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Author: Etten, Hendrick van.
Title: Mathematicall recreations. Or a collection of sundrie problemes, extracted out of the ancient and moderne philosophers, as secrets in nature, and experiments in arithmeticke, geometrie, cosmographie, horolographie, astronomie, navigation, musicke, opticks, architecture, staticke, machanicks, chimestrie, waterworkes, fireworks, &c. ... Most of which were written first in Greeke and Latine, lately compiled in French, by Henry Van Etten Gent. And now delivered in the English tongue, with the examinations, corrections, and augmentations.
Publication Info: Ann Arbor, Michigan: University of Michigan, Digital Library Production Service
2011 April (TCP phase 2)

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Print source: Mathematicall recreations. Or a collection of sundrie problemes, extracted out of the ancient and moderne philosophers, as secrets in nature, and experiments in arithmeticke, geometrie, cosmographie, horolographie, astronomie, navigation, musicke, opticks, architecture, staticke, machanicks, chimestrie, waterworkes, fireworks, &c. ... Most of which were written first in Greeke and Latine, lately compiled in French, by Henry Van Etten Gent. And now delivered in the English tongue, with the examinations, corrections, and augmentations.
Etten, Hendrick van., Leurechon, Jean, 1591-1670,, Malthus, Francis,, Oughtred, William, 1575-1660,

Printed at London: By T. Cotes, for Richard Hawkins, dwelling in Chancery Lane, neere the Rowles, 1633.
Alternate titles: Récréation mathématicque. English Récréation mathématicque.
Sometimes attributed to Jean Leurechon.
A translation of: Récréation mathématicque.
The translation is sometimes attributed to Francis Malthus or, wrongly, to William Oughtred.
With an additional title page, engraved, preceded by a letterpress explanation, and a final license leaf.
Identified as STC 15530 on UMI microfilm.
Reproduction of the original in the British Library.
Subject terms:
Science -- Early works to 1800.
Scientific recreations -- Early works to 1800.
Fireworks -- Early works to 1800.

title page
TO The thrice Noble and most generous Lo. the Lo. Lambert Verreyken, Lo. of Hinden, Wolverthem, &c.
To the Reader.
table of contents
By vvay of ad∣vertisement. Five or sixe things I have thought worthy to declare before I passe further.
PROBLEME. I. To finde a number thought upon.
Another way to finde what number was thought upon.
To finde numbers conceived upon otherwise than the former.
PROBLEM. II. How to represent to these which are in a chamber that which is with∣out, or all that which passeth by.
PROBLEM. III. To tell how much waighs the blow of ones fist, of a Mallet, Hatchet or such like, or resting without giving the blow.
PROBLEM. IIII. How to breake a staffe which is laid upon Glasses full of water, without breaking the Glasse, spilling the water, or upon two Reeds or Strawes without breaking of them.
PROBLEM. V. How to make a faire Geographicall Card in Garden Plot, fit for a Prince, or great personage.
PROBLEM. VI.w three staves, knives, or like bodies may be conceaved to hang in the Aire, without being supported by any thing, but by themselves.
PROBLEM VII. How to dispose as many men, or other thing in such sort that rejecting, or casting away the 6. 9. 10. part, unto a certaine number, there shall remaine these which you would have.
PROBLEM. VIII Three things, and three persons proposed, to finde which of them hath either of these three things.
PROBLEM. IX. How to part a vessell which is full of wine con∣taining 8. Pints, into two equall parts, by two other vessels which contained as much as the greater vessell; as the one being 5. Pints, and the other 3. Pints.
PROBLEM. X. To make a sticke stand upon the tipp of ones finger, without falling.
PROBLEM. XI. How a milstone or other Ponderositie, may be sup∣ported by a small needle, without brea∣king or any wise bowing the same.
PROBLEM. XII. To make three knives hang and move upon the point of a Needle.
PROBLEM. XIII. To finde the weight of smoake, which is exhaled of any combustible body whatsoever.
PROBLEM. XIIII. Many things being disposed circular, (or other∣wise) to find which of them, any one thinkes upon.
