the Pole that the longest day of one place exceedeth the longest day of the Vicine place which is more nigh the Aequator every where equal in excess or that the longest day equally may encrease Of Parallels between the Aequator and the Pole these Parallels shall not equally be distant one from another viz every vicine Couple but these which are more remote from the Aequator shall have a less distance than those more near the Aequator The truth of this Proposition is shewed from the precedent for if these Parallels should be equally distant from one another viz. every two Vicine the quantity of the longest day in these Parallels would not Augment by an equal encrease as we have here shewed And it is now laid down that the places or Parallels so taken equally encrease that the longest day may equally increase in them wherefore every two Vicine or near Parallels shall not so equally be distant one from another but many Parallels being taken from the Aequator towards the Pole on this condition that the longest day may equally encrease These Parallels shall not be equally distant from one another but the distance of the third from the second shall be lesser than the second from the first that of the fourth less from the third that of the fifth lesser from the fourth and so forwards Corollary and because that many of the Climates are so taken that the longest day in the final Parallel of the Climate exceedeth the longest day of the begining at the Climate by half an hour it followeth from this Proposition that the Climates more remote from the Aequator are less broad or more narrow then these more near the Aequator and therefore the Latitude and Magnitude of the Climates decreaseth towards the Pole Hence it cometh to pass seeing that the Climates at length would become very narrow towards the Pole if that the same excess should be kept viz. the excess of half an hour so that Geographers define the bounds of the Northern Climates not by half an hour but first by whole hours and then by whole daies Proposition XI The number of the hours of the longest day being given in any place or Parallel of the Earth to find the Latitude of the place or Elevation of the Pole of this Parallel and to exhibit the Parallel it self in the Globe or to exhibit those places where the longest day is so great For the finding the Latitude of a place c. The longest day in all Northern places is when the Sun is in the first Degree of Cancer Let the place of the Sun of the longest day be brought to the Meridian Let the Index be brought to the 12th hour of the Horary Cycle let the Globe be turned until the Index shew that hour of the Cycle from which the given number of the longest day is denominated and then let the point of the Tropick in the Meridian be noted Then let the first degree of Cancer be brought to the Oriental Horizon and the Meridian in the Crena be so moved to the Pole Elevated or depressed until the other noted point of the Tropick be in the Occidental Horizon but so that the first degree of Cancer be yet in the East which being done number the Degrees of the Elevation of the Pole For that is the sought for Elevation or Latitude of the Parallel which you shall find in the very Globe it self if you number so many Degrees in the Meridian from the Aequator towards the Pole and a Chalk being applyed you may turn round the Globe to the term of the Numeration For the described Parallel is that which is sought The Probation of the Method is easie Proposition XII The number of some days being given to find out the Latitude of the places or Parallels and to exhibit the place of the Frigid Zone on the Earth when the Sun for so many days setteth not and for so many more ariseth not Further concerning the Latitudes of places Let the number of the daies be divided in half and let so many Degrees be numbred in the Ecliptick from the first Degree of Cancer as that divided or half number is or as many Unites as this hath the Numeration may be made from both parts of this begining Let the term be be noted with Chalk if the daies be more than thirty the number of the Degrees must be taken lesser than an Unite Then let this noted point be brought to the Meridian and let the Degrees interrupted between that and the Pole be numbred For these are the sought for Elevation of the Pole or Latitude of the places wherein so many daies as are given the Sun setteth not and in so many daies riseth not You shall find the very places and Parallels in the Globe if that you number the found out Latitude from the Aequator towards the Pole in the Meridian and design the Parallel by Chaulk applyed to the Term. For this is that sought for and it containeth all the places sought for For the Demonstration of this Solution let the Pole be Elevated for the Latitude of the places found out and it will be manifest that the noted Degrees of the Ecliptick about the first Degree of Cancer set not beneath the Horizon but remain above it The Sun therefore passing over these points of the Ecliptick setteth not now he passeth through these points in so many days as are given as is apparent by the connstruction After the same manner we shall shew the truth of this Solution concernig the daies in which the Sun doth not arise at all in the places Parallel found Corollary It is easie therefore to find the Elevation of the Pole of those places or Climates which lie in the Frigid Zone where the longest day encreaseth not by hours but by a number of whole daies Proposition XIII To frame or compose a Table of the Climates Of the making a Table of the Climates This is called a Table of Climates in which at the beginning middle and end of every Climate the Elevation of the Pole or Là titude of the Parallel and the very quantity of the longest day is found noted as also the interval of the Climates or distance of the Parallels The Construction is easie for from the order of the Climates the quantity for the longest day for the beginning middle or end of every Climate is found by adding ¼ of an hour to twelve hours by a continual Succession Then from the quantity of the longest day of every Parallel is found out the Elevation or Latitude of the Pole of every one of them according to the XI Proposition Lastly you have the interval or Latitude of the Climates if you take the Latitude of the beginning Parallel from the Latitude of the ending Parallel All these being noted in the Table we shall have a Table of the Climates which I have hereunto annexed A Table of the Climates and Parallels Climates
