Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	divide_v	draw_v	line_n	1,670	5	9.3251	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

as AB and an houre before noone marke the extremitie of the shadow of AB which suppose it be at C. describe a Circle at that semidiamiter CDF then after noone mark when the top of the shadow of AB toucheth the Circle which admit in D divide the distance CD into two equall parts which suppose at E. draw the line EAF which is the Meridian line or line of North South now if the Arke of the Circle CD be divided into degrees place a Needle GH upon a plaine set up in the Centre and marke how many degrees the point of the Needle G is from E. so much doth the Needle vary from the North in that place PROBLEM CI. How to finde at any time which way the wind is in ones Chamber without going abroad VPon the Plancking or floore of a Chamber Parlor or Hall that you intend to have this device let there come downe from the top of the house a hollow post in which place an Iron rod that it ascend above the house 10 or 6 foot with a vane or a scouchen at it to shew the winds without and at the lower end of this rod of Iron place a Dart which may by the moving of the vane with the wind without turne this Dart which is within about which upon the plaister must be described a Circle divided into the 32 points of the Mariners Compasse pointed and distinguished to that end then may it be marked by placi● to Compasse by it for having noted the North point the East c it is easie to note all the rest of the points and so at any time comming into this Roome you have nothing to do but to look up to the Dart which will point you out what way the winde bloweth at that instant PROBLEM CII How to draw a parallel sphericall line with great ease FIrst draw an obscure line GF in the middle of it make two points AB which serves for Centres then place one foot of the Compasses in B and extend the other foot to A and describe the semicircle AC then place one foot of the Compasses in A and extend the other foot to C and describe the semicircle CD Now place the Compasses in B and extend the other foot unto D and describe the semicircle DF and so ad infinitum which being done neatly that there be no right line seene nor where the Compasses were placed will seeme very strange how possibly it could be drawne with such exactnes to such which are ignorant of that way PROBLEM CIII To measure an in accessible distance as the breadth of a River with the help of ones hat onely THe way of this is easie for having ones hat upon his head come neare to the bank of the River and holding your head upright which may be by putting a small stick to some one of your buttons to prop up the chin pluck downe the brim or edge of your hat untill you may but see the other side of the water then turne about the body in the same posture that it was before towards some plaine and marke where the sight by the brimme of the hat glaunceth on the ground for the distance from that place to your standing is the breadth of the River required PROBLEM CIIII. How to measure a height with two strawes or two small stickes TAke two strawes or two stickes which are one as long as another and place them at right Angles one to the other as AB and AC then holding AB parallel to the ground place the end A to the eye at A. and looking to the other top BC. at C. by going backward or forward untill you may see the top of the Tower or tree which suppose at E. So the distance from your standing to the Tower or Tree is equall to the height thereof above the levell of the eye to which if you adde your ovvne height you have the whole height Otherwise TAke an ordinary square which Carpenters or other workemen use as HKL and placing H. to the eye so that HK be levell go back or come nearer untill that by it you may see the top M. for then the distance from you to the height is equall to the height PROBLEM CV How to make statues letters bowles or other things which are placed in the side of a high building to be seen below of an equall bignesse LEt BC. be a Pillar 7 yards high and let it be required that three yards above the levell of the eye A viz. at B. be placed a Globe and 9 yards above B. be placed another 22. yards above that be placed another Globe how much shall the Diameter of these Globes be that at the eye at A they may all appeare to be of one and the same Magnitude It is thus done first draw a line as AK and upon K. erect a perpendicular KX divide this line into 27 parts and according to AK describe an Arke KY then from K in the perpendicular KX account● par●s viz at L. which shall represent the former three yardes and draw the line LA. from L in the said perpendicular reckon the diameter of the lesser Globe of what Magnitude it is intended to be suppose SL and draw the line SA cutting the Arke VK in N. then from K. in the perpendicular account 9 yards which admit at T. draw TA cutting YK. in O transferre the Arke MN from A to P. and draw AP. which will cut the perpendicular in V. so a line drawne from the middle of VF unto the visuall lines AI and AV shall be the diameter of the next Globe Lastly account from K. in the perpendicular XK 22 parts and draw the line WA cutting YK in Q. then take the Arke MN and transferre it from Q to R and draw AR which will cut the perpendicular in X so the line which passeth by the meddle of XW perpendicular to the visuall line AW and AX. be the Diameter of the third Globe to wit 5 6. which measures transferred in the Pillar BC. which sheweth the true Magnitude of the Globes 1 2 3. from this an Architect or doth proportion his Images the foulding of the Robes which are most deformed at the eye below in the making yet most perfect when it is set in his true height above the eye PROBLEM CVI. How to disg●is● 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 seen in a direct exact proportion I Will not strive to set a Geometricall figure here for feare it may seeme too difficult to understand but I will indeavour by discourse how Mechanically with a Candle you may perceive it sensible first there must be made a figure upon Paper such as you please according to his just proportion and paint it as

