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 starreâ— 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 samâ— 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 distanâ—e from any of the Equinoctiall points then tâ—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 â—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 Câ—passes at pâ—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 9â— 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 Gnâ—â—on or wire perpendicular
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 decliâ—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 paralâ—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 Câ—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 Hâ—rologicall â—ing It consisteth of two brâ—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 Aequinâ—ctiâ—ll is hung is divided into ninety degrees The Diameter is fastened to the Meridian in two opposite points or poles oâ—e of them being the very end of the Quadrant and is the North Pole Wherefore it is perpendicular to the â—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 littâ—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
here there must be found a number vvhich multiplied by 7 and then divided by 2 3 4 5 6 there may alvvayes remaine a number lesse by 1 than the Divisor Novv the first number vvhich arrives in this nature is 119 unto vvhich if 420 be added makes 539 vvhich also vvill do the same and so by adding 420 you may have other numbers to resolve this proposition PROBLEM XLVIII How many sorts of weights in the least manner must there be to weigh all sorts of things between 1 pound and 40 pound and so unto 121 364 pound TO vveigh things betvveen 1 and 40 take numbers in triple proportion so that their summe be equall or somewhat greater than 40 as are the numbers 1 3.9.27 I say that with â— such weights the first being of 1 pound the second being 3 pound the third being 9 pound and the fourth being 27 any weight between 1 and 40 pound may be weighed As admit to weigh 21 pound put unto the thing that is to be weighed the 9 pound weight then in the other ballance put 27 pound and 3 pound which doth counterpoise 21 pound and 9 pound and if 20 pound were to be weighed put to it in the ballance 9 and 1 and in the other ballance put 27 and 3 and so of others In the same manner take those 5 weights 1 3 9 27 81 you may weigh with them between 1 pound and 121 pound and taking those 6 weights as 1 3 9 2â— 81 243 you may weigh even from 1 pound unto 364 pound this depends upon the property of continued proportionals the latter of which containing twice all the former PROBLEM XLIX Of a deceitfull ballance which being câ—â—â—ty seemes iâ— be just because it hangs in aequilibrio notâ—ithstanding putting 12 pound in one ballance and 11 in the other it will remaine in aequilibrio ARistotle maketh mention of this ballance in his mechanick Questions and saith that the Merchants of purpose in his time used them to deceive the world the subtiltie or craft of which is thus that one arme of the ballance is longer then another by the same proportion that one weight is heavier then another As if the beame were 23 inches long and the handle placed so that 12 inches should be on one side of it and 11 inches on the other side conditionally that the shorter end should be as heavy as the longer a thing easie to be done then afterwards put into the ballance two unequal weights in such proportion as the parts of the beame have one unto another which is 12 to 11 but so that the greater be placed in the ballance which hangs upon the shorter part of the beame and the lesser weight in the other ballance it is most certaine that the ballances will hang in aequilibrio which will seem most sincere and just though it be most deceitfull abominable and false The reason of this is drawne from the experiments of Archimedes who shewes that two unequall weights will counterpoyse one another when there is like proportion betweene the parts of the beame that the handle separates and the vveights themselves for in one and the same counterpoise by hovv much it is farther from the Centre of the handle by so much it seems heavier therefore if there be a diversitie of distance that the ballances hang from the handle there must necessarily be an ineqality of weight in these ballances to make them hang in aequilibrio and to discover if there be deceit change the weight into the other ballance for as soone as the greater vveight is placed in the ballance that hangs on the longer parts of the beame it vvill vveigh dovvne the other instantly PROBLEM L. To heave or lift up a bottle with a straw TAke a stravv that is not bruised bovv it that it make an Angle and put it into the bottle so that the greatest end be in the neck then the Reed being put in the bovved part vvil cast side-vvise and make an Angle as in the figure may be seen then may you take the end vvhich is out of the bottle in your hand and heave up the bottle and it is so much surer by how much the Angle is acuter or sharper and the end which is bowed approacheth to the other perpendicular parts which come out of the bottle PROBLEM LI. How in the middle of a wood or desert without the sight of the Sunne Starres Shadow or Compasse to finde out the North or South or the foure Cardinall points of the world East West c IT is the opinion of some that the windes are to be observed in this if it be hot the South is found by the windes that blow that way but this observation is uncertaine and subject to much error nature will help you in some measure to make it more manifest than any of the former from a tree thus Cut a small tree off even to the ground and mark the many circles that are about the sap or pith of the tree which seem nearer together in some part than in other which is by reason of the