again opposite four days of the year in two of which the Sun shall obtain a middle distance from the place given if therefore the place given be North take two of those four days whereof one happeneth between the 21 of December and the 21 of March this shall be the entrance of the Spring the other between the 21 of September and the 21 of December this shall be the entrance of Autumn But if the place given be South from those four days you must take the day between the 21 of June and the 21 of September for the entrance of the Spring and for the beginning of Autumn that which happeneth between the 21 of March and the 21 of June The beginning of Winter shall be the 21 of June if the place be South but if North the 21 of December 3. If the place given be between the Aequator and the eighth degree of Latitude it shall have two Summers and two Spring seasons besides Autumn and Winter except peradventure we will cast away that second Spring which is intermedial between the two Summers as we said in the end of the preceeding Proposition and attribute a continual Summer to that time which if you do we must act no otherwise with the given place than in the former Mode If we will attribute two Summers and two Springs to it as the definitions of Summer and Spring accurately observed do require we shall first act by the first Mode as in the former Theorems viz. we shall find the entrance of Summer and Winter and except the four days of moderate distance found in the Table of those four those two which we advised to take in the former Mode for the entrance of the Spring and Autumn here again we shall take on the same conditions but of the other two days that only which is proximate to the day of the Summer shall be taken For this will shew the end of the Summer and the beginning of the second Spring but for the day of the second Summer another day of the three remaining shall be taken in that Area from which the beginning of the first Summer was taken viz. that which is distant by an equal number of days from the 21 of June and the 21 of Capricorn if the place be South the first day of the Summer So the days shall be found in which the Summer the Spring Autumn and the Winter do begin and end in the places of the Torrid Stone Proposition V. In the places in the temperate and frigid Zones the four seasons of the year are almost equal or consist of an equal number of days But in the places of the Torrid Zone they are unequal Neither are only the times of the divers seasons unequal but also the time of the season in the divers places of the Zones is unequal The seasons of the year in the places in the Temperate and Frigid Zone are equal 1. For the places of the temperate and frigid Zones what I have said is easily demonstrated For seeing that the Sun in every time of those four quarters of the Year runs through three Signs therefore the times of the Spring Summer Autumn and the Winter shall be equal or of equal days except some days viz. five in which the Summer and four in which the Spring of the Northern places exceed the Autumn and the Winter but in the Southern places it is otherwise for Autumn and Winter exceed the Spring and Summer which as we have shewed before proceedeth from the excentricity of the Sun 2. In places lying under the Aequator there are two Summers as also other Seasons but hoth short as also both the Springs viz. each Summer and each Spring hath only 32 days which is 64 days but the Autumns and Winters are longer viz. 55 days which is 110 days 3. In the places of the Torrid Zone by how much the less they are remote from the Aequator by so much the more they have the longer Summer the less Winter and more or less moderate Autumn and Spring for in places not remote above 10 degrees from the Aequator the Summer continueth six Months Now the greatness of the Summer Autumn Winter and Spring is known by the preceeding Proposition What hath hitherto been said is only to be understood concerning the Celestial Seasons that is those which depend on a Celestial Cause or from the access or recess of the Sun for from this alone cometh not light heat and cold as we have said in some places before therefore we shall consider the other causes in the following Propositions Proposition VI. In places of the Tornid Zone as the Sun by day is very near the Vertex so on the contrary by night he is beneath the Horizon Of the Motion of the Sun in places of the Torrid Frigid and Temperate Zones and very much removed from the Vertex of those places so that those places by night lye almost in the middle shadow of the Earth neither can the Air possibly any wayes be warmed by the Suns rayes by frequent reflection In places of the Frigid Zone as the Sun by day is not very nigh the Vertex so by night he doth not profoundly remain beneath the Horizon but for the greatest part of the night doth so turn round beneath the Horizon that many rayes from him by reflection do penetrate into the Air. In places of the Temperate Zone as the Sun by day cometh to the Vertex of those places by a moderate Vicinity so by night by an easie distance he is depressed beneath the Horizon so that some rayes at least are in the Air. To shew this by the Globe first let the Pole be elevated for some place scituated in the Torrid Zone or rather let the Pole be placed in the Horizon it self that the places of the Aequator may be in the Vertex of the Horizon or that the wooden Horizon may become the Horizon of the places of the Aequator then consider the depression of the Parallels which the Sun describeth by his circumrotation beneath the Horizon and the truth of the member of this Proposition will appear Then let the Pole be elevated for the places of the Frigid Zone or let the Poles be placed in the Vertex of the Horizon and the Parallels of the Sun beneath the Horizon from the first degree of Libra to the first of Aries being considered it will again be manifest that they are very little depressed below the Horizon And so we have shewed the second member or part of this Proposition Lastly let the Pole be elevated for the Latitude of any place scituated in the Temperate Zone and the depression of the Parallels beneath the Horizon again being considered the third part of this Proposition will be proved Proposition VII A place being given in the Globe and the day of the year to find the Longitude of the Crepusculum or Twilight in the place given at the day given That time is
found at the day taken and noted in the Ecliptick of the Globe Then let the Pole be Elevated for the Latitude of the Earth of the one place taken and let the Longitude of the day and the night or the stay of the Sun above or beneath the Horizon in that place at the assumed day be found by the sixth Proposition of this Chap. Then let the Pole be Elevated for the Latitude of the other place and let the Longitude of the day and night or stay of the Sun above or beneath the Horizon be found at the same assumed day Let this Longitude so found be compared with the other and the truth of this Proposition will be manifest So that the place more remote hath all the daies of one half year longer than the place more nigh On the contrary it will have all the daies of the other half year shorter Corollary What hath been shewed of all the daies of the year except the Aequinoctials the same is also of force in the quantity of the longest and shortest day And in this it is most observed and noted because here is the greatest difference between the Longitude of the night and day not so great in other daies of the year Therefore of the two places that which is more remote from the Aequator or more near to the Pole hath the longest day greater than the place more Vicine to the Aequator and the shortest day lesser Proposition VIII All places of the Earth scituated in one of the same Parallel have all the days of the year equal and therefore the same quantity of the longest day The Demonstration of this Proposition is easie by the Globe Let any Parallel be taken in the Globe and what places you please The equality of the daies according to their scituation in one of the same Parallel Let the Pole be Elevated for the Latitude of this Parallel and let any Parallel of the Sun be taken for any part of the year Out of the Degree let the Tropick of Cancer be taken