meridian The true Meridian ordinarily so called is that which directly passeth by the Poles of the World of which wee here treat which indeed as wee shall shew is the onely true magneticall Meridian But that which some haue falsly called the Magneticall Meridian is that which runneth by the Poles of the Magneticall Variation and much differs from the true because as we haue taught the variation is diuerse according to the diuersity of place therefore cannot answer in any certaine proportion to the Poles of the Terrene Globe The true Meridian Circle as it hath manifold vse in Astronomy namely to distinguish mid-day and midnight to measure the rising and setting of the Starres c. matters not to bee neglected of Geographers so hath it a more speciall vse in Geography to designe the longitudes and latitudes of the places with their distances with many other matters treated of hereafter 5 Concerning the Meridian circle wee are to know two things The Inuention of it and the Distinction The inuention is whereby wee are taught to find out the true Meridian in any place assigned 6 The Inuention of the Meridian is againe twofold the one more Accurate which is either Astronomicall or Magneticall the other Popular the Astronomicall way is performed by obseruing the celestiall motion The Meridian may bee found out the Astronomicall way in diuerse manners by Instruments deuised for this purpose by ingenious Artificers whereof some are described by Gemma Frisius in his Cosmographie But to auoid the cost of curious Instruments I will set downe our way depending on this Theoreme 1 If two seuerall Sunne-shadowes bee obserued the one in the fore-noone the other in the afternoone of the same day exactly to touch with their ends the Circumference of the same circle described in a Plaine Parallell to the plaine of the Horizon The line from the Center equally diuiding the Arch of that Circle betwixt the two shaddowes will bee the true Meridian circle for that place This Theoreme howsoeuer consisting of many parts is notwithstanding easie enough to bee vnderstood being explayned by an ocular demonstration Let there bee gotten a platforme of wood or metall and placed euenly that it may lye parallell with the plaine of the Horizon In this plaine let there bee described diuerse circles from the same Center E. In this Center let there bee raysed a Gnomon EF to right angles so that the top of this Gnomon F shall euery where bee equally distant from the circumference of each circle described in the plaine which may easily bee knowne because if it bee equally distant from any three points of any circles Circumference it will also bee equally distant from all the rest alike as Clauius hath taught in the 4 of his Gnomonicks This platforme being thus ordered let the shaddow of the Gnomon bee obserued sometimes before Noone vntill such time as it exactly shall touch the circumference of one of those circles as in EG Againe in the Afternoone let the shaddow bee obserued till with his end it meet the circumference of the same circle as in EH which will happen so many houres afternoone as the other before Noone These two points G and H being diligently obserued let the Arch of the Circle GH bee diuided into two halfes with a line drawne from the Center E which shall bee ED. This line ED will bee the true Meridian for that place on which when the shadow of the gnomon shall happen to fall wee may assure our selues that it is full Noone 7 The Magneticall Inuention is performed by the Magneticall Directory Needle This way is subiect to much errour and not so certaine as the former because as wee haue shewed before there are found very few places which admit not some of Variation yet because it may bee profitable to such who haue not the Command alwayes of the Sunne or sight of the Starres I will insert this Theoreme 1 The Line wherein the Directory needle is directed from North to South is the Meridian for the place This may bee shewed in any Marriners Compasse or 〈◊〉 Sunne-Dyall whose needle is magnetically touched For bâ—â—ing set euenly parallell to the playne of the Horizon it will shew by the needle the Miridian for that place in euery verticall point on the earth For example in the Sea-Compasse in the next page experience will witnesse in euery Region of the Earth that the one point signed out by the Lilly will alwayes turne to the North the other opposite part will turne it selfe to the South which two parts being ioyned together by a right Line will shew the Meridian foâ—â—â—at place The Meridian I say not alwayes the true for this Inuention taken from
