Selected quad for the lemma: earth_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
earth_n	north_n	pole_n	south_n	3,753	5	10.5697	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A48262	Mathematicall recreations. Or, A collection of many problemes, extracted out of the ancient and modern philosophers as secrets and experiments in arithmetick, geometry, cosmographie, horologiographie, astronomie, navigation, musick, opticks, architecture, statick, mechanicks, chemistry, water-works, fire-works, &c. Not vulgarly manifest till now. Written first in Greeke and Latin, lately compi'ld in French, by Henry Van Etten, and now in English, with the examinations and augmentations of divers modern mathematicians whereunto is added the description and use of the generall horologicall ring: and the double horizontall diall. Invented and written by William Oughtred.; Récréation mathématique. English.	Oughtred, William, 1575-1660. aut	1653 (1653)	Wing L1790; ESTC R217635	140,825	339

having his head and feet upward PROBLEM XXV Of a Ladder by which two men ascending at one time the more they ascend the more they shall be asunder notwithstanding one being as high as another THis is most evident that if there were a Ladder halfe on this side of the Centre of the earth and the other halfe on the other side and that two at the Centre of the World at one instant being to ascend the one towards us and the other towards our Antipodes they should in ascending go farther and farther one from another notwithstanding both of them being of like height PROBLEM XXVI How it is that a man having but a Rod or Pole of Land doth bragge that he may in a right line passe from place to place above 3000 miles THe opening of this is easie forasmuch as he that possesseth a Rod of ground possesseth not only the exterior surface of the earth but is master also of that which extends even to the Centre of the earth and in this wise all heritages possessions are as so many Pyramides whose summets or points meet in the centre of the earth and the basis of them are nothing else but each mans possession field or visible quantity and therefore if there were made or imagined so to be made a descent to go to the bottome of the heritage which would reach to the centre of the earth it would be above 3000 miles in a right line as before PROBLEM XXVII How it is that a man standing upright and looking which way he will he looketh either true North or true South THis happeneth that if the partie be under either of the Poles for if he be under the North-pole then looking any way he looketh South because all the Meridians concurre in the Poles of the world and if he be under the South-pole he looks directly North by the same reason PROBLEM XXVIII To tell any one what number remaines after certaine operations being ended without asking any question BId him to think upon a number and will him to multiply it by what number you think convenient and to the pro●●ct bid him adde what number you please or 〈◊〉 that secretly you consider that it ma● be divided by that which multiplied and 〈…〉 divide the sum by the number which he 〈…〉 by and substract from this Quotient the number thought upon In the same time divide apart the number which was add●d by that which multiplied so then your Quotient shall be equall to his remainder wherefore without asking him any thing you shall tell him what did remaine which will seem strange to him that knoweth not the cause for example suppose he thought 7 which multiplied by 5 makes 35 to which adde 10 makes 45 which divided by 5 yields 9 from which if you take away one the number thought because the Multiplier divided by the Divisor gives the Quotient 1 the rest will be two which will be also proved if 10 the number which was added were divided by 5 viz. 2. PROBLEM XXIX Of the play with two severall things IT is a pleasure to see and consider how the science of numbers doth furnish us not only 〈…〉 recreate the spirits but also 〈…〉 knowledge of admirable things 〈…〉 measure be shewen in this 〈…〉 the meane time to produce alwayes some of them suppose that a man hold divers things in his hand as Gold and ●ilver and in one hand he held the Gold and in the other hand he held the Silver to know subtilly and by way of divination or artificially in which hand the Gold or Silver is attribu●e t● the Gold or suppose it have a certaine price and so likewise attribute to the Silver another price conditionally that the one be odd and the other even as for example bid h●m that the Gold be valued at 4 Crownes or Shillings and the Silver at ● Crownes or 3 Shillings or any other number so that one be odde and the other even as before then bid him triple that which is in the right hand double that which is in the left hand and bid him adde these two products together and aske him if it be even or odde if it be even then the Gold is in the right hand if odde the Gold is in the left hand PROBLEM XXX Two numbers being proposed unto two severall parties to tell which of these numbers is taken by each of them AS for example admit you had proposed unto two men whose names were Peter and John two numbers or pieces of money the one even and the other odde as 10. and 9. and let the one of them take one of the numbers and the other partie take the other number which they place privately to themselves how artificially according to the