a line stricken perpendicular upon it apply the streight edg unto the wall at what time the sun shineth upon it holding the board parallel to the horizon Set the dyal thereon and move it gently every way untill the same hour and minute be shewed in both dyals and so let it stand then if the dyal have one of the sides parallel to the Meridian strike a line along that side upon the board crossing the perpendicular or else with a bodkin make a point upon the board at each end of the meridian and taking away the instrument from the board and the board from the wall lay a ruler to those two points and draw a line crossing the perpendicular for the angle which that line maketh with the perpendicular is the angle of the decli●nation of the wall And if it be a right angle the wall is exactly east or west but if that line be parallel to the perpendicular the wall is direct north or south without any declination at all You may also finde out the declination of a wall if the dial be fixed on a post not very far from that wall in this manner Your board being applyed to the wall as was shewed hang up a thred with a plummet so that the shadow of the thred may upon the board crosse the perpendicular line make two pricks in the shadow and run instantly to the dyal and look the horizontal distance of the suns Azumith or upright shadow from the meridian Then through the two pricks draw a line crossing the perpendicular and upon the point of the intersection make a circle equal to the horizon of your Instrument in which Circle you shal from the line through the two pricks measure the Horizontal distance of the upright shadow or Azumith from the meridian that way toward which the Meridian is draw a line out of the center to the end of that arch measured and the angle which this last line maketh with the perpendicular shall be equall to the declination of the wall XIII Vse How to place the dyall upon a post without any other direction but it selfe Set the diall upon the post with the stile into the North as neere as you can guesse then move it this way and that way till the same houre and minute be shewed both in the outward and inward dials by the severall shadowes as hath been already taught for then the diall standeth in its truest situation wherefore let it be nailed down in that very place XIIII Vse To finde the height of the sun at high noon everyday Seeke out the diurnall Arch or parallel of the suns course for that day by Vse III. and with a paire of Compasses setting one foot in the center and the other in the point of intersection of that parallel with the Meridian apply that same distance unto the Semidiameter divided for that measure shal therein shew the degree of of the Suns altitude above the the Horizon that day at high noon XV Vse To finde the height of the sun at any houre or time of the day Seeke out the diurnal Arch or parallel of the suns course for that day and marke what point of it is in the very houre and minute proposed And with a paire of Compasses setting one foot in the Center and the other in that point of the parallel apply the same distance upon the Semidiameter divided for that measure shall shew the degree of the suns altitude above the Horizon at that time And by this meanes you may finde the height of the Sun above the Horizon at every houre throughout the whole yeere for the making of rings and cylinders and other instruments which are used to shew the houre of the day XVI Vse The height of the sun being given to finde out the houre or what it is a clocke This is the converse of the former Seeke therefore in the Semidiameter divided the height of the sun given And with a paire of Compasses setting one foot in the center and the other at that height apply the same distance unto the diurnall arch or parallel of the Sun for that day for that point of the diurnall arch upon which that same distance lights is the true place of the sun upon the dial and sheweth among the houre lines the true time of the day XVII Use. Considerations for the use of the instrument in the night In such questions as concerne the night or the time before sun rising and after sun setting the instrument representeth the lower Hemisphaere wherein the Southerne pole is elevated And therefore the parallels which are above the Aequinoctiall toward the center shall be for the Southerne or winter parallels and those beneath the Aequinoctiall for the Northerne or Summer paral●els and the East shall be accounted for West and the West for East altogether contrary to that which was before when the Instrument represented the upper Hemisphaere XVIII Use. To finde how many degrees the sun is under the Horizon at any time of the night Seeke the Declination of the sun for the day proposed by Vse II. And at the same declination the contrary side imagine a parallel for the sun that night and mark what point of it is in the very houre and minute proposed And with a pair of compasses setting one foot in the center and the other in that point of the parallel apply that same distance unto the semidiameter divided for that measure shall shew the degree of the suns depression below the Horizon at that time XIX Use. To finde out the length of the C●epusculum or twylight every day Seek the declination of the sun for the day proposed by Vse II. And at the same declination on the contrary side imagine a parallel for the sun that night And with a paire of compasses setting one foot in the center and the other at 72 degrees upon the semidiameter divided apply that same distance