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Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
book_n	time_n	word_n	write_v	4,884	5	5.4567	4	true

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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

meale there might be a divers transmutation of place of account in some one of them in comparison of another and never the whole company to be twice alike in situation how long may the Steward entertaine them who being not skilled in this fetch may answere unadvisedly It is most certaine that there will be five thousand and forty several 1 a 1 2 b 2 6 c 3 24 d 4 120 e 5 7●0 f 6 5040 g 7 403●0 h 8 362880 i 9 3628800 k 10 39916800 l 11 479001600 m 12 6227020800 n 13 87178291200 o 14 1307674368000 p 15 20922789888000 q 16 355687537996000 r 17 6402375683928000 s 18 121645137994632000 t 19 2432902759892640000 u 20 51090957957745440000 w 21 1124001075070399680000 x 22 25852024726619192640000 y 23 6●0448593438860623360000 z 24 positions or changings in the seatings which maks 14 years time wanting 10 weeks and 3 dayes Hence from this mutability of transmutation it is no marvell tha● by 24 letters there ariseth and is made such variety of languages in the world such infinite number of words in each language seeing the diversity of syllables produceth that effect and also by the interchanging placing of letters amongst the vowels amongst themselves maketh these syllables vvhich Alphabet of 24 letters may be varied so many times viz. 620448593438860623360000 vvhich is six hundred tvventy thousand foure hundred forty eight millions of millions of millions five hundred ninety three thousand foure hundred thirty eight milions of milions more Novv allovving that a man may reade or speak one hundred thousand vvords in an houre vvhich is tvvice more vvords than there are conteined in the Psalmes of David a taske too great for any man to do in so short a time and if there were foure thousand six hundred and fifty thousand millions of men they could not speak these words according to the hourely proportion aforesaid in threescore and ten thousand yeares which variation transmutation of letters if they should be written in bookes allowing to each leaf 28000 words which is as many as possibly could be inserted and to each book a reame or 20 quire of the largest and thinnest printing paper so that each book being about 15 inches long 12 broad and 6 thick the books that would be made of the transmutation of the 24 letters aforesaid would be at least 38778037089928788 and if a Library of a mile square every way of 50 foot high were made to containe 250 Galleries of 20 foot broad apiece it would containe foure hundred mill●ons of the said books so there must be to containe the rest no lesse than 9●945092 such Libraries and if the books were extended over the surface of the Globe of the Earth it would be a decuple covering unto it a thing seeming most incredible that 24 letters in their transmutation should produce such a prodigious number yet most certaine and infallible in computation Of a Servant hired upon certaine conditions A Servant said unto his Master that he would dvvell vvith him all his life-time if he would but onely lend him land to sowe one graine of Corne with all his increase for 8 years time how think you of this bargaine for if he had but a quarter of an inch of ground for each graine and each graine to bring forth yearely of increase 40 graines the whole sum would amount unto at the terme aforesaid 6553600000000 graines and seeing that three thousand and six hundred millions of inches do but make one mile square in the superficies it shall be able to receive foureteene thousand and foure hundred millions of graines which is 14400000000. thus dividing the aforesaid 6553600000000 the Quotient will be 455 and so many square miles of land must there be to sowe the increase of one graine of Corne for 8 yeares which makes at the least foure hundred and twenty thousand Acres of land which rated but at five shillings the Acre per Annum amounts unto one hundred thousand pound which is twelve thousand and five hundred pound a yeare to be continued for 8 yeares a pretty pay for a Masters Servant 8 yeares service PROBLEM LXXXV Of Fountaines Hydriatiques Machinecke and other experiments upon water or other liquor 1. First how to make water at the foot of a mountaine to ascend to the top of it and so to descend on the other side TO do this there must be a Pipe of lead which may come from the fountaine A to the top of the Mountaine B and so to descend on the other side a little lower then the Fountaine as at C. then make a hole in the Pipe at the top of the Mountaine as at B and stop the end of the Pipe at A and C and fill this Pipe at B with water close it very carefully againe at B that no aire get in then unstop the end at A at C then will the water perpetually runne up the hill and descend on the other side which is an invention of great consequence to furnish Villages that want water 2. Secondly how to know what wine or other liquor there is in a vessell without opening the bung-hole and without making any other hole than that by which it runnes out at the top IN this problem there is nothing but to take a bowed pipe of Glasse and put it into the faucets hole and stopping it close about for then you shall see