circuit of the earth is 21600 miles From the Centre of the earth to the Moone there is neare 56 Semidiameters of the earth which is about 192416 miles unto the Sunne there is 1142 Semidiameters of the earth that is in miles 3924912 from the starry firmament to the Centre of the earth there is 14000 Semidiameters that is 48184000 miles according to the opinion and observation of that learned Ticho Brahe From these measures one may collect by Arithmeticall supputations many pleasant propositions in this manner First if you imagine there were a hole through the earth and that a Milstone should be let fall down into this hole and to move a mile in each minute of time it would be more than two dayes and a halfe before it would come to the Centre and being there it would hang in the aire Secondly if a man should go every day 20 miles it would be three yeares wanting but a fortnight before he could go once about the earth and if a Bird should fly round about it in two dayes then must the motion be 450 miles in an houre Thirdly the Moone runnes a greater compasse each houre than if in the same time she should runne twice rhe Circumference of the whole earth Fourthly admit it be supposed that one should go 20 miles in ascending towards the heavens every day he should be above 15 years before he could attaine to the Orbe of the Moone Fifthly the Sunne makes a greater way in one day than the Moone doth in 20 dayes because that the Orbe of the Sunnes circumference is at the least 20 times greater than the Orbe of the Moone Sixthly if a Milstone should descend from the pâ—ace of the Sunne a thousand miles every houre which is above 15 miles in a minute farre beyond the proportion of motion it would be above 163 dayes before it would fall dovvne to the earth Seventhly the Sunne in his proper sphere moves more than seven thousand five hundred and seventy miles in one minute of time novv there is no Bullet of a Cannon Arrovv Thunderbolt or tempest of vvinde that moves vvith such quicknesse Eightly it is of a farre higher nature to consider the exceeding and unmoveable quicknesse of the starry firmament for a starre being in the Aequator which is just between the Poles of the world makes 12598666 miles in one houre which is two hundred nine thousand nine hundred and seventy foure miles in one minute of time if a Horseman should ride every day 40 miles he could not ride such a compasse in a thousand yeares as the starry firmament moves in one houre which is more than if one should move about the earth a thousand times in one houre and quicker than possible thought can be imagined and if a starre should flye in the aire about the earth with such a prodigious quicknesse it would burne and consume all the world here below Behold therefore how time passeth and death hasteth on this made Copernicus not unadvisedly to attribute this motion of Primum mobile to the earth and not to the starry firmament for it is beyond humane sense to apprehend or conceive the rapture and violence of that motion being quicker than thought and the word of God testifieth that the Lord made all things in number measure weight and time PROBLEM XCII To finde the Bissextile yeare the Dominicall letter and the letters of the moneth LEt 123 or 124 or 125 or 26 or 27 which is the remainder of 1500 or 1600 be divided by 4 which is the number of the Leape-yeare and that which remaines of the division shewes the leap-yeare as if one remaine it shewes that it is the first yeare since the Bissextile or Leap-year if two it is the second year c. and if nothing remaine then it is the Bissextile or Leap-yeare and the Quotient shews you how many Bissextiles or Leap-yeares there are conteined in so many yeares To finde the Circle of the Sun by the fingers LEt 123 24 25 26 or 27 be divided by 28 which is the Circle of the Sunne or whole revolution of the Dominicall letters and that which remaines is the number of joynts which is to be accounted upon the fingers by Filius esto Dei coelum bonus accipe gratis and where the number ends that finger it sheweth the yeare which is present and the words of the verse shew the Dominicall letter Example DIvide 123 by 28 for the yeare and so of other yeares and the Quotient is 4 and there remaineth 11 for which you must account 11 words Filius esto Dei c. upon the joynts beginning from the first joynt of the Index and you shall have the answer For the present to know the Dominicall letter for each moneth account from January unto the moneth required including January and if there be 8 9 7 or 5 you must begin upon the end of the finger from the thumbe and account Adam degebat c. as many words as there are moneths for then one shall have the letter which begins the moneth then to know what day of the moneth it is see how many times 7 is comprehended in the number of dayes and take the rest suppose 4 account upon the first finger within without by the joynts unto the number of 4 which ends at the end of the finger from whence it may be inferred that the day required was Wednesday Sunday being attributed to the first joynt of the first finger or Index and so you have the present yeare the Dominicall letter the letter which begins the Moneth and all the dayes of the Moneth PROBLEM XCIII To finde the New and Full Moone in each Moneth ADde to tâ—e Epact for the yeare