unto the suns nocturnall parallel for that point of the parallel upon which that same distance shall light sheweth among the houre lines the beginning of the twilight in the morning or the end of the twilight in the evening XX Use. If the day of the moneth be not known to finde it out by the dyall For the working of this question either the diall must be fixed rightly on a post or else you must have a true Meridian line drawn in some window where the sun shineth wherefore supposing the diall to be justly set either upon the post or upon the Meridian Look what a clock it is by the outward diall and observe what point of the upright shadow falleth upon the very same minute in the inner diall and through that same point imagine a parallel circle for the suns course that imaginary circle in the Ecliptick shall cut the day of the moneth I The description of it THis Instrument serveth as a Diall to finde the houre of the day not in one place onely as the most part of Dials do but generally in all Countreys lying North of the Aequinoctiall and therefore I call it the generall H●rologicall ●ing It consisteth of two br●zen circles a Diameter and a little Ring to hang it by The two circles are so made that though they are to be set at right angles when you use the Instrument yet for more convenient carrying they may be one folded into the other The lesser of the two circles is for the Aequinoctiall having in the midst of the inner side or thicknesse a line round it which is the true Aequinoctiall circle divided into twice twelue hours from the two opposite points in which it is fastened within the greater The greater and outer of the two circles is the Meridian One quarter whereof beginning at one of the points in which the Aequin●cti●ll is hung is divided into ninety degrees The Diameter is fastened to the Meridian in two opposite points or poles o●e of them being the very end of the Quadrant and is the North Pole Wherefore it is perpendicular to the ●quinoctiall having his due position The diameter is broad and slit in the middle and about the slit on both sides are the moneths and dayes of the yeer And within this slit is a litt●e sliding plate pierced through with a small hole which hole in the motion of it while it is applied to the dayes of the yeer representeth the Axis of the world The little Ring whereby the Instrument hangeth is made to slip up and down along the Quadrant that so by help of a little tooth annexed the Instrument may be rectified to any elevation of the Pole II. The use of it IN using this Instrument First the tooth of the little Ring must carefully be set to the height of the Pole in the Quadrant for the place wherein you are Secondly the hole of the sliding plate within the slit must be brought exactly unto the day of the moneth Thirdly the Aeqinoctiall is to be drawn out and by means of the two studs in the Meridian staying it it is to be set perpendicular thereto Fourthly Guesse as neer as you can at the houre and turn the hole of the little plate toward it Lastly Hold the Instrument up by the little Ring that it may hang freely with the North Pole thereof toward the North and move it gently this way and that way till the beams of the Sun-shining thorow that hole fall upon that middle line within the Aequinoctiall for there shall be the houre of the day And the Meridan of the Instrument shall hang directly North and South These Instrument all Dials are made in brasse by Elias Allen dwelling over against St. Clements Church without Temple Barre at the signe of the Horse-shooe neere Essex Gate FINIS

pieces to keep the same proportion as the body to his parts so that by the greatnesse of the work and proportionable symmetrie some dare assure themselves that by knowledge of one onely part of that building one might know all the measures of that goodly structure Some Architects say that the foundation of houses and basis of columnes are as the foot the top and roofe as the head the rest as the body those which have beene somewhat more curious have noted that as in humane bodies the parts are uniforme as the nose the mouth c. these which are double are put on one side or other with a perfect equality in the same Architecture In like manner some have been yet more curious than solid comparing all the ornaments of a Corinth to the parts of the face as the brow the eyes the nose the mouth the rounding of Pillars to the vvrithing of haire the channells of columnes to the fouldings of vvomens Robes c. Novv building being a vvork of the best Artist there is much reason vvhy man ought to make his imitation from the chiefe vvork of nature vvhich is man Hence it is that Vitru●ius in his third book and all the best Architectes treate of the proportion of man amongst others Albert Durens hath made a whole book of the measures of mans body from the foot to the head let them read it who wil they may have a prefect knowledge thereof But I will content my selfe and it may satisfie some with that which followeth First the length of a man well made which commonly is called height is equall to the distance from one end of his finger to the other when the armes are extended as wide as they may be Secondly if a man have his feet and hands extended or stretched in forme of S. Andrews Crosse placing one foot of a paire of Compasses upon his navill one may describe a circle which will passe by the ends of his hands and feet and drawing lines by the termes of the hands and feet you have a square within a circle Thirdly the breadth of man or the space which is from one side to another the breast the head and the neck make the 6 part of all the body taken in length or height Fourthly the length of the face is equall to the length of the hand taken from the small of the arme unto the extremity of the longest finger Fiftly the thicknesse of the body taken from the belly to the