PROBLEM. XV. How to make a dore, or a Gate, which shall open on both sides.
PROBLEM. XVI. To shew how a Ponderositie, or heavie thing, may be supported upon the end of a staffe (or such like) upon a Table, and nothing holding or touching it.
PROBLEM. XVII. Of a deceitfull Bowle to play withall.
PROBLEM. XVIII. To part an Apple into 2. 4. or 8 like parts, without breaking the Rind.
PROBLEM. XIX. To finde a number thought upon without asking of any questions, certain opera∣tions being done.
PROBLEM. XX. How to make an uniforme, & an inflexible body, to passe through two small holes of divers formes, as one being circular, & the other square, Quadrangular, and Tri∣angularwise, yet so that the holes shall be exactly filled.
PROBLEME. XXI. How with one uniforme body or such like to fill three severall holes: of which the one is round, the other a just square; and the third an ovall forme.
PROBLEM XXII. To finde a number thought upon after another manner, than that which is formerly delivered.
PROBLEM. XXIII. To finde out many numbers that sundry per∣sons, or one man hath thought upon.
PROBLEM. XXIIII. How is it that a man in one and the same time, may have his head upward, and his feet upward, being in one and the same place.
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 a∣nother.
PROBLEM. XXVI. How it is that a man having but a Rode or Pole of land; doth bragge that he may in a right line passe from place to place above 3000 miles.
PROBLEM. XXVII. How it is that a man standing upright, and looking which way he will, he loo∣keth true North or South.
PROBLEM. XXVIII. To tell any one what number remaines after certaine operations being ended, without asking any question.
PROBLEM. XXIX. Of the play with two severall things.
PROBLEM. XXX. Two numbers being proposed unto two seve∣rall parties, to tell which of these num∣bers is taken by each of them.
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.
PROBLEM. XXXII. How to change a Circle into a square forme.
PROBLEM. XXXIII. With one and the same compasses, and at one and the same extent, or opening, how to describe many Circles concentricall, that is, greater or lesser one than another.
PROBLEM. XXXIIII. Any numbers under 10. being thought upon, to finde what numbers they were.
PROBLEM. XXXV. Of the Play with the Ring.
PROBLEM. XXXVI. The Play of 3 4. or more Dice.
PROBLEM. XXXVII. How to make water in a Glasse seeme to boyle and sparkle.
PROBLEME XXXVIII. Of a fine vessell which holds wine or water, being cast into it at a certaine height, but being filled higher, it will runne out of its owne accord.
PROBLEM. XXXIX. Of a Glasse very pleasant.
PROBLEM. XL. If any one should hold in each hand, as many peeces of money as in the other, how to finde how much there is.
PROBLEM. XLI. Many Dice being cast, how artificially to discover the number of the points that may arise.
PROBLEM. XLII. Two mettals as Gold and Silver, or of other kind weighing alike, being privately placed into two like Boxes, to finde which of them the Gold or Silver is in.
PROBLEM: XLIII. Two Globes of diverse mettles, (as one gold and the other copper) yet of equall weight being put into a boxe as B. G. to finde in which end the gold or copper is.
PROBLEM. XLIIII. How to represent diverse sorts of Raine∣bowes here below.
PROBLEM. XLV. How that if all the Powder in the world were in∣closed within a bowle of paper or glasse, and being fired on all parts, it could not breake that bowle.
PROBLEM. XLVI. To finde a number which being divided by 2 there will remaine 1, being divided by 3, there will remaine 1; and so likewise being divided by 4, 5, or 6. there would still remaine 1: but be∣ing divided by 7, there will remaine nothing.
PROBLEME XLVII. One had a certaine number of crownes, and coun∣ting them by 2 and 2, there rested 1: counting them by 3 and 3, there rested 2: counting them by 4 and 4, there rested 3: counting them by 5 and 5, there rested 4: counting them by 6 and 6, there rested 5: but counting them by 7 and 7, there remained nothing: how many crownes might hee have.
PROBLEM. XLVIII. How many sorts of weights in the least manner must there be to weigh all sorts of things be∣tweene 1 pound and 10 pound, and so unto 121, and 364 pound.