Suns motion about the tree for that the humiditie of the parts of the tree towards the South by the heat of the Sun is rarified and caused to extend and the Sâ—n not giving such heat towards the North-part of the tree the sap is lesser rarefied but condensed by which the circles are nearer together on the North-part than on the South-part therefore if a line be drawne from the widest to the narrowest part of the circles it shall shew the North South of the world Another Experiment may be thus Take a small needle such as women work with place it gently downe flatwise upon still water and it will not sink which is against the generall tenet that Iron will not swimme which needle will by little and little turne to the North and South-points But if the needle be great and will not swim thrust it through a small piece of Cork or some such like thing and then it will do the same for such is the property of Iron when it is placed in aequilibrio it strives to finde out the Poles of the world or points of North and South in a manner as the magnes doth EXAMINATION HEre is observable that the moisture which aideth to the growth of the tree is dilated and rarefied by the Meridionall heat and contracted by the Septentrionall cold this rarefaction works upon the part of the humour or moisture that is more thinne which doth easily dissipate and evaporate which evaporation carries a part of the salt with it and because that solidation or condensation so that there is left but a part of the nourishment which the heat bakes up and consumes so contrarily on the other side the condensation and restrictive quality of the moisture causeth lesse evaporation and perdition and so consequently there remaines more nourishment which makes a greater increase on that side than on the other
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 Statiâ—k 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 LONDON Printed for William Leake at the Signe of the Crown in Fleetstreet between the two Temple Gates MDCLIII On the Frontispice and Booke ALL Recreations do delight the minde But these are best being of a learned kinde Here Art and Nature strive to give content In shewing many a rare experiment Which you may read on their Schemes here look Both in the Frontispice and in the Book Upon whose table new conceits are set Like dainty dishes thereby for to whet And winne your judgement with your appetite To taste them and therein to taka delight The Senses objects are but dull at best But Art doth give the Intellect a feast Come hither then and here I will describe What this same Table doth for you provide Here Questions of Arithmetick are wrought And hidden secrets unto light are brought The like it in Geometrie doth unfold And some too in Cosmographie are told It divers pretty Dyals doth descrie With strange experiments in Astronomie And Navigation with each severall Picture In Musick Opticks and in Architecture In Statick Machanicks and Chymistrie In Water-works and to ascend more hie In Fire-works like to Joves Artillerie All this I know thou in this Book shalt finde And here 's enough for to content thy minde For from good Authors this our Author drew These Recreations which are strange and true So that this Book 's a Centre and t is fit That in this Centre lines of praise should meet W. MATHEMATICALL Recreations Or a Collection of sundrie excellent Problemes out of ancient moderne Phylosophers Both vsefull and Recreatiue Printed for William Leake and are to be solde at the Crowne in fleet streete betweene the two Temple gates TO The thrice Noble and most generous Lo. the Lo. Lambert Verreyken Lo. of Hinden Wolverthem c. My honourable Lo. AMongst the rare and curious Propositions which I have learned out of the studies of the Mathematicks in the famous University of Pont a Mousson I have taken singular pleasure in certaine Problemes no lesse ingenious than recreative which drew me unto the search of demonstrations more difficult and serious some of which I have amassed and caused to passe the Presse and here dedicate them now unto your Honour not that I account them worthy of your view but in part to testifie my affectionate desires to serve you and to satisfie the curious who delight themselves in these pleasant studies knowing well that the Nobilitie and Gentrie rather studie the Mathematicall Arts to content and satisfie their affections in the speculation of such admirable experiments as are extracted from them than in hope of gaine to fill their Purses All which studies and others with my whole indevours I shall alwayes dedicate unto your Honour with an ardent desire to be accounted ever Your most humble and obedient Nephew and Servant H. VAN ETTEN By vvay of advertisement Five or six things I have thought worthy to declare before I passe further FIrst that I place not the speculative demonstrations with all these Problems but content my self to shew them as at the fingers end which was my plot and intention because those which understand the Mathematicks can conceive them easily others for the most part will content themselves onely with the knowledge of them without seeking the reason Secondly to give a greater grace to the practice of these things they ought to be concealed as much as they may in the subtiltie of the way for that which doth ravish the spirits is an admirable effect whose cause is unknowne which if it were discovered halfe the pleasure is lâ—st therefore all the finenesse consists in the dexterity of the Act concealing the meanes and changing often the streame Thirdly great care ought to be had that one deceive not himselfe that would declare by way of Art to deceive another this will make the matter contemptible to ignorant Persons which will rather cast the fault upon the Science than upon him that shewes it when the cause is not in the Mathematicall