yet may the rest compared amongst themselues be ranged in a certaine order as the Second Third Fourth Fifth and so along till we come againe to the First being in all reduced to the number of 180 answering to 360 Degrees as wee haue taught So much for the Meridians 11 The Parallels are equidistant Circles passing from the East to the West directly I haue defined the Parallell Circles in a larger sense then former Geographers vsually haue taken it in as willing vnder this generall name not onely to include the Parallels commonly so called but also the Equatour because I see no reason why the Equatour being euery where equidistant from each other Circle should not suffer this acception The common sort of Cosmographers vnder this name would onely comprize the minor Circles which are conceiued to bee equally distant and correspondent to the Equinoctiall Circle so that all should bee so called in respect of the Equatour to whom they are said to answer not in site and position for as much as they decline from the middle of the Earth to the North and South but in Comparison and Proportion for as the Equatour is drawne from East to West and diuides the whole Spheare of the Earth into the North and South Hemispheares So the other also diuide the Globe of the Earth though not into two equall parts as the Equatour but vnequall These Parallels many wayes are distingushed from the Meridians first because the Meridians are drawne directly from North to South but the Parallels from East to West Secondly the Meridians how many soeuer they are imagined to bee concurre and meete all in the Poles of the Earth whereas the Parallels howsoeuer drawne out at length will neuer concurre or meete in any point Whence it must needes follow that all Parallels and Meridians in the Globe must cut one the other and make right angles These Parallels although infinite in number may bee in the Spheare reduced to the number of the Meridians because they are drawne through the opposite points and degrees of the Meridian Semi-circle which would make vp the number of 180 but yet for Conueniency they haue not painted so many in the face of the Artificiall Spheare for as much as so many lines and circles might beget Confusion Wherefore Ptolomy and the Ancients haue distinguished the Parallels on both sides the Equator North and South with such a Distance that where the day should increase one quarter of an houre a new Parallel should be placed So that the longest day of one Parallell should surpasse the longest day of another for one quarter of an houre By which appeares that the Parallels are not of one greatnesse but by how much neerer the Pole they are placed so much lesse are they and so much greater by how much farther off from the Poles and neerest the Equatour These Circles are of great vse in Geographie as to distinguish the Zone Climats and Latitudes of Regions to shew the Eleuation of the Pole and to designe out the length and shortnesse of the day in any part of the Earth 12 A Parallell Circle is of two sorts either greater or lesser The greater is the Equatour or equinoctiall Circle 13 The Equatour is the greatest of the Parallels passing through the middest of the Earth and exactly diuiding them from the Poles into two equall halfes or Hemispheares whereof the one is North the other South This Circle is called the Equatour or Equinoctiall of Astronomers because that when the Sunne passeth vnder it as vpon the 11 of March and the 13 of September it makes the Day and Night equall This Circle of Astronomers is esteemed the most notable being the measure of the Diurnall and most regular Motions The Laâ—ines haue taken the name and appellation of this Circle from the Day as the Greeks from the Night Wherein the Sense is no way varyed because the equality of the Day argues the like equality of the Night The two Poles of the Circle are the same with the Poles of the Vniuersall Earth to wit the Articke or North-Pole and the Antarticke and Southerne Pole whereof the former is alwayes conspicuous in our Horizon the other lies couched and hidde from our Sight It is called the Articke-pole from the Constellation of the little Beare in the Heauens neere to the which it is situated in opposition to the which the other is called Antarticke It hath manifold vse in Astronomy copiously by Astronomers And no lesse in Geography for without this Equinoctiall Circle no Description of the Earth can be absolute perfect neither any Citie or Place in the Terrestriall Globe or Mappe set in his due and proper place This Equinoctiall Circle in regard of the Earth passeth through the middle-most part almost of Africa by Ethiopia America and Taprobana So that it exactly diuideth the Globe of the Earth into two halfes the Northerne and Southerne Hemispheares so that these people which dwell vnder the Equatour are said to inhabite the middle of the world because they incline neither to the North nor to the South hauing so much distance from the Articke Antarticke-Pole of the Earth Moreouer by this Circle as wee will declare hereafter are noted out vnto vs the East and West part of the Spheare no way to be neglected of Geographers 1 Concerning the Equatour two things are to be obserued either the Inuention or the Site and Position The Inuention is either Astronomicall or Magneticall