Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	north_n	point_n	west_n	1,518	5	9.4299	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

here there must be found a number vvhich multiplied by 7 and then divided by 2 3 4 5 6 there may alvvayes remaine a number lesse by 1 than the Divisor Novv the first number vvhich arrives in this nature is 119 unto vvhich if 420 be added makes 539 vvhich also vvill do the same and so by adding 420 you may have other numbers to resolve this proposition PROBLEM XLVIII How many sorts of weights in the least manner must there be to weigh all sorts of things between 1 pound and 40 pound and so unto 121 364 pound TO vveigh things betvveen 1 and 40 take numbers in triple proportion so that their summe be equall or somewhat greater than 40 as are the numbers 1 3.9.27 I say that with ● such weights the first being of 1 pound the second being 3 pound the third being 9 pound and the fourth being 27 any weight between 1 and 40 pound may be weighed As admit to weigh 21 pound put unto the thing that is to be weighed the 9 pound weight then in the other ballance put 27 pound and 3 pound which doth counterpoise 21 pound and 9 pound and if 20 pound were to be weighed put to it in the ballance 9 and 1 and in the other ballance put 27 and 3 and so of others In the same manner take those 5 weights 1 3 9 27 81 you may weigh with them between 1 pound and 121 pound and taking those 6 weights as 1 3 9 2● 81 243 you may weigh even from 1 pound unto 364 pound this depends upon the property of continued proportionals the latter of which containing twice all the former PROBLEM XLIX Of a deceitfull ballance which being c●●●ty seemes i● be just because it hangs in aequilibrio not●ithstanding putting 12 pound in one ballance and 11 in the other it will remaine in aequilibrio ARistotle maketh mention of this ballance in his mechanick Questions and saith that the Merchants of purpose in his time used them to deceive the world the subtiltie or craft of which is thus that one arme of the ballance is longer then another by the same proportion that one weight is heavier then another As if the beame were 23 inches long and the handle placed so that 12 inches should be on one side of it and 11 inches on the other side conditionally that the shorter end should be as heavy as the longer a thing easie to be done then afterwards put into the ballance two unequal weights in such proportion as the parts of the beame have one unto another which is 12 to 11 but so that the greater be placed in the ballance which hangs upon the shorter part of the beame and the lesser weight in the other ballance it is most certaine that the ballances will hang in aequilibrio which will seem most sincere and just though it be most deceitfull abominable and false The reason of this is drawne from the experiments of Archimedes who shewes that two unequall weights will counterpoyse one another when there is like proportion betweene the parts of the beame that the handle separates and the vveights themselves for in one and the same counterpoise by hovv much it is farther from the Centre of the handle by so much it seems heavier therefore if there be a diversitie of distance that the ballances hang from the handle there must necessarily be an ineqality of weight in these ballances to make them hang in aequilibrio and to discover if there be deceit change the weight into the other ballance for as soone as the greater vveight is placed in the ballance that hangs on the longer parts of the beame it vvill vveigh dovvne the other instantly PROBLEM L. To heave or lift up a bottle with a straw TAke a stravv that is not bruised bovv it that it make an Angle and put it into the bottle so that the greatest end be in the neck then the Reed being put in the bovved part vvil cast side-vvise and make an Angle as in the figure may be seen then may you take the end vvhich is out of the bottle in your hand and heave up the bottle and it is so much surer by how much the Angle is acuter or sharper and the end which is bowed approacheth to the other perpendicular parts which come out of the bottle PROBLEM LI. How in the middle of a wood or desert without the sight of the Sunne Starres Shadow or Compasse to finde out the North or South or the foure Cardinall points of the world East West c IT is the opinion of some that the windes are to be observed in this if it be hot the South is found by the windes that blow that way but this observation is uncertaine and subject to much error nature will help you in some measure to make it more manifest than any of the former from a tree thus Cut a small tree off even to the ground and mark the many circles that are about the sap or pith of the tree which seem nearer together in some part than in other which is by reason of the Suns motion about the tree for that the humiditie of the parts of the tree towards the South by the heat of the Sun is rarified and caused to extend and the S●n not giving such heat towards the North-part of the tree the sap is lesser rarefied but condensed by which the circles are nearer together on the North-part than on the South-part therefore if a line be drawne from the widest to the narrowest part of the circles it shall shew the North South of the world Another Experiment may be thus Take a small needle such as women work with place it gently downe flatwise upon still water and it will not sink which is against the generall tenet that Iron will not swimme which needle will by little and little turne to the North and South-points But if the needle be great and will not swim thrust it through a small piece of Cork or some such like thing and then it will do the same for such is the property of Iron when it is placed in aequilibrio it strives to finde out the Poles of the world or points of North and South in a manner as the magnes doth EXAMINATION HEre is observable that the moisture which aideth to the growth of the tree is dilated and rarefied by the Meridionall heat and contracted by the Septentrionall cold this rarefaction works upon the part of the humour or moisture that is more thinne which doth easily dissipate and evaporate which evaporation carries a part of the salt with it and because that solidation or condensation so that there is left but a part of the nourishment which the heat bakes up and consumes so contrarily on the other side the condensation and restrictive quality of the moisture causeth lesse evaporation and perdition and so consequently there remaines more nourishment which makes a greater increase on that side than on the other