principles but in him that failes in the acting of it Fourthly in certaine Arithmeticall propositions they have onely their answers as I found them in sundry Authors which any one being studious of Mathematicall learning may finde their originall and also the way of their operation Fifthly because the number of these Problemes and their dependances are many and intermixed I thought it convenient to gather them into a Table that so each one according to his fancie might make best choise of that which might best please his palate the matter being not of one nature nor of like subtiltie But whosoever will have patience to read on shall finde the end better than the beginning To the Reader IT hath been observed by many that sundry fine wits as well amongst the Ancient as Moderne have sported and delighted themselves upon severall things of small consequence as upon the foot of a fly upon a straw upon a point nay upon nothing striving as it were to shew the greatnesse of their glory in the smalnesse of the subject And have amongst most solid and artificiall conclusions composed and produced sundry Inventions both Philosophicall and Mathematicall to solace the minde and recreate the spirits which the succeeding ages have imbraced and from them gleaned and extracted many admirable and rare conclusions judging that borrowed matter often-times yeelds praise to the industry of its author Hence for thy use Courteous Reader I have with great search and labour collected also and heaped up together in a body of these pleasant and fine experiments to stirre up and delight the affectionate out of the writings of Socrates Plato Aristotle Demosthenes Pythagoras Democrates Plinie Hyparchus Euclides Vitruvius Diaphantus Pergaeus Archimedes Papus Alexandrinus Vitellius Ptolomaeus Copernicus Proclus Mauralicus Cardanus Valalpandus Kepleirus Gilbertus Tychonius Dureirus Josephus Clavius Gallileus Maginus Euphanus Tyberill and others knowing Art imitating Nature that glories alwayes in the variety of things which she produceth to satisfie the minde of curious inquisitors And though perhaps these labours to some humourous persons may seeme vaine and ridiculous for such it was not undertaken But for those which intentively have desired and â—ought after the knowledge of those things it being an invitation and motive to the search of greater matters and to imploy the minde in usefull knowledge rather than to be busied in vaine
Pamphlets Play-books fruitlesse Legends and prodigious Histories that are invented out of fancie which abuse many Noble spirits dull their wits alienate their thoughts from laudable and honourable Studies In this Tractate thou maist therefore make choise of such Mathematicall Problemes and Conclusions as may delight thee which kinde of learning doth excellently adorne a man seeing the usefulnesse thereof and the manly accomplishments it doth produce is profitable and delightfull for all sorts of people who may furnish and adorne themselves with abundance of matter in that kinde to help them by way of use and discourse And to this we have also added our Pyrotechnie knowing that Beasts have for their object only the surface of the earth but hoping that thy spirit which followeth the motion of fire will abandon the lower Elements and cause thee to lift up thine eyes to soare in an higher Contemplation having so glittering a Canopie to behold and these pleasant and recreative fires ascending may cause thy affections also to ascend The Whole whereof we send forth to thee that desirest the scrutability of things Nature having furnished us with matter thy spirit may easily digest them and put them finely in order though now in disorder A Table of the particular heads of this Book contracted according to the severall Arts specified in the Title-page Experiments of Arithmetick PAge 1 2 3 16 19 22 28 33 39 40 44 45 51 52 53 59 60 69 71 77 83 85 86 89 90 91 124 134 135 136 137 138 139 140 178 179 181 182 183 184 185 188 208 210 213. Experiments â—n Geometrie Pag. 12 15 24 26 27 30 35 37 41 42 47 48 49 62 65 72 79 82 113 117 118 119 214 215 217 218 234 235 236 239 240. Experiments in Cosmographie Pag. 14 43 75 106 107 219 220 225 227 228 229 230 232. Experiments in Horologiographie Pag. 137 166 167 168 169 171 234. Experiments in Astronomie Pag. 220 221 222 223 224. Experiments in Navigation Pag. 105 233 234 237 238. Experiments in Musick Pag. 78 87 126. Experiments in Opticks Pag. 6 66 98 99 100 102 129 131 141 142 143 144 146 149 151 152 153 155 156 157 158 160 161 162 163 164 165. Experiments in Architecture Pag. 16 242 243. Experiments in Staticke Pag. 27 30 32 71 199 200 201 283 204 205 207. Experiments in Machanicks Pag. 56 58 68 88 95 108 110 128 173 174 176 246 248 258 259. Experiments in Chymistrie Pag. 198 255 256 257 260 262 263 264. Experiments in Water-workes Pag. 190 191 192 193 194 196 247 249 250 252 253. Experiments in Fireworkes From page 265. to the end FINIS A Table of the Contents and chiefe points conteined in this Book PROBLEM II. HOw visible objects that are without and things that passe by are most lively represented to those that are within Page 6 Prob. 1 Of finding of numbers conceived in the minde 1 2 3 Prob. 5 Of a Geographicall Garden-plot fit for a Prince or some great personage 14 Prob. 37 Any liquid substance as water or wine placed in a Glasse may be made to boile by the motion of the finger and yet not touching it 54 Prob. 3 How to weigh the blow of ones fist of a Mallet a Hatchet or such like 9. Prob. 30 Two severall numbers being taken by two sundry persons how subtilly to discover which of those numbers each of them took 46 Prob. 4 That a staffe may be broken placed upon two Glasses without hurting of the Glasses 12 Prob. 7 How to dispose Lots that the 5 6 9 c. of any number of persons may escape 16 Prob. 13 How the