back the one or the other is the tenth part of the whole body or as some will have it the ninth part little lesse Sixtly the height of the brow the length of the nose the space between the nose and the chinne the length of the eares the greatnesse of the thumbe are perfectly equall one to the other What would you say to make an admirable report of the other parts if I should reckon them in their least but in that I desire to be excused and will rather extract some conclusion upon that which is delivered In the first place knowing the proportion of a man it is easie to Painters Image-makers c. perfectly to proportionate their work and by the same is made most evident that which is related of the images and statues of Greece that upon a day diverse workmen having enterprised to make the face of a man being severed one from another in sundry places all the parts being made and put together the face was found in a most lively and true proportion Secondly it is a thing most cleare that by the help of proportion the body of Hercules was measured by the knowledge of his foot onely a Lion by his claw the Giant by his thumb and a man by any part of his body For so it was that Pythagoras having measured the length of Hercules foot by the steps which were left upon the ground found out all his height and so it was that Phidias having onely the claw of a Lion did figure and draw out all the beast according to his true type or forme so the exquisite Painter Timantes having painted a Pygmey or Dwarfe which he measured with a fadome made with the inch of a Giant it was sufficient to know the greatnesse of that Giant To be short we may by like methode come easily to the knowledge of many fine antiquities touching Statues Colossus and monstrous Giants onely supposing one had found but one only part of them as the head the hand the foot or some bone mentioned in ancient Histories Of Statues of Colossus or huge images VItruvius relates in his second book that the Architect Dinocrates was desirous to put out to the world some notable thing went to Alexander the great and proposed unto him a high and speciall piece of work which he had projected as to figure out the mount Athos in forme of a great Statue which should hold in his right hand a Towne capable to receive ten thousand men and in his left hand a vessell to receive all the water that floweth from the Mountaine which with an ingine should cast into the Sea This is a pretty project said Alexander but because there was not field-roome thereabout to nourish and reteine the Citizens of that place Alexander was wise not to entertaine the designe Now let it be required of what greatnesse this Statue might have been the Towne in his right hand and the receiver of water in his left hand if it had been made For the Statue it could not be higher than the Mountaine it selfe and the Mountaine was about a mile in height plumb or perpendicular therefore the hand of this Statue ought to be the 10th part of his height which would be 500 foot and so the breadth of his hand would be 250 foot the length now multiplyed by the breadth makes an hundred twenty five thousand square feet for the quantitie of his hand to make the towne in to lodge the said 10 thousand men allowing to each man neere about 12 foot of square ground now judge the capacitie of the other parts of this Collossus by that which is already delivered Secondly Plinie in his 34 book of his natural History speakes of the famous Colossus that was at Rhodes between whose legges a Shippe might passe with his sailes open or displayed the Statue being of 70 cubits high and other Histories report that the Sarasens having broken it did load 900 Camels with the mettal of it now what might be the greatnesse and weight of this Statue For answer it is usually allowed for a Camels burthen 1200 pound weight therefore all the Collosus did weigh 1080000 pound weight which is ten hundred and fourescore thousand pound vveight Novv according to the former rules the head being the tenth part of the body this Statues head should be of 7 cubits that is to say 10 foot and a halfe and seeing that the Nose the brovv and the thumbe are the third part of the face his Nose

Compasses so much is the distance between the two places If the distance of two places be required in a particular Map then with the Compasses take the distance between the two places and apply it to the scale of Miles so have you the distance if the scale be too short take the scale between the Compasses and apply that to the two places as often as you can so have you the distance required Of the Longitude Latitude Declination and distance of the Starres THe Declination of a starre is the nearest distance of a Star from the Aequator the Latitude of a Starre is the nearest distance of a Sarre from the Ecliptick the Longitude of a Starre is an Ark of the Ecliptick conteined between the beginning of Aries and the Circle of the Starres Latitude which is a circle drawne from the Pole of the Ecliptick unto the starre and so to the Ecliptick The distance between two Sarres in Heaven is taken by a Crosse-staffe or other Instrument and upon a Globe it is done by taking between the feet of the Compasses the two Starres and applying it to the Aequator so have you the distance betweene those two starre● 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 notwithstanding they dyed together in one and the sam● moment also THis is easie to be answered let one of them travell toward the West and the other towards the East then that which goes towards the West followeth the Sunne and therefore shall have the day somewhat longer than if there had been no travell made and that which goes East by going against the Sunne shall have the day shorter and so in respect of travell though they dye at one and the selfe same houre and moment of time the one shall