congruity and excellency of numbers to finde which of them did take 10. and which 9. without asking any qustion and this seems most subtill yet delivered howsoever differing little from the former and is thus performed Take privately to your selfe also two numbers the one even and the other odde as 4. and 3. then bid Peter that he double the number which he took and do you privately double also your greatest number then bid John to triple the number which he hath and do you the like upon your last number adde your two products together mark if it be even or odde then bid the two parties put their numbers together and bid them take the halfe of it which if they cannot do then immediately tell Peter he took 10. and John 9. because the aggregate of the double of 4. and the triple of 3. makes odde and such would be the aggregate or summe of the double of Peters number and Johns number if Peter had taken 10. if otherwise then they might have taken halfe and so John should have taken 10. and Peter 9. as suppose Peter had taken 10. the double is 20. and the triple of 9. the other ●umber is 27. which put together makes 47. odde in like manner the double of your number conceived in minde viz. 4. makes 8. and the triple of the 3. the other number makes 9. which set together makes 17. odde Now you cannot take the halfe of 17 nor 47. which argueth that Peter had the greater number for otherwise the double of 9. is 18. the triple of 10. is 30. which set together makes 48. the halfe of it may be taken therefore in such case Peter the took lesse number and John the greater and this being don cleanly carries much grace with it PROBLEM XXXI How to describe a Circle that shall touch 3 Points placed howsoever upon a plaine if they be not in a right line LEt the three points be A.B.C. put one foot of the Compasse upon A. and describe an Arch of a Circle at pleasure and placed at B. crosse that Arch in the two points E. and F. and placed in C. crosse the Arch in G. and H. then lay a ruler upon G.H. and draw

be indifferently had and here note that if the day be between the 13 of September and the 10 of March then the sunnes declination for that day must be taken out of the distance of the sunne from the zenith at noone so shall you have the Latitude as before PRBOLEM XCV Of the Climates of countreys and to finde in what C●imate any countrey is under CLimates as they are taken Geographically signifie nothing else but when the l●ngt● of the longest day of any place is half an houre longer or shorter than it is in another place and so of the sh●rtest day and this account to begin from the Equinoctia●l Circle seeing all Countreys under it have the shortest and longest day that can be but 12 houres But all other Countreys that are from the Equinoctiall Circle either towards the North or South of it unto the Poles themselves are said to be in some one Climate or other from the Equinoctiall to either of the Poles Circles which are in the Latitude of 66 degr 30 m. between each of which Polar Circles and the Equinoctial Circle there is accounted 24 Climates which differ one from another by halfe an hours time then from each Polar Circle to each Pole there are reckoned 6. other Climates which differ one from another by a moneths time so the whole earth is divided into 60 Climates 30 being allotted to the Northerne Hemisphere and 30● to the Southerne Hemispheare And here note that though these Climats which are betweene the Equinoctiall and the Polar Circles are equall one unto the other in respect of time to wit by halfe an houre yet the Latitude breadth or internall conteined between Climate and Climate is not equall and by how much any Climate is farther from the Equinoctiall than another Climate by so much the lesser is the intervall between that Climate and the next so those that are nearest the Equinoctial are largest and those which are farthest off most contracted and to finde what Climate any Countrey is under subtract the length of an Equinoctiall day to wit 12 houres from the length of the longest day of that Countrey the remainder being doubled shews the Climate So at London the longest day is neare 16 houres and a halfe 12 taken from it there remaines 4 houres and a halfe which doubled makes 9 halfe houres that is 9 Climates so London is in the 9 climate PROBLEM XCVI Of Longitude and Latitude of the Earth and of the Starres LOngitude of a Countrey or place is an arcke of the Aequator conteined between the Meridian of the Azores and the Meridian of the place and the greatest Longitude that can be is 360 degrees Note That the first Meridian may be taken at pleasure upon the Terrestriall Globe or Mappe for that some of the ancient Astronomers would have it at Hercules Pillars which is at the straights at Gibraltar Ptolomy placed it at the Canary Isl●nds but now in these latter times it is held to be neare the Azores But why it was first placed by Ptolomy at the Canary Islands were because that in his time these Islands were the farthest westerne parts of the world that vvas then discovered And vvhy it reteines his place novv at Saint Michaels neare the Azores is that because of many accurate observations made of late by many expert Navigators and Mathematicians they have found the Needle there to have no variation but to point North and South that is to each Pole of the world and why the Longitude from