weight of smoke of a combustible body which is exhaled may be weighed 27 Prob. 12 Of three knives which may be so disposed to hang in the aire and move upon the Point of a needle 27 Prob. 17 Of a deceitfull bowle to bowle withall 32 Prob. 16 A ponderous or heavy body may be supported in the aire without any one touching it 30 Prob. 18 How a Peare or Apple may be parted into any parts without breaking the rinde thereof 33 Prob. 15 Of a fine kinde of dore which opens and shuts on both sides 30 Prob. 9 How the halfe of a Vessell which containes 8 measures may be taken being but onely two other measures the one being 3 and the other 8 measures 22 Prob. 8 Three persons having taken each of them severall things to finde which each of them hath taken 19 Prob. 6 How to dispose three staves which may support each other in the aire 15 Prob. 14 Many things being disposed Circular or otherwise to finde which of them any one thinks upon 28 Prob. 19 To finde a number thought upon without asking questions 33 Prob. 11 How a Milstone or other ponderosity may hang upon the point of a Needle without bowing or any wise breaking of it 26 Prob. 20 and 21 How a body that is uniforme and inflexible may passe through a hole which is round square and Triangular or round square and ovall-wise and exactly fill those severall holes 35 37 Prob. 10 How a stick may stand upon ones finger or a Pike in the middle of a Court without falling 24 Prob. 22 To finde a number thought upon after another manner than those which are formerly delivered 39 Prob. 23 To finde out many numbers that sundry persons or any one hath thought upon 40 Prob. 24 How is it that a man in one the same time may have his head upward and his feet upward being in one and the same place 4â— Prob. 25 Of a Ladder by which two men ascending at one time the more they ascend the more they shal be asunder notwith standing the one be as high as the other 42 Prob. 26 How is it that a man having but a Rod or Pole of land doth brag that he may in a right line passe from place to place 3000 miles 42 Prob. 27 How is it that a man standing upright and looking which way he will he looketh true North or South 43 Prob. 28 To tell any one what number remaines after certaine operations being ended without asking any question 44 Prob. 29 Of the play with two severall things 45 Prob. 31 How to describe a circle that shall touch 3 points placed howsoever upon a plaine if they be not in a right line 47 Prob. 32 How to change a circle into a square forme 48 Prob. 33 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 49 Prob. 34 Any number under 10. being thought upon to finde what numbers they were 51 Prob 35 Of the play with the Ring 52 Prob. 36 The play of 3 4 or more Dice 53 Prob. 38 Of a fine Vessell which holds Wine or Water being cast into it at a certain height but being filled higher it will runne all out of its owne
as they vvould be if there vvere a liquid substance in the Glasse hence they have an assured proofe to conclude that the hollovv of the Glasse is totally empty 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 BId him that holds the money that he put out of one hand into the other vvhat number you think convenient provided that it may be done this done bid him that out of the hand that he put the other number into that he take out of it as many as remaine in the other hand and put it into that hand for then be assured that in the hand which was put the first taking away there will be found just the double of the number taken away at the first Example admit there were in each hand 12 Shiâ—lings or Counters and that out of the right hand you bid him take 7. and put it into the left and then put into the right hand from the left as many as doth remaine in the right which is 5. so there will be in the left hand â—4 which is the double of the number taken out of the right hand to wit 7. then by some of the rules before delivered it is easie to finde how much is in the right hand viz. 10. PROBLEM XLI Many Dice being cast how artificially to discover the number of the points that may arise SVppose any one had cast three Dice secretly bid him that he adde the points that were upmost together then putting one of the Dice apart unto the former summe adde the points which are under the other two then bid him throw these two Dice and mark how many points a paire are upwards which adde unto the former summe then put one of these Dice away not changing the side mark the points which are under the other Dice and adde it to the former summe lastly throw that one Dice and whatsoever appeares upward adde it unto the former summe and let the Dice remaine thus this done comming to the Table note what points do appeare upward upon the three Dice which adde privately together and unto it adde â—1 or 3 times 7 so this Addition or summe shall be equall to the summe which the party privately made of all the operations which he formerly made As if he should throw three Dice and there should appeare upward 5 3 2. the sum of them is 10. and setting one of them apart as 5. unto 10 adde the points which are under 3 and 2 which is 4 and 5 and it makes 19. then casting these two Dice suppose there should appeare 4 and 1 this added unto 19 makes 24. and setting one of these two Dice apart as the 4. unto the former 24 I adde the number of points which is under the other Dice viz. under 1 that is 6 which makes 30. Last of all I throw that one Dice and suppose there did appeare 2 which I adde to the former 30 and it makes 32 then leaving the 3 dice thus the points which are upward will be these 5 4 2 unto which adde secretly 21 as before was said so have you 32 the same number whiâ—h he had and in the same manner you may practise with 4 5 6 or many Dice or other bodies observing only that you must adde the points opposite of the Dice for upon