for the longest day let one of the places taken be constituted under the Meridian that so it may possess the Vertex of the Horizon or that the Wooden Horizon may be the Horizon of the place Then let the Arch of the Tropick above the Horizon be noted or the two points of the same which are in the Horizon for the Arch in these denoteth the stay of the Sun above the Horizon of the place then let the second place be brought to the Meridian or Vertex that the Wooden Horizon may be the Horizon of it and let the Arch of the Tropick above the Horizon again be marked which if it be compared with the former we shall find that they are equal The same may be shewed also by hours on the Horary Circle Therefore the Sun remaineth an equal time above the Horizons of those places and therefore the daies shall be equal as also the nights Definitions From these aforesaid Propositions the Original of the division of the Earth into Climates is easily to be understood Observations concerning a Climate For a Climate is said to be one part of the Earth of those parts into which the Superficies scituated between the Aequator and the Pole is so cut by drawn Parallels that the longest day in the Parallel more remote from the Aequator exceedeth the longest day of the Parallel more near the Equator in a certain part of an hour or number of hours Viz. Half an hour in places scituated even to the Artick Circle in other places a whole hour or some hours and daies The begining of a Climate is called a Parrallel with which the Climate begineth and is more nigh the Aequator The end of a Climate is called a Parallel terminating the Climate The middle of a Climate is called a Parallel drawn almost through the middle Superficies of a Climate so that in that the longest day exceedeth the longest day of the begining of a Climate by a quarter of an hour or an half difference wherein the longest day of the end of a Climate exceedeth the longest day of the begining of a Climate A Parrallel space is said to be that which the middle Parrallel of a Climate comprehendeth with the begining or end of a Climate Proposition IX If more places of the Earth be taken from the Aequator towards the Pole whose distance from the Aequator equally augmenteth from one degree to 10 20 30 40 degrees The longest days in these places shall not be equally greater or not equally augment but they shall more augment in places more remote and where the place is more near to the Pole Touching the length of daies of Places taken from the Aequator towards the Pole To shew the Verity of this Proposition by the Globe let places be taken remote from the Aequator towards the Pole by an equal encrease of distance viz. for conveniency Parallels of 10 20 30 40 50 60 degrees of Latitude For these Parallels in the Globe let the Pole be Elevated to the Latitude of 10 degrees and the first degree of Cancer being brought to the Oriental Horizon and that being noted let the point of the Tropick be also noted which then is in the Occidental Horizon For the Arch of the Tropick then being above the Horizon sheweth the stay of the Sun above the Horizon of the place 10 degrees of Latitude The hours of this his stay may also be known by the Index and Horary Circle Then let the Pole be Elevated according to the Latitude of the second place 20 degrees and the first degree of Cancer being again brought to the Oriental Horizon let the point of the Tropick be noted in the Occidental for the Arch above the Horizon will again note the stay which also may be known by the Index and the Circle in the Hours The same may be used with places whose Latitude is 40 50 60 70 degrees and the like which being done let the Diurual hours of the Suns stay above the the Horizon or the Arch of the Tropick be compared and it will be manifest that the quantity of the longest day doth much more increase in places more remote than in the places more adjacent to the Aequator and therefore the encrease of the longest day doth more augment than the encrease of the distance of the places from the Aequator Note what hath been said and shewed concerning the longest day that is true of all the daies of one half of the year and is demonstrated after the same manner if instead of the Tropick of Cancer the Parallel of the place be taken And therefore although Generals must be delivered generally yet because the Doctrine of Climates especially requireth the Explication of the increase of the longest day therefore we do not observe in this Doctrine that Law 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Proposition X. If so many places or Parallels are so taken between the Aequator and
above almost maketh up and moderateth them To wit in the Regions of the Northern Temperate Zone it is Spring and Summer the Sun going from Aries by Cancer to Libra because then he is more near them Then the Sun going from Libra through Capricorn to Aries it is Autumn and Winter But in the Southern Temperate Zone the matter is contrary neither can those other causes altogether disable the force of this first and induce a new course of the seasons and be able to alter the times as in the Torrid Zone 2. Yet those Seasons of divers places vary so that in one place there may be more Heat or Cold or Rain than in another although the places lie in the same Climate but yet they cause not the Winter to be changed into Summer or Summer into Winter A Rocky Marshish and Maritim Land findeth somewhat another degree of heat or cold than Vallies or a Chalk and Maritim Land 3. The places in the Tropicks for the most part in the Summer have an excessive heat others a Pluvial Season so that they almost approach to the nature of the places of the Torrid Zone So in the part of the Kingdom of Guzarat lying without the Tropick at the same time the wet and dry months are observed which in the part lying beyond the Aequator the Summer is changed into a Pluvial Season yet then there is greater heat than the dry part of the year where they have a moderate cold and in truth in the places of the Temperate Zones we judg the Summer and Winter not from the drought and rains but from the heat and cold Now in the Coasts of Persia and Ormus there is so great heat without Rains in the Summer by reason of the vicinity of the Sun rhat both the Men and their Wives ly in Cisterns full of Water The like heat is in Arabia The Regions of Africa on the Mediterranean Sea are called the coast of Barbary Throughout all Barbary the middle of October being past Showers and Cold begin to increase and in December and January the cold is perceived more intense and that only in the morning and withal so remiss that the Fire is not desired February taketh away the greatest part of the cold from the Winter but yet it is so inconstant that sometimes 5 or 6 times in one day the Air changeth In the month of March the North and West Winds blow violently and cause whole trees to be vested with blossoms April giveth form almost to all Fruits so that the entrance of May and the end of April is wont naturally to produce Cherries In the middle of May they gather Figs and in the middle of June in some places are ripe Grapes Of the seasons of the year of Barbary the Figs or Autumn are gathered in August and there is no greater plenty of Figs and Pears than in September There is not so great intemperies of the year in those places but that the three months of the Spring are always temperate The