the wine or liquor to ascend in this Pipe untill it be just even with the liquor in the vessel by which a man may fill the vessel or put more into it and so if need were one may empty one vessel into another without opening the bung-hole 3. Thirdly how is it that it is said that a vessell holds more water being placed at the foot of a Mountaine than standing upon the top of it THis is a thing most certaine because that water and all other liquor disposeth it selfe sphericaliy about the Centre of the earth and by how much the vessel is nearer the Centre by so much the more the surface of the water makes a lesser sphere and therefore every part more gibbous or swelling than the like part in a greater sphere and therefore when the same vessell is farther from the Centre of the earth the surface of the water makes a greater sphere and therefore lesse gibbous or swelling over the vessell from whence it is evident that a vessell near the Centre of the Earth holds more water than that which is farther remote from it and so consequently a vessel placed at the bottome of the Mountaine holds more water than being placed on the top of the Mountaine First therefore one may conclude that one and the same vessel will alwayes hold more by how much it is nearer the Centre of the earth Secondly if a vessell be very neare the Centre of the earth there will be more water above the brims of it than there is within the vessel Thirdly a vessel full of water comming to the Centre wil

of Crownes that two men had 136 About the houre of the day 137 Of Pythagoras Schollers 137 Of the number of Apples given amongst the Graces and the Muses 138 Of the testament or last will of a dying Father 138 Of the cups of Croesus 139 Of Cupids Apples 139 Of a Mans Age. 140 Of the Lion of Bronze placed upon a fountaine with his Epigram ibid. Prob. 77 In Opticks excellent experiments Principles touching reflections 141 Experiments upon flat and plaine Glasses 142 How the Images seeme to sink into a plaine Glasse and alwayes are seene perpendicular to the Glasse an● also inversed 143 The things which passe by in a street may by help of a plaine glasse be seen in a Chamber and the height of a tower or tree observed 143 How severall Candles from one Candle are represented in a plaine Glasse and Glasses alternately may be seene one within another as also the back-parts of the body as well as the fore-parts are evidently represented 144 How an Image may be seene to hang in the aire by help of a Glasse and writing read or easily understood 146 Experiments upon Gibbous or convex Sphericall Glasses How lively to represent a whole City fortification or Army by a Gibbous Glasse 147 How the Images are seen in Concave Glasses 149 How the Images are transformed by approaching to the centre of the Glasse or point of concourse and of an exceeding light that a Concave Glasse gives by help of a Candle 151 How the Images as a man a sword or hand doth come forth out of the Glasse 152 153 Of strange apparitions of Images in the aire by help of sundry Glasses 152 154 Of the wonderfull augmentation of the parts of mans body comming neare the point of inflammation or centre of the Glasse 155 How writing may be reverberated from a Glasse upon a VVall and Read 156 How by help of a Concave Glasse to cast light into a Campe or to give a perspective light to Pyoneers in a Mine by one Candle only 156 How excellently by help of a Concave Glasse and a Candle placed in the centre to give light to read by 157 Of other Glasses of pleasure 158 Of strange deformed representations by Glasses causing a man to have foure eyes two Mouthes two Noses two heads Of Glasses which give a colour to the visage and make the face seeme faire and foule 160 Prob. 78 How to shew one that is suspicious what is in another Chamber or Roome notwithstanding the interposition of that wall 160 Corolary 1. To see the Besiegers of a place upon the Rampa●●t of a fortification 161 Corolary 2. and 3. Notwithstanding the interposition of VValls and Chambers by help of a Glasse things may be seen which passe by 162 Prob. 79 How with a Musket to strike a marke not looking towards it as exactly as one aimed at it 162 How exactly to shoot out of a Mu●ket to a place which is not seene being hindred by some obstacle or other interposition 163 Prob. 80 How to make an Image to be seen hanging in the aire having his head downward 164 Prob. 81. How to make a company of representative souldiers seeme to be as a regiment or how few in number may be multiplyed to seem to be many in number 165 COROLARIE Of an excellent delightfull Cabinet made of plaine Glasses 165 Prob. 82 Of fine and pleasant Dyalls in Horologiographie Of a Dyall of herbs for a Garden 166 Of the Dyall upon the finger and hand to finde what of the Clock it is 167 Of a Dyall which was about an Obelisk at Rome 168 Of Dyals with Glasses 168 Of a Dyall which hath a Glasse in the place of the stile 169 Of Dyals with water which the Ancients use● 171 Prob. 83 Of shooting out of Cannons or great Artillery How to charge a Cannon without powder 173 To finde how much time the Bullet of a Cannon spends in the Aire before it falls to the ground 174 How it is that a Cannon shooting upward the Bullet flies with more violence than being shot point blanke or shooting downeward 174 VVhether is the discharge of a Cannon so