which depends the whole demonstration or secret of the play for alwayes that which is above and underneath makes 7. but if it make another number then must you adde as often that number PROBLEM XLII Two mettals as Gold and Silver or of other kinâ—â— weighing alike being privately placed into two like Boxes to finde which of them the Gold or Silver is in But because that this experiment in water hath divers accidents and therefore subject to a caution and namely because the matter of the chest mettall or other things may hinder Behold here a more subtill and certaine invention to finde and discover it out without weighing it in the water Now experience and reason sheweth us that two like bodies or magnitudes of equall weight and of divers mettalls are not of equal quantity and seeing that Gold is the heaviest of all mettalls it will occupie less roome or place from which will follow that the like weight of Lead in the same forme will occupie or take up more roome or place Now let there be therefore presented two Globes or Chests of wood or other matter alike equall one to the other in one of which in the middle there is another Globe or body of lead weighing 12. l. as C and in the other a Globe or like body of Gold weighing 12 pound as B. Now it is supposed that the wooden Globes or Chests are of equall weight forme and magnitude and to discover in which the Gold or Lead is in take a broad paire of Compasses and clip one of the Coffers or Globes somewhat from the middle as at D. then fix in the Chest or Globe a small piece of Iron between the feet of the Compasses as EK at the end of which hang a vveight G so that the other end may be counterpoysed and hang in aequilibrio and do the like to the other Chest or Globe Novv if that the other Chest or Globe being clipped in like distance from the end and hanging at the other end the same weight G. there be found no difference then clip them nearer tovvards the middle that so the points of the Compasse may be against some of the mettall vvhich is inclosed or just against the extremitie of the Gold as in D and suppose it hang thus in aequilibrio it is certaine that in the other Coffer is the Lead for the points of the Compasses being advanced as much as before as at F vvhich takes up a part of the Lead because it occupies a greater place than the Gold therefore that shall help the vveight G. to vveigh and so vvill not hang in aequilibrio except G be placed neare to F. hence vve may conclude that there is the Lead and in the other Chest or Globe there is the Gold EXAMINATION IF the two Boxes being of equall magnitude weighed in the aire be found to be of equall weight they shall necessarily take up like place in the water and therefore weigh also one as much as another hence there is no possibilitie to finde the inequalitie of the mettalls which are inclosed in these Boxes in the water the intention of Archimedes was not upon contrary mettalls inclosed in 〈…〉 Boxes but consisted of comparing mettaâ—â—â— simple in the water one with another therefore the inference is false and absurd 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 THis is discovered by the changing of the places of the tvvo Bovvles or Globes
same time take heed to the parts about it and choose one only point which is equall distant from an infinite of other points which are in the circumference which is very difficult Aristotle confirmes this amongst his morals and seems to explaine the difficultie which is to be found in the middle of vertue for it may want a thousand wayes and be farre separated from the true Centre of the end of a right mediocritie of a vertuous action for to do well it must touch the middle point which is but one and there must be a true point which respects the end and that 's but one only Now to judge which is the most difficult as before is said either to draw the round or to finde the Centre the round seems to be harder than to finde the Centre because that in finding of it it is done at once and hath an equall distance from the whole But as before to draw a round there is a visible point imagined about which the circle is to be drawne I esteeme that it is as difficult therefore if not more to make the circle without a Centre as to finde the middle or Centre of that circle PROBLEM LVII Any one having taken 3 Cards to finde how many points they containe THis is to be exercised upon a full Pack of Cards of 52 then let one choose any three at pleasure secretly from your sight and bid him secretly account the points in each Card and will him to take as many Cards as will make up 15 to each of the points of his Cards then will him to give you the rest of the Cards for 4 of them being rejected the rest shew the number of points that his three Cards which he took at the first did conteine As if the 3 Cards were 7 10 and 4 now 7 wants of 15 8. take 8 Cards therefore for your first Card the 10 wants of 15 5 take 5 cards for your second card lastly 4 wants of 15 11 take 11 Cards for your third Card giving him the rest of the Cards there will be 25 from which take 4 there remaines 21 the number of the three Cards taken viz. 7 10 and 4. Whosoever would practise this play with 4 5 6 or more Cards and that the whole number of Cards be more or lesse than 52 and that the terme be 15 14 12 c this generall rule ensuing may serve multiply the terme by the number of Cards taken at first to the product adde the number of Cards taken then subtract this summe from the whole number of Cards the remainder is the number which must be subtracted from the Cards which remaines to make up the game if there remaine nothing after the Subtraction then the number of Cards remaining doth justly shew the number of points which were in the Cards chosen If the Subtraction cannot be made then subtract the number of Cards from that number and