entrance of the Spring that is the Terrestrial not the Celestial is as they reckon on the 15th of February and the end the 18th of May in all which time the Air is most grateful to them If from the 25th of April to the 5 of May they have no Rain they esteem the same as ominous They count their Summer even to the 16th of August at which time they have a very hot and serene Air. Their Autumn from the 17 of August to the 16 of November and they have that for two months to wit August and September yet not great That which is included between the 15 of August and the 15 of September was wont to be termed by the Antients the Furnace of the whole year and that because it produced Figs Pears and that kind of Fruit to maturity From the 15 of November they reckoned their Winter which they extend to the 14 of February At the entrance of this they begin to till their Land which is the plain but the mountainous in the month of October The Africans have a certain perswasion that the year hath 40 very hot days and on the other side so many cold The Opinion of the Arabians days which they say begin from the 12 of December They begin the Aequinoxes on the 16 of March and on the 16 of September Their Solstices on the 16 of June and the 16 of December The end of their Autumn all their Winter and a good part of their Spring is full of violent Winds accompanied with Hail Lightnings and dreadful Thunders neither is there wanting in many places of Barbary an abundance of Snow In Mount Atlas 7 degrees distant from the Tropick of Cancer they divide the year only into two parts for from October even to April they have a continual Winter and from April again to October they have Summer In this there is no day in which the Mountains tops glitter with Snow The seasons of Numidia In Numidia the parts of the year swiftly pass away for in May they reap their Corn in October they gather their Dates but from the middle of September to January a violent Frost continueth October abstaining from Rains all hopes of Sowing is taken from the Husbandman the same hapneth if that April produceth not Pluvial Water Leo Astricanus remembreth many Mountains of Snow in Africa not far from the Tropick of Cancer Of China The North part of China although no more remote from the Aequator than Italy yet it hath a cold more sharp for great Rivers and Lakes are congealed up with Frost the cause of which is not yet sufficiently known except we should refer it to the Snowy Mountains of Tartaria not far remote to the avoyding of which cold they abound with the Skins of Foxes and Scythilian Rats New England New England although it lie in 42 degrees of North Latitude and therefore no more removed from the Aequator than Italy yet in the month of June when Sir Francis Drake was there the Air was so vehement cold that he was compelled to sayl back to the South for the Mountains were then covered with Snow The cause is the Frigid temperature of the Earth being Stony The seasons of Aegypt In Aegypt which is bounded with the Tropick of Cancer the Spring and Temperate Season of the year is observed about January and February The Summer beginneth with March and April and continueth June July and August The Autumn possesseth September and October The Winter hath November and December About the beginning of April they Reap their Corn and presently thresh it After the 20 of May not an Ear of Corn is to be seen in the Fields no Fruits on the trees On the Ides of June the inundation of the Nilus beginneth The seasons in the streights of Magellan In the Streights of Magellan and the adjacent Regions although they be no more distant from the Aequator than our parts
departed from the Meridian for that is equal to the Latitude of the place Proposition X. The Places of the Earth scituated under the Aequator have no Latitude or elevation of the Pole but both the Poles lye in their Horizon The places under the Aequator have no Latitude The places under the Pole have the Latitude of 90 degrees viz. the Pole in the Vertex and the Aequator in the Horizon The places between the Poles and the Aequator have a less Latitude than Ninety Degrees The truth of this Proposition is evident therefore it needs no Explication Proposition XI If we are either on the Sea or Land and know not the place where we are let the Latitude be found to exhibit that Parallel in the Globe that we may be certain that we are in one point of it This is done after the same manner that we have shewed in the sixth Proposition viz. a Parallel must be described at the given or observed Latitude and this is the Parallel demanded The same is also easie in Maps CHAP. XXIV Of the division of the Earth into Zones and the Celestial Appearances in the divers Zones Proposition I. From the proper or Annual motion of the Sun there ariseth a certain division of the Superficies of the Earth into five parts or Zones THe division of the Earth into 5 Zones See Scheme SEEing that the Sun doth not always continue in the Aequator but declining from it describeth by his Motion a path which cutteth the Aequator so that his greatest declination is in 23½ degrees as well towards the North from the Aequator as towards the South in which declination he describeth the Tropicks of Cancer and Capricorn thence it is that he is not perpetually vertical to the Places lying under the Aequator neither doth he always keep one distance from other places for sometimes he is more nigh and sometimes more remote from a certain place and variously changeth heat cold rain and other conditions of the Seasons These which we have now spoken of may be shewed as well on the Globe as in Maps A Zone is termed a part of the Earth included within the Tropick and the Polary Circle A Zone what And because there are two Tropicks and two Polary Circles thence it cometh to pass that there are five Zones viz. 1. Torrid 2. Temperate and 2. Frigid Torrid zone The Torrid Zone is that part of the Earth which lieth between the Tropicks of Cancer and Capricorn Temperate Zones The Temperate Zones which lye between one of the Tropicks and the adjacent Polary Circle the Northernly Temperate Zone is that which lieth between the Tropick of Cancer and the Artick Circle the Southernly temperate Zone is that which lieth between the Tropick of Capricorn and the Antartick Circle Frigid Zones The Frigid or Cold Zones are those parts of the Earth which lye about the Poles even to the Polary Circles and they are as well Northernly as Southernly cold Circles Proposition II. The Places according to their Latitudes in what Zones they are in Those places of the Earth whose Latitude is less than 23 degrees and 30 minutes they lie in the Torrid Zone Those whose Latitude is 23 degrees and 30 minutes they lie in the Tropicks viz. in the extremity of the Torrid Zone Those whose Latitude is greater than 23 degrees and 30 minutes and less than 66 degrees and 30 minutes they lie in the Temperate Zone Those whose Latitude is 66 degrees and 30 minutes they lie in the Polary Circles viz. in the term of the Temperate Zone Those whose Latitude is greater than 66 degrees and 30 minutes they lie in the Frigid Zones These are manifest from the definitions of the Tropical and Polary Circles which we have treated of in the 23th Chapter Proposition III. The Aequator of the Earth passeth through these Places Places which the Aequator passeth through Through the Island of St. Thomas in the great Bay