Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	east_n	point_n	west_n	1,970	5	9.4719	5	true

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