the Moneth from March then subtract that surplus from 30 and the rest is the day of the Moneth that it vvill be New Moone and adding unto it 14 you shall have that Full Moone Note THat the Epact is made alwayes by adding 11 unto 30 and if it passe 30 subtract 30 and adde 11 to the remainder and so ad infinitum as if the Epact were 12 adde 11 to it makes 23 for the Epact next year to vvhich adde 11 makes 34 subtract 30 rests 4 the Epact for the yeare after and 15 for the yeare follovving that and 26 for the next and 7 for the next c. PROBLEM XCIV To finde the Latitude of â— Countrey THose that dwell between the North-Pole and the Tropicke of Cancer have their Spring and Summer between the 10 of March and the 13 of September and therefore in any day between that time get the sunnes distance by instrumentall observation from the zenith at noone and adde the declination of the sun for that day to it so the Aggragate sheweth such is the Latitude or Poles height of that Countrey Now the declination of the sunne for any day is found out by Tables calculated to that end or Mechanically by the Globe or by Instrument it may
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
water 198 11 To finde the weight of water 199 12 To finde the charge that a vessell may carry as Ships Boats or such like 200 13 How comes it that a ship having safely sailed in the vast Ocean and being come into the port or harbour will sinke down right 200 14 How a grosse body of metall may swim upon the water 201 15 How to weigh the lightnesse of the aire 203 16 Being given a body to mark it about and shew how much of it will sink in the water or swim above the water 204 17 To finde how much severall metalls or other bodies do weigh lesse in the water than in the aire 204 18 How is it that a ballance having like weight in each scale and hanging in Aequilibrio in the aire being removed from that place without diminishing the weights in each balance or adding to it it shall cease to hang in Aequilibrio sensibly yea by a great difference of weight 205 19 To shew what waters are heavier one than another and how much 206 20 How to make a pound of water weigh as much as 10 20 30 or a hundred pound of Lead nay as much as a thousand or ten thousand pound weight 207 Prob. 86. Of sundry questions of Arithmetick and first of the number of sands calculated by Archimedes and Clavius 208 2 Divers metalls being melted together in one body to finde the mixture of them 210 3 A subtile question of three partners about equality of Wine and Vessels 213 4 Of a Ladder which standing upright against a wall of 10 foot high the foot of it is pulled out 6 foot from the wall upon the pavement how much hath the top of the Ladder descended 214 Prob. 87 Witty suits or debates between Caius and Sempronius upon the forme of figures which Geometricians call Isoperimeter or equall in circuit or Compasse 214 1 Incident of changing a field of 6 measures square for a long rectrangled fiel of 9 measures in length and 3 in breadth both equall in circuit but not in quantity 215 2 Incident about two sacks each of them hoâ—ding but a bushell and yet were able to hold 4 bushels 217 3 Incident sheweth the deceit of pipes which conveygh water that a pipe of two inches diameter doth cast out foure times as much water as a pipe of one such diameter 218 7 Heapes of Corne of 10 foot every way is not as much as one heap of Corne of 20 foot every way 218 Prob. 88 Of sundry questions in matter of Cosmographie and Astronomy In what place the middle of the earth is supposed to be 219 Of the depth of the earth and height of the Heavens and the compasse of the World how much 219 How much the starry Firmament the Sun and the Moone are distant from the centre of the earth 220 How long a Mill-stone would be in falling to the centre of the earth from the superficies if it might have passage thither 220 How long time a man or a bird may be in compassing the whole earth 220 If a man should ascend by supposition 20 miles every day how long it would be before he approach to the Moone 221 The Sunne moves more in one day than the Moone in 20 dayes 221 If a milstone from the orbe of the Sun should descend a thousand miles in an houre how long it would be before it come to the earth 221 Of the Sunnes quick motion of more than 7500 miles in one minute 221 Of the rapt and violent motion of the starry Firmament which if a Horseman should ride every day 40 miles he could not in a thousand yeares make such a distance as it moves every houre 221 To finde the Circle of the Sunne by the fingers 223 Prob. 93 Of finding the new and full Moone in each moneth 224 Prob. 94 To finde the latitude of Countreys 225 Prob. 95 Of the Climates of Countreys and how to finde them 225 Prob. 96 Of longitude and latitude of the places of the earth and of the Starres of the Heavens 227 To finde the Longitude of a Countrey 228 Of the Latitude of a Countrey 229 To finde the Latitude of a Countrey 230 To finde the distance of places 230 Of the Longitude Latitude Declination and distance of the starres 231 How is it that two Horses or other creatures comming into the World at one time and dying at one and the same instant yet the one of them to be a day older than the other 232 Certaine fine Observations In what places of the World is it that the needle hangs in Aequilibrio