the remainder added unto the Cards that did remaine the summe will be the number of points in the Cards taken as if the Cards were 7 10 5 8 and the terme given were 12 so the first wants 5 the second wants 2 the third wants 7 and the fourth wants 4 Cards which taken the party gives you the rest of the Cards then secretly multiply 12 by 4 makes 48 to which adde 4 the number of Cards taken makes 52 from which 52 should be taken rest nothing therefore according to the direction of the remainder of the Cards which are 30 is equall to the points of the foure Cards taken viz. 7 10 5 8. Againe let these five Cards be supposed to be taken 8 6 10 3 7 their differences to 15 the termes are 7 9 5 12 8 which number of Cards taken there will remaine but 6 Cards then privately multiply 15 by 5 makes 75 to which adde 5 makes 80 from this take 52 the number of Cards rest 28 to vvhich add the remainder of Cards make 34. the summe with 8 6 10 3 7. PROBLEM LVII Many Cards placed in diverse ranks to finde which of these Cards any one hath thought TAke 15 Cards and place them in 3 heaps in rank-wise 5 in a heap now suppose any one had thought one of these Cards in any one of the heaps it is easie to finde vvhich of the Cards it is and it is done thus ask him in vvhich of the heaps it is vvhich place in the middle of the other tvvo then throvv dovvne the Cards by 1 and 1 into three severall heaps in rank-vvise untill all be cast dovvne then aske him in which of the rankes his Card is which heap place in the middle of the other two heaps alwayes and this do foure times at least so in putting the Cards altogether look upon the Cards or let their back be towards you and throw out the eight Card for that was the Card thought upon without faile PROBLEM LVIII Many Cards being offered to sundry persons to finde which of these Cards any one thinketh upon ADmit there were 4 persons then take 4 Cards and shew them to the first bid him think one of them and put these 4 away then take 4 other Cards and shew them in like manner to the second person and bid him think any one of these Cards and so do to the third person and so the fourth c. Then take the 4 Cards of the first person and dispose them in 4 rankes and upon them the 4 Cards of the second person upon them also these of the third person and lastly upon them these of the fourth person then shew unto eaeh of these parties each of these ranks and aske him if his Card be in it which he thought for infallibly that vvhich the first partie thought upon vvill be in the first rank and at the bottome the Card of the second person vvill be in the second ranke the Card of the third thought upon will be in the third rank and the fourth mans Card will be in the fourth rank and so of others if there be more persons use the same method This may be practised by other things ranking them by certaine numbers allotted to pieces of money or such like things PROBLEM LIX How to make an instrument to help hearing as Galileus made to help the sight THink not that the Mathematickes which hath furnished us with such admirable helps for seeing is wanting for that of hearing it s well knowne that long trunks or pipes make one heare well farre off and experience shewes us that in certaine places of the Orcades in a hollow vault that a man speaking but softly at one corner thereof may be audibly understood at the other end notwithstanding those which are between the parties cannot heare him speak at all And it is a generall principle that pipes do greatly help to strengthen the activitie of naturall causes we see that 〈◊〉 contracted in a pipe burnes 4 or 5 foot high which would scarce heat being in
his most glorious beauty This Glasse hath also a most excellent use in observing the body of the Moone in time of Eclipses for it augments it manifold and most manifestly shewes the true forme of the cloudy substance in the Sunne and by it is seene when the shadow of the earth begins to eclipse the Moon when totally she is over shadowed besides the celestiall uses which are made of this Glasse it hath another noble property it farre exceedeth the ordinary perspective Glasses which are used to see things remote upon the earth for as this Glasse reacheth up to the heavens and excelleth them there in his performance so on the earth it claimeth preheminency for the objects which are farthest remote and most obscure are seen plainer than those which are neere at hand scorning as it were all small and triviall services as leaving them to an inferiour help great use may be made of this Glass in discovering of Ships Armies c. Now the apparell or parts of this instrument or Glasse is very meane or simple which makes it the more admirable seeing it performes such great service having but a convex Glasse thickest in the middle to unite and amasse the rayes and mak the object the greater to the augmenting the visuall Angle as also a pipe or trunk to amasse the Species and hinder the greatness of the light which is about it to see well the object must be well inlightened and the eye in obscurity then there is adjoyned unto it a Glasse of a short sight to distinguish the rayes which the other would make more confused if alone As for the proportion of those Glasses to the Trunk though there be certaine rules to make them yet it is often by hazard that there is made an excellent one there being so many difficulties in the action therefore many ought to be tryed seeing that exact proportion in Geometricall calculation cannot serve for diversity of sights in the observation PROBLEM LXVII Of the Adamant or Magnes and the needles touched therewith WHo would beleeve if he saw not with his eyes that a needle of steel being once touched with the magnes turnes not once not a yeare but as long as the World lasteth his end towards the North and South yea though one remove it and turne