be older than the other From which consideration may be inferred that a Christian a Jew and a Saracen may have their Sabbaths all upon one and the same day though notwithstanding the Saracen holds his Sabath upon the Friday the Jew upon the Saturday and the Christian upon the Sunday For being all three resident in one place if the Saracen and the Christian begin their travell upon the Saturday the Christian going West and the Saracen Eastwards shall compasse the Globe of the earth thus the Christian at the conclusion shall gaine a day and the Saracen shall lose a day and so meet with the Jew every one upon his owne Sabbath Certaine fine observations 1 UNder the Equinoctiall the Needle hangs in equilibrio but in these parts it inclines under the Horizon and being under the Pole it is thought it will hang verticall 2 In these Countreys which are without the Tropicall Circles the Sunne comes East and West every day for a halfe yeare but being under the Equinoctiall the Sun is never East nor West but twice in the yeare to wit the 10. of March and the 13 of September 3 If a ship be in the Latitude of 23 gr 30 m. that is if it have either of the Tropicks verticall then at what time the Sunnes Altitude is equall to his distan●e from any of the Equinoctiall points then t●e Sunne is due East or West 4 If a ship be betweene the Equinoctiall and either of the Tropicks the Sunne will come twice to one point of the compasse in the forenoone that is in one and the same position 5 Vnder the Equinoctiall neare Guinea there is but two sorts of windes all the year 6 moneths a Northerly winde and 6 moneths a Southerly winde and the flux of the Sea is accordingly 6 If two ships under the Equinoctiall be 100. leagues asunder and should sayle Northerly untill they were come under the Articke circle they should then be but 50 leagues asunder 7 Those which have the Artick circle verticall when the Sunne is in the Tropick of Cancer the Sun setteth not but toucheth the western part of the Horizon 8 If the complement of the Sunnes height at noon be found equall to the Sunnes Declination for that day then the ●quinoctiall is verticall or a shippe making such an observation the Equinoctiall is in the Zenith or direct over them by which Navigators know when they crosse the line in their travels to the Indies or other parts 9 The Sunne being in the Equinoctiall the extremity of the stile in any Sunne-dyall upon a plaine maketh a right line otherwise it is Eclipticall Hyperbolicall c. 10 When the shadow of a man or other thing upon a Horizontall 〈◊〉 is equall unto it in length then is the Sunne in the middle point between the Horizon and the Zenith that is 45 degrees high PROBLEM XCVII To make a Triangle that shall have three right Angles OPen the C●passes at p●easure and upon A describe an Arke BC. then at the same opening place one of the feet in B and describe the Ark AC Lastly place one of the feet of the Compasses in C. and describe the Arke AB· so shall you have the sphericall Aequilaterall Triangle ABC right angled at A at B and at C. that is each angle comprehended 9● degrees which can never be in any plaine Triangle whether it be Equilaterall Isocelse scaleve Orthogonall or Opigonall PROBLEM XCVIII To divide a line in as many equall parts as one will without compasses or without seeing of it THis Proposition hath a fallacie in it cannot be practised but upon a Maincordion for the Mathematicall line which proceeds from the flux of a point cannot be divided in that wise One may have therefore an Instrument which is called Maincordion because there is but one cord and if you desire to divide your line into 3 parts run your finger upon the frets untill you sound a third in musick if you would have the fourth part of the line then finde the fourth sound a fifth c. so shall you have the answer PROBLEM XCIX To draw a line which shall incline to another line yet never meet against the Axiome of Parallels THis is done by help of a Conoeide line produced by a right line upon one the same plaine held in great account amongst the Ancients and it is drawne after this manner Draw a right line infinitely and upon some end of it as at I draw a perpendicular line I A. augment it to H. then from A. draw lines at pleasure to intersect the line I. M. in each of which lines from the right line IM transferre IH viz. KB LC.OD.PE.QF.MG then from those points draw the line H.B.C.D.E.F.G. which will not meet with the line IM and yet incline nearer and nearer unto it PROBLEM C. To observe the variation of the compasses or needle in any places FIrst describe a Circle upon a plaine so that the Sun may shine on it both before noone and afternoone in the centre of which Circle place a Gn●●on or wire perpendicular

side for as trees have their growth in winter because of their pores and these of the earth are shut up so in the spring when their pores are open and when the sappe and moisture is drawne by it there is not such cold on the North-side that it may be condensed at once But contrarily to the side which is South the heat may be such that in little time by continuance this moisture is dissipated greatly and cold is nothing but that which hardneth and contracteth the moisture of the tree and so converteth it into wood PROBLEM LII Three persons having taken Counters Cards or other things to finde how much each one hath taken CAuse the third party to take a number which ma● be divided by 4 and as often as he takes 4 let the second party take 7 and the first take 13 then cause them to put them all together and declare the summe of it which secretly divide by 3 and the Quotient is the double of the number which the third person did take Or cause the third to give unto the second and first as many as each of them hath then let the second give unto the first and third as many as each of them hath lastly let the third