thence is accounted Eastwards is from the motion of the Sunne Eastward or that Ptolomy and others did hold it more convenient to begin from the Westerne part of the world and so account the Longitude Eastward from Countrey to Countrey that was then knowne till they came to the Easterne part of Asia rather than to make a beginning upon that which was unknowne and having made up their account of reckoning the Longitude from the Westerne part to the Eastern part of the world knowne they supposed the rest to be all sea which since their deaths hath been found almost to be another habitable world To finde the Longitude of a Countrey IF it be upon the Globe bring the Countrey to the Brasen Meridian and whatsoever degree that Meridian cuts in the Equinoctiall that degree is the Longitude of that Place if it be in a Mappe then mark what Meridian passeth over it so have you the Longitude thereof if no Meridian passe over it then take a paire of Compasses and measure the distance betweene the Place and the next Meridian and apply it to the divided parallel or Aequator so have you the Longitude required Of the Latitude of Countreys LAtitude of a Countrey is the distance of a Countrey from the Equinoctiall or it is an Arke of the Meridian conteined between the Zenith of the place and the Aequator which is two-fold viz. either North-Latitude or South-Latitude either of which extendeth from the Equinoctiall to either Pole so the greatest Latitude that can be is but 90 degrees If any Northern Countrey have the Artick Circle verticall which is in the Latitude of 66. gr 30. m. the Sun will touch the Horizon in the North part thereof and the longest day will be there then 24 houres if the Countrey have lesse Latitude than 66. degrees 30. m. the Sun will rise and set but if it have more Latitude than 66. gr 30 m. it will be visible for many dayes and if the Countrey be under the Pole the Sun will make a Circular motion above the Earth and be visible for a half yeare so under the Pole there will be but one day and one night in the whole yeare To finde the latitude of Countreys IF it be upon a Globe bring the place to the Brasen Meridian and the number of degrees which it meeteth therewith is the Latitude of the place Or with a paire of Compasses take the distance between the Countrey and the Equinoctiall which applied unto the Equinoctiall will shew the Latitude of that Countrey which is equall to the Poles height if it be upon a Mappe Then mark what parallel passeth over the Countrey and where it crosseth the Meridian that shall be the Latitude but if ●o parallel passeth over it then take the distance betweene the place and the next parallel which applied to the divided Meridian from that parallel will shew the Latitude of that place To finde the distance of places IF it be upon a Globe then with a paire of Compasses take the distance betweene the two Places and apply it to the divided Meridian or Aequator and the number of degrees shall shew ●e distance each degree being 60. miles ●f it be in a Mappe according to Wrights pro●ection take the distance with a paire of Com●asses between the two places and apply this distance to the divided Meridian on the Mappe right against the two places so as many degrees as is conteined between the feet of the

side for as trees have their growth in winter because of their pores and these of the earth are shut up so in the spring when their pores are open and when the sappe and moisture is drawne by it there is not such cold on the North-side that it may be condensed at once But contrarily to the side which is South the heat may be such that in little time by continuance this moisture is dissipated greatly and cold is nothing but that which hardneth and contracteth the moisture of the tree and so converteth it into wood PROBLEM LII Three persons having taken Counters Cards or other things to finde how much each one hath taken CAuse the third party to take a number which ma● be divided by 4 and as often as he takes 4 let the second party take 7 and the first take 13 then cause them to put them all together and declare the summe of it which secretly divide by 3 and the Quotient is the double of the number which the third person did take Or cause the third to give unto the second and first as many as each of them hath then let the second give unto the first and third as many as each of them hath lastly let the third give unto the second and first as many as each of them hath and then aske how much one of them hath for they will have then all alike so halfe of that number is the number that the third person had at the first which knowne all is knowne PROBLEM LIII How to make a consort of musick of many parts with one voyce or one instrument only THis Probleme is resolved so that a finger or player upon an instrument be neare an Echo which answereth his voice or instrument and if the Echo answereth but once at a time he may make a double if twice then a triple if three times then an harmonie of foure parts for it must be such a one that is able to exercise both tune and note as occasion requires As when he begins ut before the Echo answer he may begin sol and pronounce it in the same tune that ●he Echo answereth by which meanes you ●ave a fifth agreeable consort of musick then in the same time that the Echo followeth to sound the second note sol he may sound forth