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.

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Title:	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.
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Print source:	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. Oughtred, William, 1575-1660. aut London: printed for William Leake, at the signe of the Crown in Fleetstreet, between the two Temple Gates, M D C LIII. [1653]
Alternate titles:	Récréation mathématique. English.
Subject terms:	Science -- Problems, exercises, etx. -- Early works to 1800. Mathematics -- Problems, exercises, etc. -- Early works to 1800. Fireworks -- Early works to 1800. Scientific recreations -- Early works to 1800. Sundials -- Early works to 1800.
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title page

On the Frontispice and Booke.

frontispiece

TO The thrice Noble and most generous Lo. the Lo. Lambert Verreyken, Lo. of Hinden, Wolverthem, &c.

By vvay of advertisement. Five or six things I have thought worthy to declare before I passe further.

To the Reader.

A Table of the particular heads of this Book, contracted ac∣cording to the severall Arts specified in the Title-page.

A Table of the Contents, and chiefe points con∣teined in this Book. PROBLEM. II.

Ad Authorem D.D. Henricum Van Etenium, Alumnum Academiae Ponta Mousson.

PROBLEM 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.

Note.

EXAMINATION.

PROBLEM II. How to represent to those which are in a Chamer that which is without, or all that which passeth by,

EXAMINATION.

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

EXAMINATION.

PROBLEM IV. How to break a staffe which is laid upon two Glasses full of water, without breaking the Glasses, spilling the water, or upon two reeds or straws without breaking of them.

EXAMINATION.

PROBLEM V. How to make a faire Gegraphicll Card in a Garden Plot, fit for a Prince, or great personage.

PROBLEM VI. How three staves, knives, or like bodies, may be conceived to hang in the aire, without being supported by any thing but by themselves.

PROBLEM VII. How to dispose as many men, or other things in such sort, that rejecting, or casting away the 6, 9, 10 part, unto a certain 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 Vessel which is full of wine conteining eight pints into two equall parts, by two other vessels which conteine as much as the greater vessell; as the one being 5 pints, and the other 3 pints.

PROBLEM. X. To make a stick stand upon the tip of ones finger, without falling.

EXAMINATION.

PROBLEM XI. How a milstone or other Ponderosity, may be sup∣ported by a small needle, without break∣ing o 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 Smoak, which is exhaled of any combustible body whatsoever.

EXAMINATION.

PROBLEM XVI. Many things being disposed circular, (or otherwise) to finde which of them, any one thinks upon▪

PROBLEM XV. How to make a Door or Gate, which shall open on both sides.

PROBLEM XVI. To shew how a Ponderosity, or heavy thing, may be supported upon the end of a staffe (or such like) upon a Table, and nothing holding or touching it.

EXAMINATION.

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 Rinde.

PROBLEM XIX. To finde a number thought upon without asking of any question, certaine ope∣rations 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, and the other square, Quadrangular, and Triangular-wise, yet so that the holes shall be ex∣actly filled.

PROBLEM. 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?

EXAMINATION.

PROBLEM XXII. To finde a number thought upon fter another manner, then what is formerly delivered

PROBLEM XXIII. To finde out many numbers that sundry persons, or one man hath thought upon.

PROBLEM XXIV. 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 another

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.

PROBLEM. XXVII. How it is, that a man standing upright, and looking which way he will, he looketh either true North or true 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 severall par∣ties, to tell which of these numbers 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 compsses, and at one and the same extent, or opening, how to describe many Circles concentricall, that is, greater or lesser one then another?

PROBLEM XXXIV. 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 34. or more Dice.

PROBLEM. XXXVII. How to make water in a Glasse seeme to boyle and sparkle?

EXAMINATION.

PROBLEM. XXXVIII. Of a fine vessell which holds wine or water, being cast ino it at a certaine height, but being filled higher, it will runne out of its owne accord.

EXAMINATION.

PROBLEM. XXXIX. Of a Glasse very pleasant.

PROBLEM. XL. If any one should hold in each hand, as many pieces 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 kin weighing alike, being privately placed into two like Boxes, to finde which of them the Gold or Silver is in.

EXAMINATION.

PROBLEM. XLIII. Two Globes of diverse mettalls, (as one Gold, and the other Copper) yet of equall weight being put into a box, as BG, 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 break 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 being di∣divided by 7, there will re∣maine nothing.

PROBLEM. XLVII. One had a certaine number of crownes, and count∣ing 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 & 6, there rested 5. but counting them by 7 and 7, there remained nothing: how many crownes might he have?

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.

PROBLEM. XLIX. Of a deceitfull ballance which being cty 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.

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, Shadow or Com∣passe, to finde out the North or South, or the foure Cardinall points of the world, East, West, &c?

EXAMINATION.

PROBLEM. LII. Three persons having taken Counters, Cards, or other things, to finde how much each one hath taken.

PROBLEM. LIII. How to make a consort of musick of many parts with one voyce, or one instrument only?

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.