of Africa which is called the Aethiopian Ocean Through Aethiopia Through the Indian Ocean Through the middle of Sumatra Through the Chersonesus of Malacca and other Islands in the Indian Ocean Through the Moluccas themselves and the Pacifick Ocean Through the entrance of the Province of Peruana By the Lake Parima Through the Atlantick Ocean even to the Island of St. Thomas The Aequator divideth the Torrid Zone into two equal parts so that they may deservedly be termed two Torrid Zones one Northern and the other Southern These Places lie in the Torrid Zone Places which lie in the Torrid Zone The greatest part of Africa the Indian Ocean Abyssine part of Arabia Cambaja India The Isles of the Indian Sea Java Ceilan Peruvia Mexico great part of the Atlantick Ocean the Island of St. Helena Brazil New Guinee Places which the Tropick of Cancer passeth through The Tropick of Cancer passeth through these places viz. through the Confines of Lybia and other places in the Inland Africa through Syena in Aethiopia Thence passing the Red Sea beyond the Mountain Sinai and Mecca the Birth-place of Mahomet it passeth through Arabia Felix hence it entreth the Indian Ocean and toucheth the borders of Persia and passeth over Cambaja India and the Borders of China until it come into the Pacifick Sea which being passed over it falleth in with California into the Kingdom of Mexico and again entring into the Atlantick Ocean passing the Gulph of Mexico it sweepeth the Coast of the Isle of Cuba and thence returneth to the Occidental shoar of Africa Places which the Tropick of Capricorn passeth through The Tropick of Capricorn passeth through very few places of the Earth its greatest part lying in the Sea The places through which it passeth are through the Tongue of Africa through Monomotapa Madagascar the Indian Ocean New Guinee the Pacifick Ocean Peru Brazil and through the Atlantick Ocean Places scituate in the Northern and Southern temperate Zones Many places in the Earth lie in the Northern temperate Zone and those almost all known and inhabited viz. all Europe all Asia except part of India Malacca and the Isles of the Indian Ocean great part of America Septentrionalis and part of the Atlantick and Pacifick Ocean In the Southern temperate Zone few places lie and those not fully known with a large portion of the Sea viz. part of the Prominent part of Africa Monomotapa a great part of Terra Magellanica part of Brazil Chili the Streights of Magellan and a great part of the Atlantick Indian and Pacifick Ocean Places which the Artick and Antartick Polary Circles pass through The Artick Polary Circle passeth almost through the middle of Izland through the Upper Norway the North Sea Lapland the Bay of Russia Samojeda Tartaria America Septentrionalis and Groenland The Antartick Polary Circle passeth through Terra Magellanica of which we have little or no knowledge at this day Places which lie in the cold Northern and Southern
or Heaven which the Meridian line being found is easie to do by the Mariners Compass or the Magnetick Needle The Globe being thus placed at every moment of the day when the Sun shineth on the Globe may be seen the part of the Earth illuminated and the part not illuminated Those places which lie in the middle Semicircle of the part illuminated are those which will have the Meridies at that moment of time To those which are seated in the Oriental Semicircle dividing the illuminated part from the part not illuminated the Sun setteth but to those which are in the Occidental Semicircle separating the illuminated part from the part not illuminated the Sun riseth To find out the place of the Sun in the Ecliptick let the Needle or Spherical Gromon be moved hither and thither perpendicularly about the middle of the part illuminated until it maketh no shadow and let the point in the Globe be noted 〈◊〉 for this being brought to the Meridian here will shew the declination of the Ecliptick point in which the Sun is at the time of the Observation whence according to the condition of the time to wit Spring Summer Autumn or Winter the place of the Sun shall be known and thence the day of the year Also the place in the Globe unto which the Needle being affixed gave no shadow is that to which the Sun is vertical at that moment of time and the Parallel passing through this place will exhibit all the places in which the Sun will be vertical on that day Moreover to find the hour of the place in which the Globe is so placed or hung let that place be brought to the Meridian to which the Sun is vertical the Index to the 12th hour of the horary Circle and let the Globe be turned round until our place or that in which the Globe is seated do come to the Meridian the Index will shew the hour But because the Globe cannot be turned round when it is affixed by the Iron Style to the Horizontal plain therefore it will be convenient that the Quadrant be tied to the Pole or part of the Circle of the Periphery 113 â— â— for here the Arch being brought to the place of the Needle will shew the declination of the Sun from the Aequator whence the place of the Sun and the day of the year shall be found The same Arch will shew the degree in the Aequator from whence if that the degrees be numbred to the Brazen Meridian and these degrees be changed into hours or parts of hours Fifteen Degrees make an Hour you shall have the hour of the place If so be that the Sun be between the Occident and the Brazen Meridian that is of our place but if that it be between the East and our Meridian the hour found out must be subtracted from 12 and the remaining number will shew the hours from Midnight If that such a Brazen Arch be adjoyned to the Pole of the Globe as I have described 113 ½ degrees it may be bored through from the end even to 47 degrees that is from the departure of the Sun from the Aequator and a turning Plate be inserted in it which may bear the perpendicular Style and so there will neither be need of a Needle or of a Spherical Gnomon and the operation will be less obnoxious to errour Proposition II. The Terrestrial Globe being â—o placed as in the former Proposition is declared it will also shew when the Moon shineth to what People at any moment of time in which it is above our Horizon it is conspicuous to whom it ariseth to whom it setteth and to whom it is vertical These are all manifest from the preceding Proposition See Proposit 1. Proposition III. By how much the places of the Earth are remote from the Parallel of the Sun on any day by so much the Sun is elevated to a lesser Altitude in the same hours above their Horizon Let the places in the same Meridian be taken in the Globe for these do reckon all the same hours and that at once then let a Parallel be described for any assumed day and it will be manifest that any point of this Parallel is farther distant from the more remote places than from the places more near The Sun therefore being above the points of this Parallel will be farther distant from the Vertex of the remoter places than from the Vertex of those that are nearer and therefore he shall be less elevated over the Horizon of those places than of these Proposition IV. By how much the places of the Earth are more remote from the Aequator or more near the Pole by so much the more the parts of the Horizon are distant in which the Sun riseth on the day of the Solstice and the day of the Winter as also those in which he setteth