another sol higher or lower to make an eight the most perfect consort of musick and so of others if he will continue his voice with the Echo and sing alone with two parts Now experience sheweth this to be true which often comes to passe in many Churches making one to beleeve that there are many more parts in the musick of a Quire then in effect truly there are because of the resounding and multiplying of the voic● and redoubling of the Quire PROBLEM LIIII T● make or describe an Ovall form or that which neare resembles unto it at one turning with a paire of common Compasses THere are many fine wayes in Geometricall practices to make an Ovall figure or one neare unto it by severall centres any of which I will not touch upon but shew how it may be done promptly upon one centre only In which I will say nothing of the Ovall forme which appeares when one describeth circles with the points of a common Compasses somewhat deep upon a skinne stretched forth hard which contracting it selfe in some parts of the skinne maketh an Ovall forme But it will more evidently appeare upon a Columne or Cylinder if paper be placed upon it then with a paire of Compasses describe as it were a circle upon it which paper afterwards being extended will not be circular but ovall-wise and a paire of Compasses may be so accommodated that it may be done also upon a plaine thus As let the length of the Ovall be H. K fasten 2 pinnes or nailes neare the end of that line as F. G and take a threed which is double to the length of G. H or F. K then if you take a Compasse which may have one foot lower than another with a spring between his legges and placing one foot of this Compasse in the Centre of the Ovall and guiding the threed by the other foot of the Compasses and so carrying it about the spring will help to describe and draw the Ovall forme But in stead of the Compasses it may be done with ones hand only as in the figure may appeare PROBLEM LV. Of a pu●se difficult to be opened IT is made to shut and open with Rings first at each side there is a strap or string as AB and CD at the end of which are 2 rings B D and the string CD passeth through the ring B so that it may not come out againe or be parted one from another and so that the ring B may slide up and downe upon the string CD then over the purse there is a piece of Leather EFGH which covers the opening of the purse and there is another piece of Leather AE which passeth through many rings which hath a slit towards the end I so great that the string BC may slide into it Now all the cunning or craft is how to make fast or to open the purse which consists in making the string BC slide through the side at I therefore bring down B to I then make the end I passe through the ring B and also D with his string to passe through the slit I so shall the purse be fast and then may the strings be put as before and it will seem difficult to discover how it was done Now to open the purse put through the end I through the ring B and then through the slit I by which you put through the string DC by this way the purse will be opened PROBLEM LVI Whether it is more hard and admirable without Compasses to make a perfect circle or being made to finde out the Centre of it IT is said that upon a time past two Mathematicians met and they would make tryall of their industry the one made instantly a Perfect circle without Compasses and the other immediately pointed out the Centre thereof with the point of a needle now which is the chiefest action it seems the first for to draw the most noblest figure upon a plaine Table without other help than the hand and the minde is full of admiration to finde the Centre is but to finde out only one point but to draw a round there must be almost infinite points equidistant from the Centre or middle that in conclusion it is both the Circle and the Centre together But contrarily it may seem that to finde the Centre is more difficult for what attention vivacitie and subtiltie must there be in the spirit in the eye in the hand which will chuse the true point amongst a thousand other points He that makes a circle keeps alwayes the same distance and is guided by a halfe distance to finish the rest but he that must finde the Centre must in the

his most glorious beauty This Glasse hath also a most excellent use in observing the body of the Moone in time of Eclipses for it augments it manifold and most manifestly shewes the true forme of the cloudy substance in the Sunne and by it is seene when the shadow of the earth begins to eclipse the Moon when totally she is over shadowed besides the celestiall uses which are made of this Glasse it hath another noble property it farre exceedeth the ordinary perspective Glasses which are used to see things remote upon the earth for as this Glasse reacheth up to the heavens and excelleth them there in his performance so on the earth it claimeth preheminency for the objects which are farthest remote and most obscure are seen plainer than those which are neere at hand scorning as it were all small and triviall services as leaving them to an inferiour help great use may be made of this Glass in discovering of Ships Armies c. Now the apparell or parts of this instrument or Glasse is very meane or simple which makes it the more admirable seeing it performes such great service having but a convex Glasse thickest in the middle