and verticall 233 In what place of the world is it the sun is East or West but twice in the yeare 233 In what place of the World is it that the Sunnes Longitude from the Equinoctiall paints and Altitude being equall the Sunne is due East or West That the sunne comes twice to one point of the Compasse in the forenoone or afternoone 233 That in some place of the World there are but two kindes of winde all the yeare 233 Two ships may be two leagues asunder under the equinoctiall and sayling North at a certaine parallell they will be but just halfe so much 233 To what inhabitants and at what time the sunne will touch the north-part of the Horizon at midnight 234 How a man may know in his Navigation when he is under the Equinoctiall 234 At what day in the yeare the extremitie of the styles shadow in a Dyall makes a right line 234 What height the Sunne is of and how far from the Zenith or Horizon when a mans shadow is as long as his height 234 Prob. 97 To make a Triangle that shall have three right Angles 234 Prob. 98 To divide a line in as many parts as one will without compasses or without seeing of it 235 Prob. 99 To draw a line which shall incline to another line yet never meet against the Axiome of Parallells 236 Prob. 100 To finde the variation of the Compasse by the Sunne shining 237 Prob. 101 To know which way the winde is in ones Chamber without going abroad 238 Prob. 102 How to draw a parallel sphaericall line with great ease 239 Prob. 103 To measure an height onely by help of ones Hat 240 Prob. 104 To take an height with two strawes 240 In Architecture how statues or other things in high buildings shall beare a proportion to the eye below either equall double c. 242 Prob. 106 Of deformed figures which have no exact proportion where to place the eye to see them direct 243 Prob. 107 How a Cannon that hath shot may be covered from the battery of the Enemy 244 Prob. 108 Of a fine Lever by which one man alone may place a Cannon upon his Carriage 245 Prob. 109 How to make a Clock with one wheele 246 Of Water-workes Prob. 110 How a childe may draw up a Hogshead of water with ease 247 Prob. 111 Of a Ladder of Cords to cary in ones
be indifferently had and here note that if the day be between the 13 of September and the 10 of March then the sunnes declination for that day must be taken out of the distance of the sunne from the zenith at noone so shall you have the Latitude as before PRBOLEM XCV Of the Climates of countreys and to finde in what Câ—imate any countrey is under CLimates as they are taken Geographically signifie nothing else but when the lâ—ngtâ— of the longest day of any place is half an houre longer or shorter than it is in another place and so of the shâ—rtest day and this account to begin from the Equinoctiaâ—l Circle seeing all Countreys under it have the shortest and longest day that can be but 12 houres But all other Countreys that are from the Equinoctiall Circle either towards the North or South of it unto the Poles themselves are said to be in some one Climate or other from the Equinoctiall to either of the Poles Circles which are in the Latitude of 66 degr 30 m. between each of which Polar Circles and the Equinoctial Circle there is accounted 24 Climates which differ one from another by halfe an hours time then from each Polar Circle to each Pole there are reckoned 6. other Climates which differ one from another by a moneths time so the whole earth is divided into 60 Climates 30 being allotted to the Northerne Hemisphere and 30â— to the Southerne Hemispheare And here note that though these Climats which are betweene the Equinoctiall and the Polar Circles are equall one unto the other in respect of time to wit by halfe an houre yet the Latitude breadth or internall conteined between Climate and Climate is not equall and by how much any Climate is farther from the Equinoctiall than another Climate by so much the lesser is the intervall between that Climate and the next so those that are nearest the Equinoctial are largest and those which are farthest off most contracted and to finde what Climate any Countrey is under subtract the length of an Equinoctiall day to wit 12 houres from the length of the longest day of that Countrey the remainder being doubled shews the Climate So at London the longest day is neare 16 houres and a halfe 12 taken from it there remaines 4 houres and a halfe which doubled makes 9 halfe houres that is 9 Climates so London is in the 9 climate PROBLEM XCVI Of Longitude and Latitude of the Earth and of the Starres LOngitude of a Countrey or place is an arcke of the Aequator conteined between the Meridian of the Azores and the Meridian of the place and the greatest Longitude that can be is 360 degrees Note That the first Meridian may be taken at pleasure upon the Terrestriall Globe or Mappe for that some of the ancient Astronomers would have it at Hercules Pillars which is at the straights at Gibraltar Ptolomy placed it at the Canary Islâ—nds but now in these latter times it is held to be neare the Azores But why it was first placed by Ptolomy at the Canary Islands were because that in his time these Islands were the farthest westerne parts of the world that vvas then discovered And vvhy it reteines his place novv at Saint Michaels neare the Azores is that because of many accurate observations