The Astronomicall according to these Rules 1 The Meridian being found out to find the Equator This is easily performed by the helpe of the former Figure for therein the Meridian line being found out as we haue shewed let there bee drawne by the Center E of that Circle the line AC making right Angles with the said Meridian which line AC will bee the true Equatour and will point out vnto vs the true East and West as A the East and C the West Whence it appeares that the two lines to wit of the Equatour and the Meridian doe diuide and cut the whole Horizon into two equall Quadrants 2 Without the helpe of the Meridian to find out the Equatour In the time of either Equinoctiall in some Horizontall plaine in the Sunne-shine let there bee erected a Gnomon then in the day time let there bee noted all the points by which the end or top of the shadow hath passed for all those points in the time of Equinoctiall are in a right line because then the end of the shadow is carried in a line in the time of the Equinox in a Herizontall plaine This line will bee the true Equinoctiall-line the cause is giuen by Clauius in Gnomonicis lib. 1. prop. 1. Corollar 2. which depending on many Geometricall and Astronomicall principles as too far from my purpose I omit 15 The Magneticall inuention of the Equatour is wrought by the Magneticall Inclinatory Needle according to this Proposition 1 Wheresoeuer at any place of the Terrestriall
industriously calculated as I haue here inserted to saue others a new labour of calculation The Meridians are more easily found by hanging any directory wier or needle ouer the Terrella one end of which pointing towards the North and the other towards the South will discouer the Meridian line CHAP. VIII Of the measure of the Terrestriall Globe 1 HItherto haue we handled the Terrestriall Globe primarily in such proprieties as absolutely agree vnto its nature In the second place we are to handle such as secondarily arise out of the former Here wee are to handle two chiefe points 1 The Measure 2 The Distinction 2 The measure is that by which we find out the quantity of the whole Earth Good reason haue we to cal this the Secondary part of Geography for as much as these accidents and proprieties we here consider arise altogether out of the former In the former Treatise wee haue diuided the Naturall Spheare of the Earth from the Artificiall But in this part for auoiding of tedious repetitions of the same things wee haue ioyned them together For howsoeuer the measuring and dictinctions of the Earth bee truely grounded on the nature of the earth it selfe yet can it not be well expressed and taught without the materiall Instrument we haue therefore thought good to consider the measure of the earth before wee come vnto the Distinction because it is more simple and vncompound depending on the lineaments and measure of one circle whereas the Distinction necessarily requires the coniunction and combination of diuerse circles as Meridians and Parallels compared one with the other as shall bee taught hereafter Whether the great masse of the earth can bee measured or no seemes a matter not agreed on by all Some haue held an opinion that it cannot bee measured in regard of the infinite magnitude wherewith they thought it endowed which opinion seemes deriued from some of the Platonicks who ascribing to the Earth another figure besides the Sphericall haue cast themselues vpon vncertainties and being notable to reduce the Quantity of the Earth according to their owne grounds to any certaine measure haue denied it to bee measurable But the ground of this opinion wee haue taken away before in prouing the earth to be of a true Sphericall nature and therefore circumscribed in certaine bounds apt to be measured Another conceit more absurd then the former is not only the common people whose condition might excuse their ignorance but of such as would bee esteemed learned who contend that the greatnesse of the earth cannot bee measured the onely reasons they can alleadge for themselues are 1 That a great part of the earth is vnaccessible by reason of steepe rocks high mountaines spacious and thicke woods moorish fogges and such like impediments 2 That the parts of it are for the most part vneuen and subiect to no regular figure without the which no measure can bee exact The first cauill is of no moment because whereas wee affirme that the Earth by man may be measured we hold it not necessary that it should be trauersed ouer by iourneyes or voyages For as much as to the finding out of the Quantity of the whole Terrestriall Spheare it may seeme sufficient to know the measure and proportion of any little part in respect of the Heauens As for example what number of Miles Leagues or Furlongs answer to any degree or degrees in the Heauens wherfore we suppose the Earth to be measured ouer not with our feet but with our wits which may by Mathematicall rules be taught to march forward where our legges fayle