PROBLEM. XLIX. Of a deceitfull ballance which being empty seemes to be just, because it hangs in aequilibrio: not∣withstanding putting 12 pound in one ballance, and 11 in the other, it will remaine in aequilibrio.
PROBLEM. L. To heave or lift up a bottle with a straw.
PROBLEM. LI. How in the middle of a wood or desert, without the sight of the Sunne, Starres, Shaddow or Compasse, to finde out the North or South, or the foure Cardinall points of the world, East, West, &c.
PROBLEM. LII. Three persons having taken Counters, Cards, or other things, to finde how much each one hath taken.
PROBLEME LIII. How to make a consort of musicke of many parts with one voyce, or one instrument onely.
PROBLEM. LIIII. To make or describe an Ovall forme, or that which neare resembles unto it, at one turning with a paire of a common Compasses.
PROBLEM. LV. Of a purse difficult to 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 Center of it.
PROBLEM. LVI. Any one having taken 3 Cards, to finde how many points they containe.
PROBLEM. LVII. Many Cards placed in diverse rankes, to finde which of these Cards any one hath thought.
PROBLEM. LVIII. Many Cards being offered to sundry persons, to finde which of those Cards any one thinketh upon.
PROBLEM. LIX. How to make an instrument to helpe hea∣ring, as Gallileus made to helpe the sight.
PROBLEM. LX. Of a fine lampe which goes not out, though one carry it in ones pocket: or being rouled upon the ground will still burne.
PROBLEM. LXI. Any one having thought a Card amongst many Cards, how artificially to discover it out.
PROBLEM. LXII. Three women A. B. C. carryed apples to a mar∣ket to sell, A. had 20, B. 30, and C. 40; they sold as many for a penny, the one as the other: and brought home one as much money as another, how could this be.
PROBLEM. LXIII. Of the properties of some numbers.
PROBLEM. LXV. Of an excellent lampe which serves or fur∣nisheth it selfe with oyle, and burnes a long time.
PROBLEM. LXV. Of the play at Keyles or nine Pinnes.
PROBLEM. LXVI. Of Spectacles of pleasure.
PROBLEME LXVII. Of the Adamant or Magnes, and the needles touched therewith.
PROBLEM. LXVIII. Of the properties of Aeolipiles or bowles to blow the fire.
PROBLEM. LXIX. Of the Thermometer: or an instrument to measure the degrees of heat and cold in the aire.
PROBLEM. LXX. Of the proportion of humaine bodies of sta∣tues, of Colossus or huge images, and of monstrous Giants.
Of Statues, of Colossus, or huge images.
Of monstrous Gyants.
PROBLEM. LXXI. Of the game at the Palme, at Trappe, at Bowles, Paile-maile and others.
PROBLEM. LXXII. Of the Game of square formes.
PROBLEM. LXXIII. How to make the string of a Viole sencibly shake, without any one touching it.
PROBLEM. LXXIIII. Of a vessell which containes three severall kindes of liquor, all put in at one bung-hole, and drawne out at one tappe severally without mixture.
PROBLEM. LXXV. Of Burning-glasses.
PROBLEM. LXXVI. Containing many pleasant Questions by way of Arithmeticke.
Of the Asse and the Mule.
Of the number of Souldiers that fought before old Troy.
Of the number of Crownes that two men had.
About the houre of the day.
Of Pythagoras Schollers.
Of the number of Apples given amongst the Graces and the Muses.
Of the Testament or last Will of a dying Father.
Of the Cuppes of Craesus.
Of Cupids Apples.
Of a Mans Age.
Of the Lion of Bronze placed upon a Foun∣taine with his Epigramme.
PROBLEM. LXXVII. Divers excellent and admirable experiments upon Glasses.
Experiment upon flat and plaine Glasses.
Experiments upon Gibbous, or convex Sphaericall Glasses.
Experimenss upon hollow, or Concave Sphaericall Glasses.
Of other Glasses of pleasure.