PROBLEM. LV. Of a puse 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 Centre of it?

PROBLEM. LVII. Any one having taken 3 Cards, to finde how many points they containe

PROBLEM. LVII. Many Cards placed in diverse ranks, to finde which of these Cards any one hath thought.

PROBLEM. LVIII. Many Cards being offered to sundry persons, to finde which of these Cards any one thinketh upon.

PROBLEM. LIX. How to make an instrument to help hearing, as Galileus made to help the sight?

PROBLEM. LX. Of a fine lamp which goes not out, though one carry it in ones pocket: or being rolled 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 AB.C. carried apples to a marke 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 mo∣ney as another, how could this be?

PROBLEM. LXIII. Of the properties of some numbers.

PROBLEM. LXIV. Of an excellent lamp, which serves or furnisheth it selfe with oile, and burnes a long time.

PROBLEM. LXV. Of the play at Keyles or nine Pinnes.

PROBLEM. LXIV. Of Spectacles of pleasure.

EXAMINATION.

PROBLEM. LXVII. Of the Adamant or Magnes, and the needles touched therewith.

EXAMINATION.

PROBLEM. LXVIII. Of the properties of Aeolipiles or bowels 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 humane bodies of sta∣tues, of Colossus or huge images, and of monstrous Giants.

Of Statues, of Colossus, or huge images.

Of monstrous Giants.

PROBLEM. LXXI. Of the game at the Palme, at Trap, at Bowles, Paile-maile, and others.

PROBLEM. LXXII. Of the Game of square formes.

PROBLEM. LXXIII. How to make the string of a Viole sensibly shake, without any one touching it?

EXAMINATION.

PROBLEM. LXXIIII. Of a vessell which containes three severall kindes of liquor, all put in at one bung-hole, and drawn out at one tap severally without mixture.

PROBLEM. LXXV. Of burning-Glasses.

EXAMINATION.

PROBLEM. LXXVI. Containing mny plesant Questions by way of Arithmetick.

Of the 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 his 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 Cups of Croesus.

Of Cupids Apples.

Of a Mans Age.

Of the Lion of Bronze placed upon a Foun∣taine with this Epigramme.

PROBLEM. LXXVII. Divers excellent and admirable experiments upon Glasses.

Experiment upon flat and plaine Glasses.

EXAMINATION.

Experiments upon Gibbous, or convex Sphericall Glasses.

Exptriments upon hollow, or Concave sphericall Glasses.

EXAMINATION.

Of other Glasses of pleasure.

EXAMINATION.

PROBLEM. LXXVIII. 1 How to shew to one that is suspitious, what is done in another Chamber or Roome: notwithstand∣ing the interposition of the wall.

Corolarie. 1.

Corolarie 2.

Corolarie 3.

PROBLEM. LXXIX. How with a Musket to strike a mark, not looking towards it, as exact as one aiming at it.

Corolaries. From which may be gathered, that one may exactly shoot out of a Musket to a place which is not seen, being hindered by some obstacle, or other interposition.

PROBLEM. LXXX. How to make an Image to be seen hanging in the aire, having his head downeward.

PROBLEM. LXXXI. How to make a company of representative Souldiers seeme to be a Regiment, or how few in number may be multiplyed to seem to be many in number.

Corolarie.

PROBLEM. LXXXII. Of fine and pleasant Dyal.

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 Dyals with Glasses.

Of a Dyall which hath a Glasse in the place of the Style.

EXAMINATION.

Of Dyals with water.

PROBLEM. LXXXIII. Of Cannons or great Artillery. Souldiers, and o∣thers would willingly see Problems, which containe: three or foure subtile 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 Bull of a Cannon spend in the aire before i 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 vio∣lence than being shot point-blanke, or shooting downeward?

4. In the fourth place it may be asked, whether the discharge of a Cannon b so much the greater, by how much it is longer?

PROBLEM. LXXXIIII. Of predigious progression and multiplication, of Creatures, Plants, Fruits, Numbers, Gold, Silver, &c. when they are alwayes augmented by cer∣taine proportion.

Of graines of Mustard-seed.

Of Pigges.

Of graines of Corne.

Of the increase of Sheep.

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 certaine conditions.

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 mount∣aine to ascend to the top of it, and so to de∣scend 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 runnes out at the top?

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?

4. Fourthly, to conduct water from the top of one Mountaine, to the top of another.

5. Fifthly, of a fine Fountaine which spouts water very high, and with great violence by turning of a Cock.

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 pot for gardens.

9. Ninthly, how easily to take wine out of a vessell at the bug-hole, without piercing of a hole in the vessell?

10. Tenthly, how to measure irregular bodies by help 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 sayl∣ed in the vast Ocean, and being come into the Port or harbour, without any tempest will sink down 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 sink in the water, or swim 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, (with∣out removing any weight) it shall cease to hang in aequilibrio sensibly: yea by a great difference 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, 2•, •0, or a hundred pound of Lead; nay as much as a thousand, or ten thousand and pound weight?