made of late by many expert Navigators and Mathematicians they have found the Needle there to have no variation but to point North and South that is to each Pole of the world and why the Longitude from thence is accounted Eastwards is from the motion of the Sunne Eastward or that Ptolomy and others did hold it more convenient to begin from the Westerne part of the world and so account the Longitude Eastward from Countrey to Countrey that was then knowne till they came to the Easterne part of Asia rather than to make a beginning upon that which was unknowne and having made up their account of reckoning the Longitude from the Westerne part to the Eastern part of the world knowne they supposed the rest to be all sea which since their deaths hath been found almost to be another habitable world To finde the Longitude of a Countrey IF it be upon the Globe bring the Countrey to the Brasen Meridian and whatsoever degree that Meridian cuts in the Equinoctiall that degree is the Longitude of that Place if it be in a Mappe then mark what Meridian passeth over it so have you the Longitude thereof if no Meridian passe over it then take a paire of Compasses and measure the distance betweene the Place and the next Meridian and apply it to the divided parallel or Aequator so have you the Longitude required Of the Latitude of Countreys LAtitude of a Countrey is the distance of a Countrey from the Equinoctiall or it is an Arke of the Meridian conteined between the Zenith of the place and the Aequator which is two-fold viz. either North-Latitude or South-Latitude either of which extendeth from the Equinoctiall to either Pole so the greatest Latitude that can be is but 90 degrees If any Northern Countrey have the Artick Circle verticall which is in the Latitude of 66. gr 30. m. the Sun will touch the Horizon in the North part thereof and the longest day will be there then 24 houres if the Countrey have lesse Latitude than 66. degrees 30. m. the Sun will rise and set but if it have more Latitude than 66. gr 30 m. it will be visible for many dayes and if the Countrey be under the Pole the Sun will make a Circular motion above the Earth and be visible for a half yeare so under the Pole there will be but one day and one night in the whole yeare To finde the latitude of Countreys IF it be upon a Globe bring the place to the Brasen Meridian and the number of degrees which it meeteth therewith is the Latitude of the place Or with a paire of Compasses take the distance between the Countrey and the Equinoctiall which applied unto the Equinoctiall will shew the Latitude of that Countrey which is equall to the Poles height if it be upon a Mappe Then mark what parallel passeth over the Countrey and where it crosseth the Meridian that shall be the Latitude but if â—o parallel passeth over it then take the distance betweene the place and the next parallel which applied to the divided Meridian from that parallel will shew the Latitude of that place To finde the distance of places IF it be upon a Globe then with a paire of Compasses take the distance betweene the two Places and apply it to the divided Meridian or Aequator and the number of degrees shall shew â—e distance each degree being 60. miles â—f it be in a Mappe according to Wrights proâ—ection take the distance with a paire of Comâ—asses between the two places and apply this distance to the divided Meridian on the Mappe right against the two places so as many degrees as is conteined between the feet of the
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
of Crownes that two men had 136 About the houre of the day 137 Of Pythagoras Schollers 137 Of the number of Apples given amongst the Graces and the Muses 138 Of the testament or last will of a dying Father 138 Of the cups of Croesus 139 Of Cupids Apples 139 Of a Mans Age. 140 Of the Lion of Bronze placed upon a fountaine with his Epigram ibid. Prob. 77 In Opticks excellent experiments Principles touching reflections 141 Experiments upon flat and plaine Glasses 142 How the Images seeme to sink into a plaine Glasse and alwayes are seene perpendicular to the Glasse anâ— also inversed 143 The things which passe by in a street may by help of a plaine glasse be seen in a Chamber and the height of a tower or tree observed 143 How severall Candles from one Candle are represented in a plaine Glasse and Glasses alternately may be seene one within another as also the back-parts of the body as well as the fore-parts are evidently represented 144 How an Image may be seene to hang in the aire by help of a Glasse and writing read or easily understood 146 Experiments upon Gibbous or convex Sphericall Glasses How lively to represent a whole City fortification or Army by a Gibbous Glasse 147 How the Images are seen in Concave Glasses 149 How the Images are transformed by approaching to the centre of the Glasse or point of concourse and of an exceeding light that a Concave Glasse gives by help of a Candle 151 How the Images as a man a sword or hand doth come forth out of the Glasse 152 153 Of strange apparitions of Images in the aire by help of sundry Glasses 152 154 Of the wonderfull augmentation of the parts of mans body comming neare the point of inflammation or centre of the Glasse 155 How writing may be reverberated from a Glasse upon a VVall and Read 156 How by help of a