it from his position it will come againe to his points of North and South Who would have ever thought that a brute stone black and ill formed touching a ring of Iron should hang it in the aire and that ring support a second that to support a third and so unto 10 12 or more according to the strength of the magnes making as it vvere a chaine without a line without souldering together or without any other thing to support them onely but a most occult and hidden vertue yet most evident in this effect which penetrateth insensibly from the first to the second from the second to the third c. What is there in the world that is more capable to cast a deeper astonishment in our minds than a great massie substance of Iron to hang in the aire in the middest of a building without any thing in the world touching it only but the aire As some histories assure us that by the aid of a Magnes or Adamant placed at the roof of one of the Turkish Synagogues in Meca the sepulchre of that infamous Mahâ—met rests suspended in the aire and Plinie in his naturall Historie writes that the Architect or Democrates did begin to vault the Temple of Aâ—sinâ—e in Alexandria with store of magnes to produce the like deceit to hang the sepulchre of that Goddesse likewise in the aire I should passe the bounds of my counterpoise if I should divulge all the secrets of this stone and should expose my selfe to the laughter of the world if I should brag to shew others the cause how this appeareth than in its owne naturall sympathy for why is it that a magnes with one end will cast the Iron away attract it with the other from whence commeth it that all the magnes is not proper to give a true touch to the needle but only in the two Poles of the stone which is known by hanging the stone by a threed in the aire untill it be quiet or placed upon a peece of Cork in a dish of water or upon some thinne board for the Pole of the stone will then turne towards the Poles of the world and point out the North and South and so shew by which of these ends the needle is to be touched From whence comes it that there is a variation in the needle and pointeth not out truly the North and South of the world but only in some place of the earth How is it that the needle made with pegges and inclosed within two Glasses sheweth the height of the Pole being elevated as many degrees as the Pole is above the Horizon What 's the cause that fire and Garlick takes away the propertie of the magnes There are many great hidden mysteries in this stone which have troubled the heads of the most learned in all ages and to this time the world remaines ignorant of declaring the rrue cause thereof Some say that by help of the Magnes persons which are absent may know each others minde as if one being here at London and another at Prague in Germany if each of them had a needle touched with one magnes then the vertue is such that in the same time that the needle which is at Prague shall move this that is at London shall also provided that the parties have like secret notes or alphabets and the observation be at a set houre of the day or night and when the one party will declare unto the other then let that party move the needle to these letters which will declare the matter to the other and the moving of the other parties needle shall open his intention The invention is subtile but I doubt whether in the world there can be found so great a stone or such a Magnes which carries with it such vertue neither is it expedient for treasons would be then too frequent and open EXAMINATION THe experimentall difference of rejection and attraction proceeds not from the different nature of Stones but from the quality of the Iron and the vertue of the stone consisteth only and especially in his poles which being hanged in the Aire turnes one of his ends alwayes naturally towards the South and the other towards the North but if a rod of Iron be touched with one of the ends thereof it hath the like property in turning North and South as the magnes hath notwithstanding the end of the Iron Rod touched hath a contrary position to that end of the stone that touched it yet the same end will attract it and the other end reject it and so contrarily this may easily be experimented upon two needles touched with one or different stones though they have
one and the same position for as you come unto them apply one end of the magnes neare unto them the North of the one will abhorre the North of the other but the North of the one will alwayes approach to the South of the other and the same affection is in the stones themselves For the finding of the Poles of the magnes it may be done by holding a small needle between your fingers softly and so moving it from part to part over the stone untill it be held perpendicular for that shall be one of the Poles of the stone which you may marke out in like manner finde out the other Pole Now to finde out which of those Poles is North or South place a needle being touched with one of the Poles upon a smooth convex body as the naile of ones finger or such like and marke which way the end of the needle that was touched turneth if to the South then the point that touched it was the South-Pole c. and it is most certain and according to reason and experience that if it be suspended in aequilibrio in the aire or supported upon the water it will turne contrary to the needle that toucheth it for then the pole that was marked for the South shall turne to the North c. PROBLEM LXVIII Of the properties of Aeolipiles or bowels to blow the fire THese are concave vessels of Brass or Copper or other material which may indure the fire having a small hole very narrow by which it is filled with water then placing it to the fire before it be hot there is no effect seen but assoone as the heat doth penetrate it the water begins to rarefie