to unite and amasse the rayes and mak the object the greater to the augmenting the visuall Angle as also a pipe or trunk to amasse the Species and hinder the greatness of the light which is about it to see well the object must be well inlightened and the eye in obscurity then there is adjoyned unto it a Glasse of a short sight to distinguish the rayes which the other would make more confused if alone As for the proportion of those Glasses to the Trunk though there be certaine rules to make them yet it is often by hazard that there is made an excellent one there being so many difficulties in the action therefore many ought to be tryed seeing that exact proportion in Geometricall calculation cannot serve for diversity of sights in the observation PROBLEM LXVII Of the Adamant or Magnes and the needles touched therewith WHo would beleeve if he saw not with his eyes that a needle of steel being once touched with the magnes turnes not once not a yeare but as long as the World lasteth his end towards the North and South yea though one remove it and turne it from his position it will come againe to his points of North and South Who would have ever thought that a brute stone black and ill formed touching a ring of Iron should hang it in the aire and that ring support a second that to support a third and so unto 10 12 or more according to the strength of the magnes making as it vvere a chaine without a line without souldering together or without any other thing to support them onely but a most occult and hidden vertue yet most evident in this effect which penetrateth insensibly from the first to the second from the second to the third c. What is there in the world that is more capable to cast a deeper astonishment in our minds than a great massie substance of Iron to hang in the aire in the middest of a building without any thing in the world touching it only but the aire As some histories assure us that by the aid of a Magnes or Adamant placed at the roof of one of the Turkish Synagogues in Meca the sepulchre of that infamous Mah●met rests suspended in the aire and Plinie in his naturall Historie writes that the Architect or Democrates did begin to vault the Temple of A●sin●e in Alexandria with store of magnes to produce the like deceit to hang the sepulchre of that Goddesse likewise in the aire I should passe the bounds of my counterpoise if I should divulge all the secrets of this stone and should expose my selfe to the laughter of the world if I should brag to shew others the cause how this appeareth than in its owne naturall sympathy for why is it that a magnes with one end will cast the Iron away attract it with the other from whence commeth it that all the magnes is not proper to give a true touch to the needle but only in the two Poles of the stone which is known by hanging the stone by a threed in the aire untill it be quiet or placed upon a peece of Cork in a dish of water or upon some thinne board for the Pole of the stone will then turne towards the Poles of the world and point out the North and South and so shew by which of these ends the needle is to be touched From whence comes it that there is a variation in the needle and pointeth not out truly the North and South of the world but only in some place of the earth How is it that the needle made with pegges and inclosed within two Glasses sheweth the height of the Pole being elevated as many degrees as the Pole is above the Horizon What 's the cause that fire and Garlick takes away the propertie of the magnes There are many great hidden mysteries in this stone which have troubled the heads of the most learned in all ages and to this time the world remaines ignorant of declaring the rrue cause thereof Some say that by help of the Magnes persons which are absent may know each others minde as if one being here at London and another at Prague in Germany if each of them had a needle touched with one magnes then the vertue is such that in the same time that the needle which is at Prague shall move this that is at London shall also provided that the parties have like secret notes or alphabets and the observation be at a set houre of the day or night and when the one party will declare unto the other then let that party move the needle to these letters which will declare the matter to the other and the moving of the other parties needle shall open his intention The invention is subtile but I doubt whether in the world there can be found so great a stone or such a Magnes which carries with it such vertue neither is it expedient for treasons would be then too frequent and open EXAMINATION THe experimentall difference of rejection and attraction proceeds not from the different nature of Stones but from the quality of the Iron and the vertue of the stone consisteth only and especially in his poles which being hanged in the Aire turnes one of his ends alwayes naturally towards the South and the other towards the North but if a rod of Iron be touched with one of the ends thereof it hath the like property in turning North and South as the magnes hath notwithstanding the end of the Iron Rod touched hath a contrary position to that end of the stone that touched it yet the same end will attract it and the other end reject it and so contrarily this may easily be experimented upon two needles touched with one or different stones though they have