vs The second obiection only proues thus much that the Earth partaking of so many vnequall parts and irregular formes cannot in the measuring admit of so much exactnesse as if it were endowed with one vniforme face yet it is exact enough to contenta Cosmographer who measureth not by feet and inches but by leagues and miles in which wee little regard such a needlesse curiosity 1 The common measure by which the quantity of the Earth is knowne are Miles and Furlongs Here is to be noted that such instruments as serue for measuring are of two sorts either greater or lesser the smaller are of diuerse sorts as a Graine Inch Foot Pearch Pole and such like Some of these howsoeuer sometime vsefull in Topographie can haue little or no vse at all in the vast greatnesse of the whole Earth Wherefore the Geographer seldome descends so low but takes notice of greater measures such as are Miles Furlongs where we may obserue by the way that the vsuall measuring amongst the Grecians was by Stadia or furlongs amongst many of the Latines by miles vnder which we also cōprehend Leagues these miles are diuersly varied according to the diuersity of Countries so that in some places they are esteemed longer in other shorter which differences may be learned out of this ensuing Table The instruments of measuring the Earth are 1 Furlong containing 125 Geometicall paces or 625 feet 2 Mile which is either 1 Proper containing 8 Furlongs or 1000 paces 2 Improper which is either 1 League which is either 2 German mile which is either the 1 Old containing 12 Furlongs 2 Newer containing 16 Furlongs 3 Common of 24 Furlongs 1 Common which is 32 Furlongs or foure Italian miles 2 Greatest containing 5000 paces which is called the Suenian or Heluetian mile Howsoeuer this Distinction of miles may be many wayes profitable especially in the Topographicall part yet shall wee seldome make vse of any other then the common Germane mile or the common Italian mile To which as the most knowne the rest may easily be reduced 3 The obiect here proposed to bee measured is the Spheare of the Earth The Dimensions according to which it is measured are either Simple or Compound 4 The simple is twofold either the Perimeter or the Diameter The Perimeter otherwise called the circumference is a great circle measuring the Earth round about 5 The Inuention of the Perimeter of the Earth depends on these following Propositions 1 If two or more circles bee drawne about the same Center and from the Center to the Circumference be drawne two right lines The Arches of all the Circles comprehended within the said right lines will bee like and proportionall one to the other This Proposition being meerely Geometricall is taken here as a ground without farther demonstration whereof if any man doubt hee may haue recourse to Clauius Commentaries vpon Iohannes de Sacrobosco This principle granted will beget these two Consectaries 1 As one degree is to the number of correspondent miles or furlongs so all degrees of the circles to the number of miles or Furlongs measuring the quantity of the Perimeter of the Earth 2 Wherefore one degree or portion of the Circle being knowne by his number of miles or furlongs the whole Circumference may be found out The reason of this consequence euery Arithmetician can easily shew out of the Golden Rule The chiefe point then
in longitude 30 degrees 45 minutes in latitude 49 degrees 35 min Then wee will suppose Summatra as placed at C to haue in longitude 131 degrees but no latitude The difference of longitude will be EC of 100 degrees 15 minutes and the complement AE 79 degrees 45 minutes Then working according to the Rules of Trigonometry we shall find the signe of the Arch FC to be 6 degrees 37 ½ minutes which being added to FC being 90 degrees will produce 96 degrees 37 ½ minutes to which Arch there will answer 1449 German-miles 16 The second Case is when both places are situate without the Equatour This is againe twofold For either the two places are vnderstood to be situate towards the same Pole or else one place toward the Northerne the other towards the Southerne Pole Both which Cases shall be taught in these Rules 1 If both places whose distance is sought be situate towards the same Pole there will arise a Triangle whose sides and Angles will be knowne by the fourth Axiome of Pitiscus in Trigonometry the fourth Booke As for example in this present figure let the two places giuen bee FG the Triangle to bee knowne will be FBG whose acute Angle will be at B. Let the places giuen bee as FH the Triangle to bee resolued known will bee FBH hauing a right Angle at H. Finally if the places supposâ—ed to be giuen are as FI the Triangle to bee knowne will bee FBI with an obtuse Angle at I. 2 If the one place be situated towards the North-pole and the other towards the South-pole there will arise a Triangle whereof the one side about the Angle which is giuen will be greater then a quadrant As in the former figure let the