Concave Glasse to cast light into a Campe or to give a perspective light to Pyoneers in a Mine by one Candle only 156 How excellently by help of a Concave Glasse and a Candle placed in the centre to give light to read by 157 Of other Glasses of pleasure 158 Of strange deformed representations by Glasses causing a man to have foure eyes two Mouthes two Noses two heads Of Glasses which give a colour to the visage and make the face seeme faire and foule 160 Prob. 78 How to shew one that is suspicious what is in another Chamber or Roome notwithstanding the interposition of that wall 160 Corolary 1. To see the Besiegers of a place upon the Rampaâ—â—t of a fortification 161 Corolary 2. and 3. Notwithstanding the interposition of VValls and Chambers by help of a Glasse things may be seen which passe by 162 Prob. 79 How with a Musket to strike a marke not looking towards it as exactly as one aimed at it 162 How exactly to shoot out of a Muâ—ket to a place which is not seene being hindred by some obstacle or other interposition 163 Prob. 80 How to make an Image to be seen hanging in the aire having his head downward 164 Prob. 81. How to make a company of representative souldiers seeme to be as a regiment or how few in number may be multiplyed to seem to be many in number 165 COROLARIE Of an excellent delightfull Cabinet made of plaine Glasses 165 Prob. 82 Of fine and pleasant Dyalls in Horologiographie Of a Dyall of herbs for a Garden 166 Of the Dyall upon the finger and hand to finde what of the Clock it is 167 Of a Dyall which was about an Obelisk at Rome 168 Of Dyals with Glasses 168 Of a Dyall which hath a Glasse in the place of the stile 169 Of Dyals with water which the Ancients useâ— 171 Prob. 83 Of shooting out of Cannons or great Artillery How to charge a Cannon without powder 173 To finde how much time the Bullet of a Cannon spends in the Aire before it falls to the ground 174 How it is that a Cannon shooting upward the Bullet flies with more violence than being shot point blanke or shooting downeward 174 VVhether is the discharge of a Cannon so much the more violent by how much it hath the more length 176 Prob. 84 Of prodigious progressions and multiplications of creatures plants fruits numbers gold silver c. Of graines of Mustardseed and that one graine being sowne with the increase thereof for 20 yeares will produce a heap greater than all the earth a hundred thousand times 178 Of Pigges and that the great Turke with all his Revenne is not able to maintaine for one yeare a Sow with all her increase for 12 yeares 179 Of graines of Corne and that 1 graine with all its increase for 12 yeares will amount to 244140625000000000000 graines which exceeds in value all the treasures in the World 183 Of the wonderfull increase af Sheepe 182 Of the increase of Cod-fish 182 Of the Progressive Multiplication of soules that from one of Noahs Sonnes from the flood unto Nimrods Monarchie should be produced 111350 soules 183 Of the increase of Numbers in double proportion and that a pin being doubled as often as there are weekes in the yeare the number of pinnes that should arise is able to load 45930 ships of a thousand Tunne apiece which are worth more than tenne hundred thousand pounds a day 183 184 Of a man that gathered Apples stones or such like upon a condition 185 Of the changes in Bells in musicall instruments transmutation of Places in Numbers Letters Men and such like 185 Of the wonderfull interchange of the Letters in the Alphabet the exceeding number of men and time to expresse the words that may be made with these letters and the number of Books to comprehend them 187 188 Of a servant hired upon certaine condition that he might have land lent him to sowe one graine of Corne with its increase for 8 yeares time which amounted to more than four hundred thousand Acres of Land 188 Prob. 85 Of Fountaines Hydriatiques Stepticks Machinecks and other experiments upon water or other liquor First how water at the foot of a Mountaine may be made to ascend to the top of it and so to descend on the other side of it 190 Secondly to finde how much Liquor is in a Vessell onely by using the tap-hole 191 Thirdly how is it that a Vessell is said to hold more water at the foot of a Mountaine then at the top of it 191 4 How to conduct water from the top of one Mountaine to the top of another 192 5 Of a fine Fountaine which spouts water very high and with great violence by turning of a Cock 193 6 Of Archimedes screw which makes water ascend by descending 194 7 Of a fine Fountaine of pleasure 196 8 Of a fine watering pot for Gardens 197 9 How easily to take Wine out of a Vessell at the bung hole without piercing a hole in the Vessell 198 10 How to measure irregular bodies by help of