much the more violent by how much it hath the more length 176 Prob. 84 Of prodigious progressions and multiplications of creatures plants fruits numbers gold silver c. Of graines of Mustardseed and that one graine being sowne with the increase thereof for 20 yeares will produce a heap greater than all the earth a hundred thousand times 178 Of Pigges and that the great Turke with all his Revenne is not able to maintaine for one yeare a Sow with all her increase for 12 yeares 179 Of graines of Corne and that 1 graine with all its increase for 12 yeares will amount to 244140625000000000000 graines which exceeds in value all the treasures in the World 183 Of the wonderfull increase af Sheepe 182 Of the increase of Cod-fish 182 Of the Progressive Multiplication of soules that from one of Noahs Sonnes from the flood unto Nimrods Monarchie should be produced 111350 soules 183 Of the increase of Numbers in double proportion and that a pin being doubled as often as there are weekes in the yeare the number of pinnes that should arise is able to load 45930 ships of a thousand Tunne apiece which are worth more than tenne hundred thousand pounds a day 183 184 Of a man that gathered Apples stones or such like upon a condition 185 Of the changes in Bells in musicall instruments transmutation of Places in Numbers Letters Men and such like 185 Of the wonderfull interchange of the Letters in the Alphabet the exceeding number of men and time to expresse the words that may be made with these letters and the number of Books to comprehend them 187 188 Of a servant hired upon certaine condition that he might have land lent him to sowe one graine of Corne with its increase for 8 yeares time which amounted to more than four hundred thousand Acres of Land 188 Prob. 85 Of Fountaines Hydriatiques Stepticks Machinecks and other experiments upon water or other liquor First how water at the foot of a Mountaine may be made to ascend to the top of it and so to descend on the other side of it 190 Secondly to finde how much Liquor is in a Vessell onely by using the tap-hole 191 Thirdly how is it that a Vessell is said to hold more water at the foot of a Mountaine then at the top of it 191 4 How to conduct water from the top of one Mountaine to the top of another 192 5 Of a fine Fountaine which spouts water very high and with great violence by turning of a Cock 193 6 Of Archimedes screw which makes water ascend by descending 194 7 Of a fine Fountaine of pleasure 196 8 Of a fine watering pot for Gardens 197 9 How easily to take Wine out of a Vessell at the bung hole without piercing a hole in the Vessell 198 10 How to measure irregular bodies by help of

other numbers I● one be taken from any square number which is odde the square o● halfe of it being added to the first square will make a square number The square of halfe any even number + 1 being added to that even number makes a square number and the even number taken from it leaves a square number If odde numbers be continually added from the unitie successively there will be made all square numbers and if cubick numbers be added successively from the unitie there will be likewise made square numbers PROBLEM LXIV Of an excellent lamp which serves or furnisheth it selfe with oile and burnes a long time I Speak not here of a common lamp which Ca●danus writes upon in his book de subtilita●● for that 's a little vessell in columne-wise which is full of Oile and because there is but one little hole at the bottome neare the weeke or match the oile runnes not for feare that there be emptinesse above when the match is kindled it begins to heat the lamp and rarefying the oile it issueth by this occasion and so sends his more airie parts above to avoid vacuitie It is certaine that such a lampe the Atheniaus used which lasted a whole yeare without being touched which was placed before the statue of Minerva for they might put a certaine quantitie of oile in the lamp CD and a match to burne without being consumed such as the naturalists write of by which the lamp will furnish it selfe and so continue in burning and here may be noted that the oile may be poured in at the top of th● vessell at a little hole and then made fast againe that the aire get not in PROBLEM LXV Of the play at Keyles or nine Pinnes YOu will scarce beleeve that with one bowle and at one blow playing freely one may strike downe all the Keyles at once yet from Mathematicall principles it is easie to be demonstrated that if the hand of him that playes were so well assured by experience as reason induceth one thereto one might at one blow strike downe all the Keyles of at least 7 or 8 or such a number as one pleaseth For they are but 9 in all disposed or placed in a perfect square having three every way Let us suppose then that a good player beginning to play at 1 somewhat low should so strike it that it should strike down the Keyles 2 and 5 and these might in their violence strike downe the Keyles 3 6 and 9 and the bowle being in motion may strike down the Keyle 4 and 7 which 4 Keyle may strike the Keyle 8 so all the 9 Keyles may be striken down at once PROBLEM LXIV Of Spectacles of pleasure SImple Spectacles of blew yellow red or green colour are proper to recreate the sight and will present the objects died in like colour that the Glasses are only those of the greene do somewhat