PROBLEM: LXXVIII. 1. How to shew to one that is suspitious, what is done in another Chamber or Roome: not∣withstanding the interposition of the wall.
Corolaire. 1.
Corolaire. 2.
Corolaire. 3.
PROBLEM. LXXIX. How with a Musket to strike a marke, not looking towards it, as exact as one aymed at it.
Corolaires. From which may be gathered, that one may ex∣actly shoote out of a Musket to a place which is not seene, being hindered by some obstacle, or other in∣terposition.
PROBLEM. LXXX. How to make an Image to be seene hanging in the aire, having his head downeward.
PROBLEM. LXXXI. How to make a company of representative Soul∣diers seeme to be a Regiment, or how few in number may bee multiplyed to seeme to be many in number.
PROBLEM. LXXXII. Of fine and pleasant Dyalls.
Of a Dyall of hearbes.
Of the Dyall upon the fingers and the hand.
Of a Dyall which was about an Obe∣liske at Rome.
Of Dyalls with Glasses.
Of a Dyall which hath a Glasse in the place of the Still.
Of Dyalls with water.
PROBLEM. LXXXIII. Of Cannons or great Artillery. Souldiers, and others would willingly see this Probleme, which containes three or foure sub∣tile questions: The first is how to charge a Cannon without Powder.
2. In the second question it may be demanded, how much time doth the Bullet of Can∣non spend in the aire before it falls to the ground.
3. In the third question it may be asked, how it comes to passe, that a Cannon shooting up∣wards, the Bullet flies with more violence than being shot point-blanke, or shoo∣ting downeward.
4. In the fourth place it may be asked, whether the discharge of a Cannon be so much the greater, by how much it is longer.
PROBLEM. LXXXIIII. Of prodigious progression and multiplication, of Creatures, Plants, Fruites, Numbers, Gold, Silver, &c. when they are al∣wayes augmented by certaine proportion.
Of graines of Mustard-seed.
Of Pigges.
Of graines of Corne.
Of the increase of Sheepe.
Of the increase of Cod-fish, Carpes, &c.
Of the increase and multiplication of men.
Of the increase of numbers.
Of a man that gathered up Apples, Stones, or such like upon a condition.
Of Changes in Bells, in musicall Instruments, transmutation of places, in numbers, letters, men or such like.
Of a Servant hired upon cer∣taine conditions.
PROBLEM. LXXXV. Of Fountaines, Hydriatiques, Machinecke, and other experiments upon water, or other liquor.
1. First how to make water at the foote of a mountaine to ascend to the top of it, and so to descend on the other side.
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 runs out at the toppe.
3. Thirdly, how is it that it is said that a vessell holds more water being placed at the foote of a Mountaine, than standing upon the toppe of it.
4. Fourthly, to conduct water from the toppe of one Mountaine, to the top of another.
5. Fiftly, of a fine Fountaine which spouts wa∣ter very high, and with great violence by turning of a Cocke.
6. Sixtly, of Archimedes screw, which makes water ascend by descending.
7. Seventhly, of another fine Fountaine of pleasure.
8. Eightly, of a fine watering potte for gardens.
9. Ninthly, how easily to take wine out of a vessell at the bung-hole, without piercing of a hole in the vessell.
10. Tenthly, how to measure irregular bo∣dies by helpe of water.
11. To finde the weight of water.
12. To finde the charge that a vessell may carry, as Shippes, Boates, or such like.
13. How comes it that a Shippe having safely sayled in the vaste Ocean, and being come in∣to the Port or harbour, without any tempest will sinke downe right.
14. How a grosse body of mettle may swimme upon the water.
15. How to weigh the lightnesse of the aire.
16. Being given a body, to marke it about, and shew how much of it will sinke in the water, or swimme above the water.
17. To finde how much severall mettle or other bodies doe weigh lesse in the water than in the aire.
18. How is it that a ballance having like weight in each scale, and hanging in aequilibrio in the aire: being placed in another place, (without removing any weight) it shall cease to hang in aequilibrio sencibly: yea by a great dif∣ference of weight.