full so in C there is now but 1 pint 5 in B and 2 in A poure all that is in B into A then poure the wine which is in C into B so there is in C nothing in B onely 1 pint and in 7 A 7 pints Lastly out of A fill the pot C so there will remain in A 4 pints or be but halfe full then if the liquor in C be poured into B it will be the other half In like manner might be taken the half of a vessell which conteins 12 pints by having but the measures 5 and 7 or 5 and 8. Now such others might be proposed but we omit many in one and the same nature PROBLEM X. To make a stick stand upon the tip of ones finger without falling FAsten the edges of tvvo knives or such like of equall poise at the end of the stick leaning out somevvhat from the stick so that they may counterpoise one another the stick being sharp at the end and held upon the top of the finger vvill there rest vvithout supporting if it fall it must fall together and that perpendicular or plumb-wise or it must fall side-wise or before one another in the first manner it cannot for the Centre of gravitie is supported by the top of the finger and seeing that each part by the knives is counterpoised it cannot fall sidevvise therefore it can fall no vvise In like manner may great pieces of Timber as Joists c be supported if unto one of the ends be applied convenient proportionall counterpoises yea a Lance or Pike may stand perpendicular in the Aire upon the top of ones finger or placed in the midst of a Court by help of his Centre of gravitie EXAMINATION THis Proposition seems doubtfull for to imagine absolutely that a Pike or such like armed with two Knives or other things shall stand upright in the Aire and so remain without any other support seeing that all the parts have an infinite difference of propensity to fall and it is without question that a staff so accommodated upon his Centre of gravity but that it may incline to some one part without some remedy be applied and such as is here specified in the Probleme will not warrant the thing nor keep it from falling and if more Knives should be placed about it it should cause it to fall more swiftly forasmuch as the superiour parts by reason of the Centricall motion is made more ponderous and therefore lesse in rest To place therefore this prop really let the two Knives or that which is for counterpoise be longer always then the staffe and so it will hang together as one body and it will appear admirable if you place the Centre of gravity neer the side of the top of the finger or point for it will then hang Horizontall and seem to hang onely by a touch yet more strange if you turn the point or top of the finger upside down PROBLEM XI How a milstone or other Ponderosity may be supported by a small needle without breaking oâ— any wise bowing the same LEt a needle be set perpendicular to the Horizon and the center of gravitie of the stone be placed on the top of the needle it is evident that the stone cannot fall forasmuch as it hangs in aequilibra or is counterpoysed in all parts alike and moreover it cannot bow the needle more on the one side then on the other the needle will not therefore be either broken or bowed if otherwise then the parts of the needle must penetrate and sinke one with another that which is absurd and impossible to nature therefore it shall be supported The experiments which are made upon trencher plates or such like lesser thing doth make it most credible in greater bodies But here especially is to be noted that the needle ought to be uniforme in matter and figure and that it be erected perpendicular to the Horizon and lastly that the Center of gravity be exactly found PROBLEM XII To make three Knives hang and move upon the point of a Needle FIt the three Knives in form of a Ballance and holding a Needle in your hand and place the back of that Knife which lyes cross-wise to the other two upon the point of the Needle as the figure here sheweth you for then in blowing softly upon them they will easily turne and move upon the point of the Needle with â—ou falling PROBLEM XIII To finde the weight of Smoak which is exhaled of any combustible body whatsoever LEt it be supposed that a great heape of Fagots or a load of straw weighing 500 pound should be fired it is evident that this grosse substance will be all inverted into smoak and ashes now it seems that the smoak weighs nothing seeing it is of a thin substance now dilated in the Aire notwithstanding if it were gathered and reduced into the thickest that it was at first it would be sensibly weighty weigh therefore the ashes which admit 50 pound now seeing that the rest of the matter is not lost but is exhaled into smoake it must necessarily be that the rest of the weight to wit 450 pound must be the weight of the smoak required EXAMINATION NOw although it be thus delivered yet here may be noted that a ponderosity in his own medium is not weighty for things are said to be weighty when they are out of their place or medium and the difference of such gravity is according to the motion the smoak therefore certainly is light being in its true medium the aire if it should change his medium then would we change our discourse PROBLEM XVI Many things being disposed circular or otherwise to finde which of them any one thinks upon SUppose that having ranked 10 things as ABCDEFGHIK Circular as the figure sheweth and that one had touched or thought upon G which is the 7 ask the party at what letter he would begin to account for account he must otherwise it cannot be done which suppose at E which is the 5 place then add secretly to this 5 10 which is the number of the Circle and it makes 15 bid him account 15 backward from E beginning his account with that number hee thought upon so at E he shal account to himself 7 at D account 8 at C account 9 c. So the account of 15 wil exactly fall upon G the thing or number thought upon and so of others but to conceal it the more you may will the party from E to account 25 35 c. and it will be the same There are some that use this play at Cards turned upside downe as the ten simple Cards with the King and Queen the King standing for 12 and the Queene for 11 and so knowing the situation of the Cards and thinking a certain houre of the day cause the party to account from what Card he pleaseth with this Proviso that when you see where he intends to account set 12 to that number so in counting as