degenerate instead of shewing a lively colour it will represent a pale dead colour and it is because they are not dyed greene enough or receive not light enough for greene and colour these images that passe through these Glasses unto the bottome of the eye EXAMINATION IT is certaine that not onely Glasses dyed green but all other Glasses coloured yield the app●arances of objects strong or weak in colour according to the quantity of the dye more or lesse as one being very yellow another a pale yellow now all colours are not proper to Glasses to give colour hence the defect is not that they want facultie to receive light or resist the penetration of the beams for in the same Glasses those which are most dyed give alwayes the objects more high coloured and obscure and those which are lesse dyed give them more pale and cleare and this is daily made manifest by the painting of Glasse which hinders more the penetration of the light than dying doth where all the matter by fire is forced into the Glasse leaving it in all parts transparent Spectacles of Crystall cut with divers Angles diamond-wise do make a marvellous multiplication of the appearances for looking towards a house it becomes as a Towne a Towne becomes like a Citie an armed man seems as a whole company caused solely by the diversity of refractions for as many plaines as there are on the outside of the spectacle so many times will the object be multiplied in the appearance because of diverse Images cast into the eye These are pleasurable spectacles for avaricious persons that love Gold and silver for one piece will seeme many or one heap of money will seeme as a treasury but all the mischiefe is he will not have his end in the enjoying of it for indeavouring to take it it will appeare but a deceitfull Image or delusion of nothing Here may you note that if the finger be directed by one and the same ray or beam which pointeth to one and the same object then at the first you may touch that visible object without being deceived otherwise you may faile often in touching that which you see Againe there are Spectacles made which do diminish the thing seen very much and bring it to a faire perspective forme especially if one look upon a faire Garden plat a greater walk a stately building or great Court the industry of an exquisite Painter cannot come neare to expresse the lively forme of it as this Glasse will represent it you will have pleasure to see it really experimented and the cause of this is that the Glasses of th●se Spectacles are hollow and thinner in the middle than at the edges by which the visuall Angle is made lesser you may observe a further secret in these Spectacles for in placing them upon a window one may see those that passe to and fro in the streets without being seen of any for their property is to raise up the objects that it lookes upon Now I would not passe this Probleme without saying something of Galileus admirable Glasse for the common simple perspective Glasses give to aged men but the eyes or sight of young men but this of Galileus gives a man an Eagles eye or an eye that pierceth the heavens first it discovereth the spottie and shadowed opacous bodies that are found about the Sunne which darknet and diminisheth the splendor of that beautifull and shining Luminary secondly it shewes the new Planets that accompany Saturne and Jupiter thirdly in Venus is seen the new full and quartill increase as in the Moon by her separation from the Sunne fourthly the artificiall structure of this instrument helpeth us to see an innumerable number of stars which otherwise are obscured by reason of the naturall weaknesse of our sight yea the starres in via lactea are seen most apparantly where there seem no starres to be this Instrument makes apparantly to be seen and further delivers them to the eye in their true and lively colour as they are in the heavens in which the splendor of some is as the Sunne in

of Rockets in each of vvhich you may place 6 9 ●2 or 20 small Rockets Novv give fire at A. by help of a piece of primer going from one Lance to another all the Lances vvill instantly at once be lighted and as soone as the Lance at A is consumed it vvill fire the Channell vvhich is made in the ledge of the frame vvhich runnes under the Pots of fire and as the fire goes along burning the Pots vvill be cast forth and so the rank of Pots upon the sides of the frame AB.BC. and CD being spent the soucisons vvill begin to play being fiered also by a Channel vvhich runnes under them upon the ledges AD HI●G and RE. then when the Soucisons are spent upon the last ledge RE. there may be a secret Channel in the ledge CD which may fire the Box of Rockets at K. and may fire all the rest one after another which Boxes may be all charged with severall Fire-Workes for the Rockets of the first Box may be loaden with Serpents the second with Stars the third with Reports the fourth with Golden raine and the fifth with small flying Serpents these mounting one after another and flying to and fro will much inlighten the Aire in their ascending but when these Rockets discharge themselves above then will there be a most pleasant representation for these fires will dilate themselves in divers beautifull formes some like the branching of Trees others like fountaines of water gliding in the Aire others like flashes of lightning