19. To shew what waters are heavier one than another, and how much.
20. How to make a Pound of water weigh as much as 10, 20, 30, or a hundred pound of Lead; nay as much as a thousand, or ten thousand pound weight.
PROBLEM. LXXXVI. Of sundry Questions of Arithmeticke, and first of the number of sands.
2. Divers mettles being melted together in one body, to finde the mixture of them.
3. Three men bought a quantitie of wine, each paid alike, and each was to have alike; it happe∣ned at the last partition that there was 21 Bar∣rells, of which 7 were full, 7 halfe full, and 7 empty, how must they share the wine and vessells, that each have as many vessells one as ano∣ther, & as much wine one as another.
4. There is a Ladder which stands upright a∣gainst a wall of 10 foote high; the foot of it is pulled out 6 foote from the wall upon the pavement: how much hath the top of the Ladder descended.
PROBLEM. LXXXVII. Witty suits or debates betweene Caius and Sem∣pronius, upon the forme of figures; which Geometricians call Isoperimeter, or e∣quall in circuit or compasse.
1. Incident.
2. Incident.
3. Incident.
PROBLEM. LXXXVIII. Containing sundry Questions in matter of Cosmography.
2. Secondly, how much is the depth of the earth, the height of the heavens, and the compasse of the world.
PROBLEM. LXXXXII. To finde the Bissextile yeare, the Dominicall letter, and the letters of the moneth.
To finde the Circle of the Sun by the fingers.
PROBLEM. LXXXXIII. To finde the New and Full Moone in each Moneth.
PROBLEM. LXXXXIIII. To finde the Latitude of a Countrey.
PROBLEM. LXXXXV. Of the Climats of countries, and to finde in what Climate any countrey is under.
PROBLEM. LXXXXVI. Of Longitude and Latitude of the Earth and of the Starres.
To finde the Longitude of a Countrey.
Of the Latitude of Countries.
To finde the Latitude of Countries.
To finde the distance of Places.
Of the Longitude, Latitude, Declinati∣on, and distance of the Starres.
How it is that two Horses or other creatures being foled or brought forth into the world at one and the same time, that after cer∣taine dayes travell the one lived longer than the other, notwith∣standing they dyed together in one and the same mo∣ment also.
Certaine fine Observations.
PROBLEME LXXXXVII. To make a Triangle that shall have three right Angles.
PROBLEM. LXXXXVIII. To divide a line in as many equall parts as one will, without compasses, or without seeing of it.
PROBLEM. LXXXXVIIII. To draw a line which shall incline to another line, yet never meete: against the Axiome of Parallels.
PROBLEM. C. To observe the variation of the compasses, or needle in any places.
PROBLEM. CI. How to finde at any time which way the wind is in ones Chamber, without go∣ing abroad.
PROBLEM. CII. How to draw a parallell sphericall line with great ease.
PROBLEM. CIII. To measure an inaccessible distance: as the bredth of a River with the helpe of ones hat onely.
PROBLEM. CIIII. How to measure a height with two strawes or two small stickes.
PROBLEM. CV. How to make statues, letters, bowles, or other things which are placed in the side of a high buil∣ding, to be seene below of an equall bignesse.
PROBLEM. CVI. How to disguise or disfigure an Image, as a head, an arme, a whole body, &c. so that it hath no proportion, the eares to become long: the nose as that of a swan, the mouth as a coaches entrance, &c. yet the eye placed at a certaine point will be seene in a direct and exact proportion.
PROBLEM. CVII. How a Canon after that it hath shot, may be covered from the battery of the enemy.
PROBLEM. CVIII. How to make a Lever by which one man may alone place a Cannon upon his carriage, or raise what other weight he would.
PROBLEM. CIX. How to make a Clocke with one onely wheele.
PROBLEM. CX. How by helpe of two wheeles to make a Child to draw up alone a hogshead of water at a time: and being drawne up shall cast out it selfe into another vessell as one would have it.
PROBLEM. CXI. To make a Ladder of Cords which may be carryed in ones pocket: by which one may easily mount up a Wall, or Tree alone.