places giuen be as G and K also H and K also I and K There will still fall out a Triangle whose one side containing the Angle giuen will be greater then a quadrant as BK wherefore for the side BK you must take his complement to the Semi-circle BF that is for the Triangle GBK you must worke by the Triangle GBF and insteed of the Triangle HBK you must take the Triangle HBF and for the Triangle IBK you must worke by the Triangle IBF according to the fourth Axiome of the fourth booke of Pitiscus to which I had rather referre my Reader then intermixe our Geographicall discourse with handling the Principles of Geometry which here are to be supposed so many precedent propositions which expressed as they ought would transcend the bounds of my intended journey 17 Of the Astractiue way of finding out the Distance of places we haue spoken The Mechanicall depends on the vse of Instruments and Mechanicall operation whereof wee will shew one way in this Theoreme 1 By the working with a Semi-circle the Distance of two places may be found out This inuention by Mr Blundeuill seemes to be ascribed to Edward Wright yet hath it beene taken vp of forreine Writers as their owne and vsed in their Charts and Mappes The manner of operation is thus First let there be drawne a semi-circle vpon a right Diameter signed out will be the letters ABCD whereof D shall be the center as you find it deciphered in this present figure The greater this Semi-circle be made so much the more easie will be the operation because the degrees will be larger Then this Semi-circle being drawne and accordingly diuided imagine that by the helpe of it you desire to find out the distance betwixt London and Ierusalem which cities are knowne to differ both in longitude and latitude Now that the true distance betwixt these two places may bee found out you must first subtract the lesser longitude out of the greater so shall you finde the Difference of their longitudes which is 47 degrees Then reckon that Difference vpon the Semi-circle beginning at A and so proceed to B and at the end of that Difference make a marke with the letter E into which point by your Ruler let a right line be drawne from D the center of the Semi-circle This being in this sort performed let the lesser latitude be sought out which is 32 degrees in the foresaid Semi-circle beginning your accompt from the point E and so proceeding towards B and at the end of the lesser latitude let another point bee marked out with the letter G from which point let there be drawne a perpendicular which may fall with right Angles vpon the former line drawne from D to E and where it chanceth to fall there marke out a point with the letter H This being performed let the greater latitude which is 51 degrees 32 minutes be sought out in the Semi-circle beginning to reckon from A towards B and at the end of that latitude set downe another point signed out by the letter I from whence let there bee drawne another perpendicular line that may fall with right Angles vpon the Diameter AC and here marke out a point with the letter K This done take with your Compasse the distance betwixt K and H which distance you must set downe vpon the Diameter AC placing the one foote of your compasse vpon K and the other towards the center D and there marke out a point with the letter L Then with your compasse take the shorter perpendicular line GH and apply that widenesse vpon the longer perpendicular line IK placing the one foot of your compasse at I which is the bounds of the great latitude and extend the other towards K and there make a point at M. Then with your compasse take the distance betwixt L and M and apply the same to the semicircle placing the one foot of your compasse in A and the other towards B and there marke out a point with the letter N. Now the number of degrees comprehended betwixt A and N will expresse the true distance of the two places which will be found to be 39 degrees which being multiplyed by 60 and so conuerted into miles according to our former Rules will produce 2340 which is the distance of the said places 17 The expression of the Distance of two places may be performed either by the Globe or Map according to these Rules 1 The distance betwixt two places in the Globe being obserued by the quadrant of Altitude and applied to the degrees of the Equatour or any great circle will shew how many miles such places are distant The practise hereof is very easie as shall be taught in this example we wil for instance take Tolledo in the middest of Spaine and the Cape of Good Hope in the South Promontory of all Africa The space taken by a quadrant of Altitude or any threed applyed to the Equatour will be found to bee about 82 degrees which being multiplyed by 60 and so conuerted into miles will render 4920 the true distance betwixt these two places 2 The distance betwixt any two places in the Chart obserued by a compasse and applyed to the degrees of a greater Circle will shew how