give unto the second and first as many as each of them hath and then aske how much one of them hath for they will have then all alike so halfe of that number is the number that the third person had at the first which knowne all is knowne PROBLEM LIII How to make a consort of musick of many parts with one voyce or one instrument only THis Probleme is resolved so that a finger or player upon an instrument be neare an Echo which answereth his voice or instrument and if the Echo answereth but once at a time he may make a double if twice then a triple if three times then an harmonie of foure parts for it must be such a one that is able to exercise both tune and note as occasion requires As when he begins ut before the Echo answer he may begin sol and pronounce it in the same tune that ●he Echo answereth by which meanes you ●ave a fifth agreeable consort of musick then in the same time that the Echo followeth to sound the second note sol he may sound forth another sol higher or lower to make an eight the most perfect consort of musick and so of others if he will continue his voice with the Echo and sing alone with two parts Now experience sheweth this to be true which often comes to passe in many Churches making one to beleeve that there are many more parts in the musick of a Quire then in effect truly there are because of the resounding and multiplying of the voic● and redoubling of the Quire 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 THere are many fine wayes in Geometricall practices to make an Ovall figure or one neare unto it by severall centres any of which I will not touch upon but shew how it may be done promptly upon one centre only In which I will say nothing of the Ovall forme which appeares when one describeth circles with the points of a common Compasses somewhat deep upon a skinne stretched forth hard which contracting it selfe in some parts of the skinne maketh an Ovall forme But it will more evidently appeare upon a Columne or Cylinder if paper be placed upon it then with a paire of Compasses describe as it were a circle upon it which paper afterwards being extended will not be circular but ovall-wise and a paire of Compasses may be so accommodated that it may be done also upon a plaine thus As let the length of the Ovall be H. K fasten 2 pinnes or nailes neare the end of that line as F. G and take a threed which is double to the length of G. H or F. K then if you take a Compasse which may have one foot lower than another with a spring between his legges and placing one foot of this Compasse in the Centre of the Ovall and guiding the threed by the other foot of the Compasses and so carrying it about the spring will help to describe and draw the Ovall forme But in stead of the Compasses it may be done with ones hand only as in the figure may appeare PROBLEM LV. Of a pu●se difficult to be opened IT is made to shut and open with Rings first at each side there is a strap or string as AB and CD at the end of which are 2 rings B D and the string CD passeth through the ring B so that it may not come out againe or be parted one from another and so that the ring B may slide up and downe upon the string CD then over the purse there is a piece of Leather EFGH which covers the opening of the purse and there is another piece of Leather AE which passeth through many rings which hath a slit towards the end I so great that the string BC may slide into it Now all the cunning or craft is how to make fast or to open the purse which consists in making the string BC slide through the side at I therefore bring down B to I then make the end I passe through the ring B and also D with his string to passe through the slit I so shall the purse be fast and then may the strings be put as before and it will seem difficult to discover how it was done Now to open the purse put through the end I through the ring B and then through the slit I by which you put through the string DC by this way the purse will 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 IT is said that upon a time past two Mathematicians met and they would make tryall of their industry the one made instantly a Perfect circle without Compasses and the other immediately pointed out the Centre thereof with the point of a needle now which is the chiefest action it seems the first for to draw the most noblest figure upon a plaine Table without other help than the hand and the minde is full of admiration to finde the Centre is but to finde out only one point but to draw a round there must be almost infinite points equidistant from the Centre or middle that in conclusion it is both the Circle and the Centre together But contrarily it may seem that to finde the Centre is more difficult for what attention vivacitie and subtiltie must there be in the spirit in the eye in the hand which will chuse the true point amongst a thousand other points He that makes a circle keeps alwayes the same distance and is guided by a halfe distance to finish the rest but he that must finde the Centre must in the