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

one and the same position for as you come unto them apply one end of the magnes neare unto them the North of the one will abhorre the North of the other but the North of the one will alwayes approach to the South of the other and the same affection is in the stones themselves For the finding of the Poles of the magnes it may be done by holding a small needle between your fingers softly and so moving it from part to part over the stone untill it be held perpendicular for that shall be one of the Poles of the stone which you may marke out in like manner finde out the other Pole Now to finde out which of those Poles is North or South place a needle being touched with one of the Poles upon a smooth convex body as the naile of ones finger or such like and marke which way the end of the needle that was touched turneth if to the South then the point that touched it was the South-Pole c. and it is most certain and according to reason and experience that if it be suspended in aequilibrio in the aire or supported upon the water it will turne contrary to the needle that toucheth it for then the pole that was marked for the South shall turne to the North c. PROBLEM LXVIII Of the properties of Aeolipiles or bowels to blow the fire THese are concave vessels of Brass or Copper or other material which may indure the fire having a small hole very narrow by which it is filled with water then placing it to the fire before it be hot there is no effect seen but assoone as the heat doth penetrate it the water begins to rarefie issueth forth with a hidious and marvelous force it is pleasure to see how it blowes the fire with great noise Novv touching the forme of these vessels they are not made of one like fashion some makes them like a bovvle some like a head painted representing the vvinde some make them like a Peare as though one vvould put it to rost at the fire vvhen one vvould have it to blovv for the taile of it is hollovv in forme of a funnell having at the top a very little hole no greater than the head of a pinne Some do accustome to put vvithin the Aeolipile a crooked funnell of many foldings to the end that the vvinde that impetuously rolles to and fro vvithin may imitate the noise of thunder Others content themselves vvith a simple funnell placed right upvvard somevvhat vvider at the top than elsevvhere like a Cone vvhose basis is the mouth of the funnell and there may be placed a bovvle of Iron or Brasse vvhich by the vapours that are cast out vvill cause it to leap up and dance over the mouth of the Aeolipile Lastly some apply near to the hole smal Windmils or such like vvhich easily turne by reason of the vapours or by help of tvvo or more bovved funnels a bowle may be made to turne● these Aeolipiles are of excellent use for the melting of mettalls and such like Now it is cunning and subtiltie to fill one of these Aeolipiles with water at so little a hole and therefore requires the knowledge of a Philosopher to finde it out and the way is thus Heat the Aeolipiles being empty and the aire which is within it will become extreamely rarefied then being thus hot throw it into water and the aire will begin to be condensed by which meanes it will occupie lesse roome therefore the water will immediately enter in at the hole to avoide vacuitie thus you have some practicall speculation upon the Aeolipile PROBLEM LXIX Of the Thermometer or an instrument to measure the degrees of heat and cold in the aire THis Instrument is like a Cylindricall pipe of Glasse which hath a little ball or bowle at the toppe the small end of which is placed into a vessell of water below as by the figure may be seene Then put some coloured liquor into the Cylindricall glasse as blew red yellow green or such like such as is not thick This being done the use may be thus Those that will determine this change by numbers and degrees may draw a line upon the Cylinder of the Thermometer and divide it into 4 degrees according to the ancient Philosophers or into 4 degrees according to the Physicians dividing each of these 8 into 8 others to have in all 64 divisions by this vvay they may not only distinguish upon vvhat degree the vvater ascendeth in the morning at midday at any other houre but also one may knovv hovv much one day is hotter or colder than another by marking hovv many degrees the vvater ascendeth or descendeth one may compare the hottest and coldest dayes in a vvhole year together vvith these of another year againe one may knovv hovv much hotter one roome is than another by vvhich also one might keep a chamber a furnace a stove c. alvvayes in an equalitie of heat by making the vvater of the Thermometer rest alvvayes upon one the same degree in brief one may judge in some measure the burning of Fevers and neare unto what extension the aire can be rarefied by the greatest heat Many make use of these glasses to judge of the vveather for it is observed that if the vvater fall in 3 or 4 hours a degree or thereabout that raine insueth and the vvater vvill stand at that stay untill the vveather change marke the water at your going to bed for if in the morning it hath descended raine followeth but if it be mounted higher it argueth faire weather so in very cold weather if it fall suddenly it is snow or some sleekey weather that wiil insue PROBLEM LXX Of the proportion of humane bodies of statues of Colossus or huge images and of monstrous Giants PYthagoras had reason to say that man is the measure of all things First because he is the most perfect amongst all bodily creatures according to the Maxime of Philosophers that which is most perfect and the first in rank measureth all the rest Secondly because in effect the ordinary measure of a foot the inch the cubit the pace have taken their names and greatnesse from humane bodies Thirdly because the symmetrie and concordancie of the parts is so admirable that all workes which are well proportionable as namely the building of Temples of Shippes of Pillars and such like pieces of Architecture are in some measure fashioned and composed after his proportion And we know that the Arke of Noah built by the commandement of God was in length 300 Cubits in breadth 50 Cubits in height or depth 30 cubits so that the length containes the breadth 6 times and 10 times the depth now a man being measured you will finde him to have the same proportion in length breadth and depth Vilalpandus treating of the Temple of Solomon that chieftaine of works was modulated all of good Architecture and curiously to be observed in many