others like the glittering of starres giving great contentment and delight to those which behold them But if the worke be furnished also with Balons which is the chiefest in recreative Fire-works then shall you see ascending in the Aire but as it were onely a quill of fire but once the Balon taking fire the Aire will seeme more than 100. foot square full of crawling and flying Serpents which will extinguish with a volley of more than 500 reports and so fill the Aire and Firmament with their rebounding clamour The making of which with many other rare and excellent Fire-workes and other practises not onely for recreation but also for service you may finde in a book intituled Artificiall Fire-workes made by Mr. Malthas a master of his knowledge and are to be sold by VVilliam Leake at the Crowne in Fleet-street between the two Temple-Gates Conclusion In this Booke we have nothing omitted what was materiall in the originall but have abundantly augmented it in sundry experiments And though the examinations are not so full and manifold yet by way of brevitie we have expressed fully their substance to avoid prolixitie and so past by things reiterated FINIS Printed or sold by William Leak at the Crovvne in Fleetstreet neere the Temple these Books following YOrk's Heraldry Folio A Bible of a very fair large Roman letter 4● Orlando F●rios● Folio Callu learned Readings on the Scat. 21. Hen. 80. Cap 5 of Sewer● Perkins on the Laws of England Wi●kinsons Office of She●●●fs Vade Mecum of a Justice of Peace The book of Fees Peasons Law Mirrour of Just●ce Topicks in the Laws of England Sken de significatione Verborum Delaman's use of the Horizontal Quadrant Wilby's 2d set of Musique 345 and 6 Parts Corderius in English D●ctor Fulk's Meteors Malthus Fire-workes Nyes Gunnery Fire-workes C●to Ma●or with Annotations by Wil. Austin Esquire Mel Helliconium by Alex. Ross● Nosce teipsum by Sr John Davis Animadversions on Lil●i●s Grammer The History of Vienna Paris Lazarillo de Tormes Hero and L●ander by G. Chapman and Christoph. Marlow Al●ilia or Philotas loving folly Bishop Andrews Sermons Adams on ●eter Posing of the Accidence Am●dis de Gaule Guillieliam's Heraldry Herberts Travels Bacc●s Tales Man become guilty by John Francis Sen●●t and Englished by Henry Earl of Monmouth The Ideot in 4 books the first and second of Wisdom the third of the Mind the fourth of S●●tick Experiments of the Ballance The life and Reign of Hen. the Eighth written by the L. Herbet Cornwallis Essays Paradoxes Clenards greek G●ammar 80 A●laluci● or the house of light A discourse written in the year 1651 by SN a modern Speculator A Tragedy written by the most learned Hugo Grotius called Christus Patience and translated into Engl. by George Sand The Mount of Olives or Sollitary Devotions by Henry Vaughan Silurist VVith an excellent discourse of Man in glory written by the Reverend Anselm Arch Bishop of Canterbury The Fort Royall of Holy Scriptures by I. H. PLAYES Hen. the Fourth Philaster The wedding The Hollander Maids Tragedie King no K. The gratefull Servant The strange Discovery Othello the Moor of Venice The Merchant of Venice THE DESCRIPTION AND USE OF THE DOVBLE Horizontall Dyall WHEREBY NOT ONELY THE Houre of the Day is shewn but also the Meridian Line is found And most ASTRONOMICALL Questions which may be done by the GLOBE are resolved INVENTED AND WRITTEN BY W. O. Whereunto is added The Description of the generall HOROLOGICALL RING LONDON Printed for WILLIAM LEAKE and are to be sold at his Shop at the signe of the Crown in Fleetstreet between the two Temple Gates 1652. The description and use of the double Horizontall Diall THere are upon the Plate two severall Dyals That which is outermost is an ordinary diall divided into houres and quarters and every quarter into three parts which are five minutes a piece so that the whole houre is understood to contein 60 minutes And for this dyall the shadow of the upper oblique or slanting edge of the style or cocke doth serve The other diall which is within is the projection of the upper Hemisphaere upon the plain of the Horizon the Horizon it self is understood to be the innermost circle of the limbe and is divided on both sides from the points of East and West into degrees noted with 10.20.30 c. As far as need requireth And the center of the Instrument is the Zenith or Verticall point Within the Horizon the middle straight line pointing North and South upon which the style standeth is the Meridian or twelve a clock line and the other short arching lines on both sides of it are the houre lines distinguished accordingly by their figures and are divided into quarters by the smaller lines drawn between them every quarter conteining 15 minutes The two arches which crosse the houre lines meeting on both sides in the points of intersection of the sixe a clocke lines with the Horizon are the two semicircles of the Ecliptick or annuall circle of the sun the upper of which arches serveth for the Summer halfe yeere and the lower for the Winter half yeer and therefore divided into 365 dayes which are also distinguished into twelve moneths with longer lines having their names set down and into tenths and fifts with shorter lines and the rest of the dayes with pricks as may plainly be seene in the diall And this is for the ready finding out of the place of the Sun