issueth forth with a hidious and marvelous force it is pleasure to see how it blowes the fire with great noise Novv touching the forme of these vessels they are not made of one like fashion some makes them like a bovvle some like a head painted representing the vvinde some make them like a Peare as though one vvould put it to rost at the fire vvhen one vvould have it to blovv for the taile of it is hollovv in forme of a funnell having at the top a very little hole no greater than the head of a pinne Some do accustome to put vvithin the Aeolipile a crooked funnell of many foldings to the end that the vvinde that impetuously rolles to and fro vvithin may imitate the noise of thunder Others content themselves vvith a simple funnell placed right upvvard somevvhat vvider at the top than elsevvhere like a Cone vvhose basis is the mouth of the funnell and there may be placed a bovvle of Iron or Brasse vvhich by the vapours that are cast out vvill cause it to leap up and dance over the mouth of the Aeolipile Lastly some apply near to the hole smal Windmils or such like vvhich easily turne by reason of the vapours or by help of tvvo or more bovved funnels a bowle may be made to turneâ— these Aeolipiles are of excellent use for the melting of mettalls and such like Now it is cunning and subtiltie to fill one of these Aeolipiles with water at so little a hole and therefore requires the knowledge of a Philosopher to finde it out and the way is thus Heat the Aeolipiles being empty and the aire which is within it will become extreamely rarefied then being thus hot throw it into water and the aire will begin to be condensed by which meanes it will occupie lesse roome therefore the water will immediately enter in at the hole to avoide vacuitie thus you have some practicall speculation upon the Aeolipile PROBLEM LXIX Of the Thermometer or an instrument to measure the degrees of heat and cold in the aire THis Instrument is like a Cylindricall pipe of Glasse which hath a little ball or bowle at the toppe the small end of which is placed into a vessell of water below as by the figure may be seene Then put some coloured liquor into the Cylindricall glasse as blew red yellow green or such like such as is not thick This being done the use may be thus Those that will determine this change by numbers and degrees may draw a line upon the Cylinder of the Thermometer and divide it into 4 degrees according to the ancient Philosophers or into 4 degrees according to the Physicians dividing each of these 8 into 8 others to have in all 64 divisions by this vvay they may not only distinguish upon vvhat degree the vvater ascendeth in the morning at midday at any other houre but also one may knovv hovv much one day is hotter or colder than another by marking hovv many degrees the vvater ascendeth or descendeth one may compare the hottest and coldest dayes in a vvhole year together vvith these of another year againe one may knovv hovv much hotter one roome is than another by vvhich also one might keep a chamber a furnace a stove c. alvvayes in an equalitie of heat by making the vvater of the Thermometer rest alvvayes upon one the same degree in brief one may judge in some measure the burning of Fevers and neare unto what extension the aire can be rarefied by the greatest heat Many make use of these glasses to judge of the vveather for it is observed that if the vvater fall in 3 or 4 hours a degree or thereabout that raine insueth and the vvater vvill stand at that stay untill the vveather change marke the water at your going to bed for if in the morning it hath descended raine followeth but if it be mounted higher it argueth faire weather so in very cold weather if it fall suddenly it is snow or some sleekey weather that wiil insue PROBLEM LXX Of the proportion of humane bodies of statues of Colossus or huge images and of monstrous Giants PYthagoras had reason to say that man is the measure of all things First because he is the most perfect amongst all bodily creatures according to the Maxime of Philosophers that which is most perfect and the first in rank measureth all the rest Secondly because in effect the ordinary measure of a foot the inch the cubit the pace have taken their names and greatnesse from humane bodies Thirdly because the symmetrie and concordancie of the parts is so admirable that all workes which are well proportionable as namely the building of Temples of Shippes of Pillars and such like pieces of Architecture are in some measure fashioned and composed after his proportion And we know that the Arke of Noah built by the commandement of God was in length 300 Cubits in breadth 50 Cubits in height or depth 30 cubits so that the length containes the breadth 6 times and 10 times the depth now a man being measured you will finde him to have the same proportion in length breadth and depth Vilalpandus treating of the Temple of Solomon that chieftaine of works was modulated all of good Architecture and curiously to be observed in many
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 Hoâ—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 â— 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 Dyalâ— 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 bâ—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 fieâ—d or in some vilâ—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 accomâ—odated in the field of Mars an Obeliske of this height he made about it a pavement and by the industry of Manâ—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 PTâ—lomie wâ—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
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 placiâ— 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 accountâ— parâ—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 disgâ—isâ— 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