The same is true concerning the Moon and all the Planets Take what places you please of a diverse distance from the Aequator and let the Pole be elevated for the Latitude of every one of them and let the points be noted in the Horizon in which the Tropicks of Capricorn and Cancer cut it A comparison being made the truth of the Proposition will appear this is also shewed the same way by how much the places are more remote from the Aequator by so much the more the Sun in his Aequinoctial rising is distant in the East on every day of the year The Astronomers term it the rising Amplitude Proposition V. Stars placed between the Parallel of any place lying without the Aequator and the Pole are less elevated above the Horizon of the places between this Parallel and the other Pole of those scituated there than above the Horizon of the places scituated between this Parallel and the nearer Pole Of the elevation of Stars c. The Parallel of any Star may be designed on the Terrestrial Globe or a point only noted for a Star and any place more remote from the Pole being assumed designeth the Parallel of the place Then taking another place scituated towards the other Pole the stay of the Star above the Horizon of both places may be found and the truth of the Proposition will be manifest Proposition VI. In places scituate in and near the Aequator the Sun and Stars directly ascend above the Horizon even to the Meridian and so descend again but in places scituated above the Aequator they obliquely ascend and descend and so much the more obliquely by how much the place is more remote from the Aequator Of the ascension and descension of the Sun and Stars Let any Parallel of the Sun be described on the Globe such as some already are delineated on the Globe viz. the Aequator the Tropicks and some Intermedial ones then let the Poles be placed in the very Horizon that it may be the Horizon of the places of the Aequator and it will be evident that the points of the
Parallels directly ascend from the Horizon to the Meridian Then let the Pole be elevated for the Latitude of any other places and it will appear that the Parallels are so much the more oblique to the Horizon by how much the more the Pole is elevated that is by the Wooden Horizon becometh the Horizon of the places more remote from the Aequator or nearer to the Pole Proposition VII By how much the place is more remote from the Aequator by so much the more the Signs of the Zodiack and the other Constellations require the greater time to arise and set and they pass through the Meridians of all places at an equal time Let two places be taken on the Globe unequally distant from the Aequator and let the Pole be elevated and observed separately for each of them how much time any Sign of the Zodiack requireth to ascend above the Horizon viz. the entrance of the Sign being brought to the Oriental Horizon let the Index be placed at the 12th hour and the Globe be turned round until the whole Sign be rising the Index will shew the hours elapsed in the space whilst the Sign arose for by the comparison of the time the truth of the Proposition will be manifest Proposition VIII The day of the year being given to find or shew on the Globe those places in which the Sun ariseth in any given quarter To find the rising of the Sun in any quarter by the Globe This Problem and those that follow should be propounded and resolved concerning the Earth it self if that we would act according to Art for these affections belong unto it but they are propounded concerning the Globe because here it representeth the Earth although another method must be used in the Earth or another construction which although it can only be comprehended by the mind is sufficient that it may hinder in the practice by reason of the obstacles This is the same with that Problem The day and the quarter being given in which the rising of the Sun was observed to find the Latitude of that place or its Parallel in any point of which it is manifest that we are placed See Chap. 23. Proposit 11. The Solution of which we have delivered in the 23 Chapter Proposition 11. Proposition IX The day and the hour or part of the hour being given to shew the place on the Globe to which the Sun is then vertical First let the place of the Sun from the given day being found be noted on the Ecliptick of the Globe and that being brought to the Meridian let a mark be made with a Chalk on the supereminent point then let those places be found in whose Meridian the Sun was at the given moment of time and let them be brought to the Brazen Meridian These being done that place which is subject to the noted point of the Meridian is the place which is demanded viz. that to which the Sun is vertical at the given moment of time Proposition X. Further note The day and the hour being given to shew all the places on the Globe from whose Vertex the Sun is distant the given degrees at that hour but the given degrees must not exceed a hundred and eighty Or the day and the hour being given to shew on the Globe those places above whose Horizon the Sun hath the given Altitude or the given depression beneath it but the Altitude given must not exceed 90 degrees as likewise the depression Let the place be found on the Globe to which the Sun is vertical at the hour given and let this be brought to the Meridian and let the Quadrant be affixed to the imminent point of the Meridian Let the degree of distance from the Vertex given be noted and the Quadrant be turned round the Globe remaining immovable all the places of the Earth through which the noted degree of the Quadrant passeth are those from whom the Sun hath the given distance or above whose Horizon the Sun hath the given Altitude Proposition XI At the given hour of the day to shew on the Globe all plains unto which the Sun riseth and setteth and to which he is fixed at the Meridian and all that are illuminated and not illuminated Further concerning the rising and setting of the Sun found out by the Globe at any day or hour of the day Let the place be found in the Globe to which the Sun at the time given is vertical and let the place be brought to the Meridian and the Pole elevated for the Latitude of that place or let that place be placed in the vertex of the Horizon So all those places which are discovered under the Semicircle of the Meridian above the Horizon shall have the Meridies but those places which are beheld in the Oriental Semicircle of the Horizon are those to which the Sun then setteth but to those which lie in the Occidental Semicircle of the Horizon the Sun riseth at the given time and all the places which are above the Horizon are illuminated by the Sun on the contrary all the places scituated beneath the same then want the presence of the Sun Note that the Problem must be understood of the rising and setting of the body of the Center of the Sun for the body of the Sun illustrateth part of the Earth somewhat bigger than the Hemisphere which how big it is shall be discovered in the following Proposition Therefore we may shew the places to which the Sun riseth or setteth when we have Noon or Midnight And contrariwise those in which he setteth when he ariseth to us who then have Midnight or Mid-day Proposition XII The Semidiameter of the Sun and Earth being given and the distance of the Sun from the Earth being known to find out the part of the Earth which the Sun illuminateth See Scheme Let the Semidiameter of the Earth be A B A C A the Center A B C D E the greatest circle of the Earth S the Center of the Sun S L S O the Semidiameter of the Sun L B O C the rays touching the Globe of the Sun and Earth for these distinguish the part illuminated from the part not illuminated therefore the Arch B D C representeth the part of the superficies of the Earth illuminated and the Arch BLC the part not illuminated Let the Tangents LB O C be extended until they concur in R and B N parallels to A S therefore in the Triangle B N L let N L be given the excess S L above A B and B N of equal distance to A S the Angle B N L is direct because that B L toucheth the Circle Wherefore in the Triangle B L N let the Angle N B L be found according to this Proposition that as B N is to N L so are the whole signs to the Tangent of the Angle N B L. Moreover the two Angles L N B N B L are together equal to one streight or 90