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
shewes how one may serve himselfe with a concave Glasse to light fire in the shadow or neare such a place where the Sunne shines not which is by help of a flat Glasse by which may be made a percussion of the beames of the Sun into the concave Glasse adding unto it that it serves to good use to put fiâ—e to a Mine provided that the combustible matter be well applyed before the concave Glasse in which he saies true but because all the effect of the practice depends upon the placing of the Glasse and the Powder which he speaks not of I will deliver here a rule more generall How one may place a Burning-glasse with his combustâ—ble matter in such sort that at a convenient houre of the day the Sun shining it shall take fire and burne Now it is certaine that the point of inflammation or burning is changed as the Sun changeth place and no more nor lesse than the shadow turnes about the style of a Dyall therefore have regard to the Suns motion and â—is height and place a Bowle of Crystall in the same place that the top of the style is and the Powder or other combustible matter under the Meridian or houre of 12 1 2 3 c. or any other houre and under the Suns arch for that day now the Sunne comming to the houre of 12 to â— 2 â— c. the Sunne casting his beames through the Crystall Bowle will fire the materiall or combustible thing which meets in the point of burning the like may be observed of other Burning-glasses EXAMINATION IT is certaine in the first part of this Probleme that Conicall â—oncave and sphericall Glasses of what matter soever being placed to receive the beames of the Sun will excite heat and that heat is so much the greater by how much it is neere the point of concâ—rse or inflamatioâ— But that Archimedes or Proclus dâ—d fire or burne Shipps with such Glasses the ancient Histories are silent yea the selves say nothing besides the great difficultie that doth oppose it in remotenesse and the matter that the effect is to work upon Now by a common Glasse we fire things neare at hand from which it seems very facil to such which are lesse read to do it at a farre greater distance and so by reâ—ation some deliver to the World by supposition that which never was done in action this we say the rather not to take away the most excellent and admirable effects which are in Burning-glasses but to shew the variety of Antiquity and truth of History and as touching to burne at a great distance as is said of some it is absolutely impossible and that the Parabolicall and Ovall Glasses were of Archimedes and â—roclus invention is much uncertaine for besides the construction of such Glasses they are more difficult than the obtuse concave ones are and further they cast not a great heat but neere at hand for if it be cast farre off the effect is little and the heat weake or otherwise such Glasses must be greatly extended to contract many beames to amasse a sufficient quantity of beames in Parabolicall and Conicall Glasses the point of inflammation ought to concur in a point which is very difficult to be done in a due proportion Moreover if the place be farre remote as is supposed before such a Glasse cannot be used but at a great inclination of the Sunne by which the effâ—ct of â—urning is dâ—minâ—shed by reason of the weaknesse of the Sunne-beames And here may be noted in the last part of this Probleme that by râ—ason of obstacles if one plaine Glasse be not sufficient a second Glasse may be applyed to help it that so if by one simple reflection it cannot be done yet by a double reflection the Sun-beames may be â—ast into the said Caverne or Mine and though the reflected beams in this case be weak yet upon a 〈◊〉 câ—mbustible matter it will not faile to do the effect PROBLEM LXXVI Containing mâ—ny pleâ—sant Questions by way of Arithmetickâ— J Will not inâ—ert iâ— this Probleme that which is drawne from the â—reek Epigrams but proposing the Question immediately will give the anâ—wer also without â—â—aying to shew the manner how they are answered in this J will 〈◊〉 be tied to the â—reek tearms wâ—â—ch J account noâ— proper to this place neiâ—â—er to my purpose â—et tâ—oâ—e â—ead that will Diâ—phanta Sâ—â—â—â—biliuâ— upon Euâ—liâ—â— and others and they may be satisfâ—ed Of the 〈…〉 the Mule JT 〈◊〉 â—hat â—he Mule and the Asse upon a day 〈◊〉 a voyage each of them carried a Barrell full of Wine now the lasâ—e Asse fâ—lt her selfe over-loaden complained and bowed under her burthen which thâ— Mule seeing said unto her being angry for it was in the time when beasts spake Thou great Asse wherefore complainest thou if I had but onely one measure of that which thou carriest I should be loaden twice as much as thou art and if J should give a measure of my loading to thee yet my burthen would be as much as thine Now how many measures did each of them