PROBLEM. CXII. How to make a Pumpe whose strength is marue∣lous by reason of the great weight of wa∣ter that it is able to bring up at once, and so by con∣tinuance.
PROBLEM. CXIII. How by meanes of a Cisterne, to make water of a Pit continually to ascend without strength, or the assistance of any other Pumpe.
PROBLEM. CXIIII. How out of a fountaine to cast the wa∣ter very high: different from a Probleme formerly delivered.
PROBLEME CXV. How to empty the water of a Cisterne by a Pipe which shall have a motion of it selfe.
PROBLEM. CXVI. How to squirt or spout out a great height, so that one pot of water shall last a long time.
PROBLEM. CXVII. How to practise excellently the reanimation of simples, in case the plants may not be transported to be replanted by reason of distance of places.
PROBLEM. CXVIII. How to make an infalliable perpetuall motion.
PROBLEM. CXIX. Of the admirable invention of making the Phi∣losophers Tree, which one may see with his eye to grow by little and little.
PROBLEM. CXX. How to make the representation of the great world.
PROBLEM CXXI. How to make a Cone, or a Pyramidall body move upon a Table without springs or other Arti∣ficiall meanes: so that it shall move by the edge of the Table without falling.
PROBLEM. CXXII. To cleave an Anvill with the blow of a Pistoll.
PROBLEM. CXXIII. How to rost a Capon carried in a Budget at a Saddle bow, in the space of ri∣ding 5. or 6. miles.
PROBLEM. CXXIIII. How to make a Candle burne and continue three times as long as otherwise it would.
PROBLEM. CXXV. How out of a quantitie of wine to extract that which is most windy, and evill, that it hurt not a sicke Person.
PROBLEM. CXXVI. How to make two Marmouzets one of which shall light a Candle, and the other put it out.
PROBLEM. CXXVII. How to keepe wine fresh as if it were in a celler though it were in the heate of Summer, and without Ice or snow, yea though it were carried at a saddles bow, and exposed to the Sunne all the day.
PROBLEM. CXXVIII. To make a Cement which indureth or lasteth as marble, which resisteth ayre and wa∣ter without ever disjoyning or uncemiting
PROBLEM. CXXIX. How to melt mettle very quicke, yea in a shell upon little fire.
PROBLEM. CXXX. How to make Iron or Steele exceeding hard.
PROBLEM. CXXXI. To preserve fire as long as you will, imitating the inextinguable fire of Vostales.
Artificiall fire-VVorkes: Or the manner of making of Roc∣kets and Balls of fire, as well for the Water, as for the Ayre; with the com∣position of Stars, Golden-raine, Serpents, Lances, Wheeles of fire, and such like, pleasant and Recreative.
Of the composition for Rockets.
For Rockets of one ounce.
For Rockets of 2, or 3. ounces.
For Rockets of 4. ounces.
For Rockets of 5. or 6. ounces.
For Rockets of 7, or 8. ounces.
Of Rockets of 10, or 12, ounces.
For Rockets of 14, or 15, ounces.
For Rockets of 1, pound.
Of Rockets of 2, pound.
For Rockets of 3, pound.
For Rockets of 4, 5, 6. or 7, pound.
For Rockets of 8 9 or 10, pound.
Of the making of Rockets and other Fireworkes.
Of recreative fires.
How to make fire runne up and downe, forward and backward.
How to make Wheeles of fire.
Of Night Combatants.
Of standing Fires.
Of Pots of fire for the Ayre, which are throwne out of one Case one after another of a long continuance.
Of Pots of fire for the ground.
Of Balles of fire.
Of fire upon the Water.
Of Balles of fire which moves upon the water.
Of Lances of fire.
How to shoote a Rocket Horizontall, or otherwise.
How a Rocket burning in the water for a cer∣taine time, at last shall fly up in the Ayre with an exceeding quicknesse.
Of the framing of the parts of a Fire-Works together that the severall workes may fire one after another.
Ad Authorem D. D. Henricum Van Etenium, Alumnum Academiae Ponta Mousson.
A Table of the particurall heads of this Booke, contracted according to the severall Arts spe∣cified in the Title page.