PROBLEM. LXXXVI. Of sundry Questions of Arithmetick, and first of the number of sands.

2. Divers metalls 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 happened at the last partition that there were 21 Barrells, 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 another, & as much wine one as another?

4. There is a Ladder which stands upright against a wall of 10 foot high, the foot of it is pulled out 6 foot from the wall upon the pave∣ment: how much hath the top of the Ladder descended?

PROBLEM. LXXXVII. Witty suits or debates between Caius and Sempro∣nius, upon the forme of fgures, which Geo∣metricians call Isoperimeter, or equall 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. XCII. 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. XCIII. To finde the New and Full Moone in each Moneth.

Note

PROBLEM. XCIV. To finde the Latitude of Countrey.

PRBOLEM XCV. Of the Climates of countreys, and to finde in what Cimate any countrey is under.

PROBLEM. XCVI. Of Longitude and Latitude of the Earth and of the Starres.

Note.

To finde the Longitude of a Countrey.

Of the Latitude of Countreys.

To finde the latitude of Countreys.

To finde the distance of places.

Of the Longitude, Latitude, Declinati∣on, and distance of the Starres.

How is it that two Horses or other creatures being foaled or brought forth into the world at one and the same time, that after certaine dayes travell the one lived more dayes than the other, not∣withstanding they dyed together in one and the sam moment also?

Certaine fine observations.

PROBLEM. XCVII. To make a Triangle that shall have three right Angles.

PROBLEM. XCVIII. To divide a line in as many equall parts as one will, without compasses, or without seeing of it.

PROBLEM. XCIX. To draw a line which shall incline to another line, yet never meet: 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 going abroad?

PROBLEM. CII. How to draw a parallel sphericall line with great ease?

PROBLEM. CIII. To measure an in accessible distance, as the breadth of a River with the help of ones hat onely.

PROBLEM. CIIII. How to measure a height with two strawes or two small stickes.

Otherwise.

PROBLEM. CV. How to make statues, letters, bowles, or other things which are placed in the side of a high build∣ing, to be seen below of an equall bignesse.

PROBLEM. CVI. How to disgis or disfigure an Image, as a head, an arme, a whole body, &c. so that it hath no pro∣portion the eares to become long: the nose as that of a swan, the mouth as a coaches en∣trance, &c yet the eye placed at a certaine point will be seen in a direct & exact proportion.

PROBLEM. CVII. How a Cannon 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 Clock with one onely wheele.

PROBLEM. CX. How by help of two wheeles to make a Childe 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 marve∣lous by reason of the great weight of water that it is able to bring up at once, and so by continuance.

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 water very high: different from a Probleme formerly delivered.

PROBLEM. 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. CXVIII. How to practise excellently the reanimation of sim∣ples, in case the plants may not be transported to be replanted by reason of distance of places.

PROBLEM. CVIII. How to make an infalliable perpetuall motion.

PROBLEM. CXIX. Of the admirable invention of making the Philo∣sophers 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 Artifi∣ciall 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 rst a Capon carried in a Budget at a Saddle-bowe, in the space of riding 5 or 6 miles?

PROBLEM. CXXIV. 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 sick Person?

PROBLEM CXXVI. How to make two Marmouzets, one of which shall light a Candle, and the other put it out?

PROBLEM. XXVII. How to keepe wine fresh as if it were in a celler though it were in the heat of Summer, and without Ice or snow, yea though it were carried at a saddles bow, and ex∣posed to the Sun all the day?

PUOBLEM. CXXVIII. To make a Cement which indureth or lasteth as marble, which resisteth aire and wa∣ter without ever disjoyning or uncementing?

PROBLEM. CXXIX. How to melt metall very quickly, yea in a shell upon a little fire.

PROBLEM. CXXX. How to make Iron or steele exceeding hard?

PRBOLEM CXXXI. To preserve fire as long as you will, imitating the inextinguible fire of Vestales.

Artificiall fire-Workes: Or the manner of making of Rockets and Balls of fire, as well for the Wa∣ter, as for the Aire; with the com∣position of Starres, Golden-rain, Serpens, Lances, Whees 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 run up and downe, forward and backward

How to make Wheels of fire.

Of night-Combatants.

Of standing Fires.

Of Pots of fire for the Aire, which are throwne out of one Case one after another of a long continuance.

Of Pots of fire for the ground.

Of Balles of fre.

Of fire upon the Water.

Of Balles of fire which move upon the water.

Of Lances of fire.

How to shoot a Rocket Horizontall, or otherwise.

How a Rocket burning in the water for a certaine time, at last shall fly up in the Aire with an exceeding quickness.

Of the framing of the parts of a Fire-Worke, together, that the severall workes may fire one after another.

Conclusion.

Printed or sold by William Leak, at the Crovvne in Fleetstreet neere the Temple, these Books following.

title page

The description, and use of the double Horizontall Diall.

I The description of it.

II. The use of it.