be found in the Hemisphere only except the Horizon of the Pole which is the very Aequator So we shall have three or four chief Points through which the Horizon ought to pass To find out the other Points there is no more commodious way than by the benefit of the Globe viz. let the Pole be Elevated for the Latitude of the place assumed then in every Parallel let one Point be chosen through which the first Meridian passeth and let that be brought to the Meridian which done let the degree under the Meridian be noted and so you must do in every Parallel These being noted let so many degrees be reckoned on both sides from every Parallel from the Meridian of the place given in the Map on the Aequator viz. for 10th 20th 30th and so on and where the Meridians cut the convenient Parallels they shall be the points demanded to wit through which the Horizon is to be drawn and the scituation of the other places may be examined in some measure at that By this Method the whole Superficies of the Earth may almost be represented on one Table if that either of the Poles viz. the Antarctick be assumed for the Eye if a Table or Glass plain be taken of any Parallel near the Pole for instance the plain of the Arctick Pole and the Antarctick Circle on one plain neither doth any thing else remain to be done or added to the former construction but that the Meridian Lines should be protracted and the Parallels drawn from the other part of the Aequator Then let the whole Ecliptick be drawn and if you please let the Horizon be compleated But seeing that the parts and degrees scituated beyond the Aequator towards the Antarctick Pole by this Mode would become far greater than the parts about and in the Aequator which is contrary to the truth of the matter therefore it is better to make the projecture on two Hemispheres that one may shew the Arctick Orb the other the Antarctick Tables described according to this Method are very few to general Maps of Right Lines two other Maps very small described in this Method are wont to be added whereof one exhibiteth the Regions about the Arctick Pole the other those about the Antarctick which the Reader may look upon for the better understanding of what hath been said But these are better learned from practice than from precepts The second Mode the Eye being placed in the plain of the Aequator The second Mode See Scheme The preceeding Mode of describing of Geographical Maps doth neither fitly shew the Magnitudes and scituation of places neither is commodious to describe the Hemisphere intercepted between the two Poles and to represent all the places lying in the same Meridian moreover it seemeth to be repugnant to our conception that the Pole of the Earth should fall into the Center and therefore those described Tables afford a more difficult imagination Therefore another Method hath been found which is somewhat more hard than the former but more aptly representeth the places of the Earth and removeth the Pole from the Aequator For the conceiving of this Method we must understand the Superficies of the Earth to be cut into two Hemispheres from the whole Periphery of the Meridian and in two Tables we exhibit those Hemispheres one in one the other in the gther The Eye is placed in the Point of the Aequator which is removed 90 degrees from the first Meridian the Table or Glass in which this representation ought to be made is assumed the place of the first Meridian and Hemisphere which lyeth beneath that Plain in respect of the Eye is taken to represent it on the Plain In this form of projecture the Semicircle of the Aequator becometh a right Line and that Meridian which is distant from the first 90 degrees unto which the eye is conceived eminent will also become the Right Line all the other Meridians and all the Parallels of the Aequator become the Arches of the Circles because their Cones are cut from the Plain of the Tables by a subcontrary Section The explication of which must be demanded from the Conical Doctrine and may better be shewed than expressed But the Ecliptick becometh a portion of the Eclipsis for the Cause alledged in the former Method The description Mathematically explained This Description is thus made the point E being taken for the Center in the Table a great or small Periphery of the Circle is described A B C D as we desire to have the Table great or small This representeth the first Meridian and its opposite viz. the Diameter B D being drawn there arise two Semiperipheries whereof one B A D is the first Meridian the other B C D is the opposite or of Longitude 180. This Diameter B D representeth the Meridian 90 degrees distant from the first and his point D is one Pole viz. the Arctick but the point D is the Pole Antarctick the Diameter A C to B D is the perpendicular Line of the Aequator Let these Quadrants A B B C C D D A be divided every one into 90 degrees Moreover we must do thus for the representation of the Meridians and Parallels or for the finding out the Arches of the Meridians and Parallels First the Line of the Aequator A C must be divided into its degrees to wit 180 because it only sheweth half the Aequator or A E E C into 90 after this Mode from the point D let the Semiperipheries right Lines A B C be drawn to every degree or which is as well let the Rule be applyed to the point D and to every degree of the Semiperiphery A B C these Lines shall cut the Line of the Aequator into 180 parts which shall represent the degrees which are the degrees of Longitude and therefore the numbers 1 2 3 4 and the like must be ascribed beginning from the first Meridian D A B. Through every one of these points 1 2 3 and both the Poles B D the Arches of the Circles must be described which shall represent the Meridians But how the Periphery must be described through these three given points for Example B D or B 2 D and the like is taught by Geometry viz. you must find the Centers for every Periphery to be described which Centers are placed in the very Line of the Aequator as is the Center E of the Meridian D A B. Those points are found according to Euclids Method Proposition 1. Lib. 3. if the Lines B 1 B 2 B 3 See Euclide lib. 3. Proposition 1. c. be doubly cut by the perpendicular lines this is most easy by the application of the Rule where these perpendicular lines fall into the protracted Line E C of the Aequator if there be need there are the Centers for the describing of the Arches B 1 D B 2 D c. But the Centers of the Arches B 91 D B 92 D B 93 D c.