but somewhat scattering notwithstanding it casteth a very great beautifull light Lastly those which feare to hurt their sight by the approach of Lampes or Candles may by this artifice place at some corher of a Chamber a Lamp with a hollow Glasse behinde it which will commodiously reflect the light upon a Table or to a place assigned so that the Glasse be somewhat raised to make the light to streeke upon the Table with sharp Angles as the Sunne doth when it is but a little elevated above the Horizon for this light shall exceed the light of many Candles placed in the Roome and be more pleasant to the sight of him that useth it Of other Glasses of pleasure FIrst the Columnary and Pyramidall Glasses that are contained under right lines do represent the Images as plaine Glasses do and if they be bowing then they represent the Image as the concave and convex Glasses do Secondly those Glasses which are plaine but have ascents of Angels in the middle will shew one to have foure Eyes two Mouthes two Noses c. EXAMINATION TH●se experiments will be found different according to the diverse meeting of the Glasses which commonly are made scuing-wise at the end 〈◊〉 which there will be two divers superficies in the Glasse making the exteriour Angle somewhat raised at the interiour onely one superficies which may be covered according to ordinary Glasses to c●use a reflexion and so it will be but one Glasse which by refraction according to the different thicknesse of the Glasse and different Angles of the scuing forme do differently present the Images to the eye as foure eyes two mouthes two noses sometimes three eyes one mouth and one nose the one large and the other long sometimes two eyes onely with the mouth and the nose deformed which the Glasse impenetrable will not shew And if there be an interiour solid Angle according to the difference of it as if it be more sharp there will be represented two distinct double Images that is two entire visages and as the Angle is open by so much the more the double Images will reunite and enter one within another which will present sometimes a whole visage extended at large to have foure eyes two noses and two mouthes and by moving the Glasse the Angle will vanish and so the two superficies will be turned into one and the duplicity of Images will also vanish and appeare but one onely and this is easily experimented with two little Glasses of steel or such like so united that they make divers Angles and inclinations THirdly there are Glasses which make men seeme pale red and coloured in diverse manners which is caused by the dye of the Glasse or the diverse refraction of the Species and those which are made of Silver Latine Steele c. do give the Images a diverse colour also In which one may see that the appearances by some are made fairer younger or older than they are and contrarily others will make them foule and deformed and give them a contrary visage for if a Glasse be cut as it may be or if many pieces of Glasse be placed together to make a conveniable reflexion there might be made of a Mole as it were a mountaine of one Haire a Tree a Fly to be as an Elephant but I should be too long if I should say all that which might be said upon the property of Glasses I will therefore conclude this discourse of the properties of these Glasses with these foure recreative Problemes following PROBLEM LXXVIII 1 How to shew to one that is suspitious what is done in another Chamber or Roome notwithstanding the interposition of the wall FOr the performance of this there must be placed three Glasses in the two Chambers of which one of them shall be tyed to the planching or seeling that it may be common to communicate the Species to each Glasse by reflexion there being left some hole at the top of the Wall against the Glasse to this end the two other Glasses must be placed against the two Walls at right Angles as the figure here sheweth at B. and C. Then the sight at E by the line of incidence FE shall fall upon the Glasse BA and reflect upon the superficies of the Glasse BC in the point G so that if the eye be at G it should see E and E would reflect upon the third Glass in the point H and the eye that is at L will see the Image that is at E. in the point of the Cath●r● which Image shall come to the eye of the suspicious viz. at L. by help of the third Glasse upon which is made the second reflexion and so brings unto the eye the object though a wall be between it Corolarie 1. BY this invention of reflections the besiegers of a Towne may be seene upon the Rampart notwithstanding the Parapet which the besieged may do by placing a Glasse in the hollow of the Ditch and placing another upon the toppe of the wall so that the line of incidence comming to the bottom of the Ditch make an Angle equall to the Angle of reflexion then by this situation and reflexion the Image of the besiege● 〈◊〉 will be seen to him is upon the Rampart Corolarie 2. BY which also may be inferred that the same reflexions may be seen in a Regular Polygon and placing as many Glasses as there are sides counting two for one for then the object being set to one of the Glasses and the eye in the other the Jmage will be seen easily Corolarie 3. FArther notwithstanding the interposition of many Walls Chambers or Cabinets one may see that which passeth through the most remotest of them by placing of many Glasses as there are openings in the walls making them to receive the incident angles equall that is placing them in such sort by some Geometricall assistant that the incident points may meet in the middle of the Glasses but here all the defect will be that the Jmages passing by so many reflexions will be very weak and scarce observable PROBLEM LXXIX How with a Musket to strike a mark not looking towards it as exact as one aiming at it AS let the eye be at O and the mark C place a plaine Glasse perpendicular as AB so the marke C shall be seen in Catheti CA viz. in D and the line of reflexion is D now let the Musket FE upon a rest be moved to and fro untill it be seen in the line OD which admit to be HG so giving fire to the Musket it shall undoubtedly strike the mark 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 AS let the eye be at M the mark C and the wall which keeps it from being seene admit to be QR then set up a plaine Glass as AB and let the Musket by GH placed upon his rest PO. Now