two kinds of scituation the quarter of the second place is not varied at the intermedial places for Example Let Amsterdam be taken for the first place from whence the Voyage is to be begun and Fernambuck in Brasilia for the second or unto which the Voyage is appointed Let Amsterdam therefore be brought to the Brass Meridian and let the Pole be Elevated for the Latitude of the same for so the Wooden Horizon representeth the Horizon of the place let the Quadrant be affixed to the Vertex and let it be applyed to Fernambuck it will shew the quarter in the Horizon in which Fernambuck lyeth from Amsterdam And the Arch interjected between these two places exhibiteth on the Globe the intermedial points It must therefore be shewed that the quarters in which Fernambuck lyeth from every one of these points are not the same but all divers or that from every one of those intermedial places Fernambuck doth not lie towards one and the same quarter For the understanding of this we must repeat from the preceding Doctrine that the Angle with the Meridian of this assumed place maketh with the Vertical passing through the other place sheweth the quarter of another place from some one place assumed or the Arch of the Horizon intercepted between the Meridian and this Vertical as the Angle sheweth the quarter of Fernambuck from Amsterdam which the Quadrant with the Brass Meridian maketh which is of Amsterdam it self Therefore to prove the truth of this Proposition let what points you please be taken between Amsterdam and Fernambuck in the Arch subject to the Quadrant and let the Meridians passing through by them be conceived It is best to take those points through which on the Globe the Meridians pass or the Circles of Longitude because therefore the Quadrant passeth through every one of these places and Fernambuck it self it will represent the Vertical of every place in which Fernambuck lyeth from them Therefore the Angles which it maketh with the Meridians of each place are the Angles of Position and shew the quarters in which or towards which Fernambuck lyeth from every intermedial place Now these Angles are unequal and of a different Magnitude therefore the quarters also towards which Fernambuck lyeth from those places are divers Now that these Angles are unequal is manifest from the very sight or more evident if that by any interval of the Compass you draw an Arch from each point and measure these Arches intercepted between each Meridian and the Vertical or if that we have ready by it self a Crooked portion which may be fitted to the Superficies of the Globe or if that the places themselves be brought to the Brazen Meridian and the Pole be Elevated for their Latitude let the Quadrant be applyed to the Vertex and to Fernambuck and in that scituation let the degrees of the Arch of the Horizon be reckoned Streight lined and Sea Maps are defective Corollary Therefore the streight lined and Sea Maps are very defective which do so represent the places that if that any two places be taken at one of which the scituation or quarter of the other be examined this other doth seem to be in one and the same quarter from the intermedial places which yet is false The cause of the fault is that they exhibit the Meridians Parallels which yet do meet in the Poles but Seamen regard not this fault so that they do but relate the Course or quarter which they ought to have observed in Sailing from one place to another Proposition IV. If a Voyage be to be made or that a Ship be to Sail from one place to another which two places are not in one Meridian or both of them in the Aequator by a most short cut or by this means that it may never recede from the interposed Arch of the Vertical in such a Voyage the quarter is changed every moment or the quarter becometh another and another into which the Voyage is to be taken or the Ship is to be Sailed This Proposition is manifest from the foregoing See Prop. 3. For let the Voyage be taken from Amsterdam to Fernambuck by the nearest way that is through the Arch of the Quadrant affixed at Amsterdam and passing through by Fernambuck Because therefore every where in the whole Voyage or in every point the Voyage is directed towards Fernambuck and it is shewed in the precedent Proposition that the quarters are divers towards which from those middle points Fernambuck lyeth therefore it is manifest that the quarter becometh another and another in every moment and in each point into which the Ship is to Sail or to be Sailed that it may respect Fernambuck But if that the places be scituated in one Meridian or if that both be in the Aequator the Case is otherwise For in them the same quarter of the Voyage of the North or South remaineth in these the Cardinal quarter of the East or West Proposition V. A Voyage cannot be so undertaken or a Ship so directed that it may tend in each moment to other and other quarters but for some time at the least whilst it is moved it tendeth to one and the same quarter in appearance Therefore whilst we are to Sail from one place to another such a way or line of a way is most convenient whose every two near points are scituated in one and the same quarter in shew although that this way be not the shortest A Ship in a moment cannot move from one quarter to another A Ship cannot tend from one quarter to another in a moment of time but whilst that it is moved for some time at the least it tendeth to it Moreover it can by no means be done that the Seamen should know the quarters unto which the Ship should be Sailed if that another quarter were so often to be assumed Therefore it is evident that that passage between two places is most commodious for Navigation whose every two vicine points are scituated in one and the same quarter so that the Ship may be continually directed unto one quarter and to come by such a direction to the place appointed This being supposed let us enquire what way is thence for the Motion of the Ship Which way indeed if that the places be scituated in one Meridian shall be part of the Meridian it self if in the Aequator that way shall be a portion of the Aequator it self if in one Parallel it shall be a part of this Parallel if in any other Circle besides these that way shall be another Line not that Circle as we shall shew in the following Propositions Proposition VI. If that a Voyage be appointed or that a Ship be directed to the North or South quarter that is if that the place from whence and the place unto which be in one Meridian the line of the Motion of the Ship it self shall be a part of the Meridian It is proved from the first Proposition of