because the marke C is seen at D move the Musket to and fro untill it doth agree with the line of reflection MB which suppose at LI so shall it be truly placed and giving fire to the Musket it shall not faile to strike the said mark at C. PROBLEM LXXX How to make an Image to be seen hanging in the aire having his head downeward TAke two Glasses and place them at right Angles one unto the other as admit AB and CB of which admit CB Ho●izontall and let the eye be at H and the object or image to be DE so D will be reflected at F so to N so to HE then at G so to ● and then to H and by a double reflection ED will seeme in QR the highest point D in R and the point L in Q inversed as was said taking D for the head and E for the feet so it will be a man inversed which will seem to be flying in the aire if the Jmage had wings unto it and had secretly 〈◊〉 motion and if the Glasse were bigge enough to receive many reflexions it would deceive the sight the more by admiring the changing of colours that would be seen by that motion 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 TO make the experiment upon men there must be prepared two great Glasses but in stead of it we will suppose two lesser as GH and FI one placed right against another perpendicular to the Horizon upon a plaine levell Table betvveene vvhich Glasses let there be ranged in Battalia-vvise upon the same Table a number of small men according to the square G H I F or in any other forme or posture hen may you evidently see hovv the said battel vvill be multiplyed and seem farre bigger in the appearance than it is in effect Corolarie BY this invention you may make a little Cabinet of foure foot long and tvvo foot large more or lesse vvhich being filled vvith Rockes or such like things or there being put into it Silver Gold Stones of luster Jewels c. and the walls of the said Cabinet being all covered or hung with plaine glasse these visibles will appeare manifoldly increased by reason of the multiplicitie of reflexions and at the opening of the said Cabinet having set something which might hide them from being seen those that look into it will be astonished to see so few in number which before seemed to be so many PROBLEM LXXXII Of fine and pleasant Dyal● COuld you choose a more ridiculous one than the natural Dyall written amongst the Greek Epigrams upon which some sound Poet made verses shewing that a man carrieth about him alwayes a Dyall in his face by meanes of the Nose and Teeth and is not this a jolly Dyall for he need not but open the mouth the lines shall be all the teeth and the nose shall serve for the style Of a Dyall of hearbes CAn you have a finer thing in a Garden or in the middle of a Compartemeet than to see the lines and the number of houres represented with little bushie hearbes as of Hysope or such which is proper to be cut in the borders and at the top of the style to have a Fanne to shew which way the winde b●oweth this is very pleasant and useful Of the Dyall upon the fingers and the hand IS it nor a commoditie very agreeable when one is in the fie●d or in some vil●age vvithout any other Dyall to see onely by the hand what of the clock it is vvhich gives it very neare and may be practised by the left hand in this manner Take a stravv or like thing of the length of the Index or the second finger hold this straw very right betvveen the thumb and the fore-finger then stretch forth the hand and turne your back and the palm of your hand tovvards the Sunne so that the shadovv of the muscle vvhich is under the Thumb touch the line of life vvhich is betvveen the middle of the tvvo other great lines vvhich is seen in the palme of the hand this done the end of the shadovv vvill shevv vvhat of the clock it is for at the end of the first finger it is 7 in the morning or 5 in the evening at the end of the Ring-finger it is 8 in the morning or 4 in the evening at the end of the little finger or first joynt it is 9 in the morning or 3 in the after-noone 10 2 at the second joynt 11 and 1 at the third joynt and midday in the line follovving vvhich comes from the end of the Index Of a Dyall which was about an Obeliske at Rome WAs not this a pretty fetch upon a pavement to choose an Obeliske for a Dyall having 106 foot in height without removing the Basis of it Plinie assures us in his 26 book and 8 Chap. that the Emperour Augustus having accom●odated in the field of Mars an Obeliske of this height he made about it a pavement and by the industry of Man●lius the Mathematician there were enchaced markes of Copper upon the Pavement and placed also an Apple of Gold upon the toppe of the said Obeliske to know the houre and the course of the Sunne with the increase and decrease of dayes by the same shadow and in the same manner do some by the shadow of their head or other style make the like experiments in Astronomie Of Dyals with Glasses PT●lomie w●ites as Cardanus reports that long ago there were Glasses which served for Dyals and presented the face of the beholder as many times as the houre ought to be twice if it were 2 of the clock 9 if it were 9 c. But this was thought to be done by the help of water and not by Glasses which did leake by little and little out of the vessell discovering anon one Glasse then anon two Glasses then 3 4 5 Glasses c. to shew so many faces as there were houres which was onely by leaking of water Of a Dyall which hath a Glasse in the place of the Style WHat will you say of the invention of Mathematicians which finde out daily so many fine and curious novelties they have now a way to make Dyals upon the wainscot or seeling of a Chamber and there where the Sunne can never shine or the beames of the Sunne cannot directly strike and this is done in placing of a little Glasse in the place of the style which reflecteth the light with the same condition that the shadow of the style sheweth the houre and it is easie to make experiment upon a common Dyall changing only the disposition of the Dyall and tying to the end of the style a piece of plaine Glasse The Almaines use it much who by this way have no greater trouble but to put their Noses out of their beds and see what a clock it is which is reflected