carry Answer the Mule did carry 7 measures and the Asse 5 measures for if the Mule had one of the measures of the Asses loading then the Mule would have 8 measures which is double to 4 and giving one to the Asse each of them would have equall burthens to wit 6 measures apiece Of the number of Souldiers that fought before old Troy HOmer being asked by Heâ—iodus how many Grecian Souldiers came against Troy who answered him thus The Grecians said Homer made 7 fires or had 7 Kitchins and before every fire or in every Kitchin there were 50 broaches turning to rost a great quantitie of flesh and each broach had meat enough to satisfie 900 men now judge how many men there might be Answer 315000. that is three hundred and fifteen thousand men which is cleare by multiplying 7 by 50 and the product by 900 makes the said 315000. Of the number of Crownes that two men had JOhn and Peter had certaine number of crowns John said to Peter If you give me 10 of your crownes I shall have three times as much as you have but Peter said to Jâ—hn If you give me 10 of your crownes I shall have 5 times as much as you have how much had each of them Answere John had 15 crownes and 5 sevenths of a crowne and Peter had 18 crownes and 4 sevenths of a crowne For if you adde 10 of Peters crownes to those of Johns then should John have 25 crownes and 5 sevenths of a crowne which is triple to that of Peters viz. 8 and 4 sevenths and John giving 10 to Peter Peter should have then 28 crownes and 4 sevenths of a crowne which is Quintupla or 5 times as much as John had left viz. 5 crownes and 5 sevenths In like manner two Gamesters playing together A and B after play A said to B Give me 2 crownes of thy money and I shall
have twice as much as thou hast and B said to A Give me 2 crownes of thy money and I shall have 4 times as much as thou hast now how much had each Answer A had 3 and 5 seventhes and B had 4 and 6 seventhes About the houre of the day SOme one asked a Mathemacian what a clocke it was who answered that the rest of the day is foure thirds of that which is past now judge what a clock it is Answer if the day were according to the Jewes and ancient Romanes which maâ—e it alwayes to be 12 houres it was then the â— houre and one seventh of an houâ—e so there remained of the whole day 6 that is 6 houres and 6 sevenths of an hour Now if you take the 1 â— of 5 â— 7 it is â—2 7 or â— and â— 7 which multipled by 4 makes 6 and 6 7 which is the remainder of the day as before but if the day had been 24 houres then the houre had been 10 of the clock and two seventhes of an houre which is found out by dividing 12 or 24 by â— There might have been added many curious propositions in this kinde but they vvould be too difficult for the most part of people therefore I have omiâ—ted them Of Pythagoras his Schollers PYthagoras being asked what number of Schollers he had ansvvered that halfe of them studied Mathematickes the fourth part Physick the seventh part Rethorick and besides he had 3 vvomen novv judge you saith he hovv many Schollers I have Ansvver he had in all 28 the halfe of vvhich is 14 the quarter of which is 7 and the seventh part of which is which 14 7 and 4 makes 25 and the other 3 to make up the 28 were the 3 women Of the number of Apples given amongst the Graces and the Muses THe three Graces carrying Apples upon a day the one as many as the other met with the 9 Muses who asked of them some of their Apples so each of the Graces gave to each of the Muses alike and the distribution being made they found that the Graces the Muses had one as many as the other The question is how many Apples each Grace had and how many they gave to each Muse â—o ansvver the qeustion joyne the number of Graces and Muses together vvhich makes 12 and so many Apples had each Grace Novv may you take the double triple c. of 12 that is 24 36 c. conditionally that if each Grace had but 12 then may there be allotted to each Muse but one onely if 24 then to each 2 Apples if â—6 then to each Muse 3 Apples and so the distribution being made they have a like number that is one as many as the other Of the Testament or last Will of a dying Father A Dying Father left a thousand Crovvnes amongst his tvvo children the one being legitimate and the other a Bastard conditionally that the fifth part which his legittimate Sonne should have should exceed by 10 the fourth part of that which the Bastard should have what was each 〈◊〉 part Answer the legitimate Sonne had 577 crownes and 7 â— and the Bastard 42â— crownes and 2 9 now the fifth part of 577 and 7 ninthes is 1â—5 and 5 9 and the fourth part of 422 and â— is 105 and â— which is lesse then â—15 â— by 10 according to the Will of the Testator Of the Cups of Croesus CRoesus gave to the Temple of the â—ods six Cups of Gold which weighed together â—00 Drammes but each cup was heavier one than another by one Dram how much did each of them therefore weigh Answer the first weighed 102 Drammes and a halfe the second 101 Drammes and a halfe the third 100 Drammes and â— the fourth 99 a halfe the fifth 98 a halfe and the sixt Cup weighed 97 Drammes and a halfe which together makes 600 Drams as before Of Cupids Apples CVpid complained to his mother that the Muses had taken away his Apples Clio said he took from me the fifth part Euterp the twelfth part Thalia the eighth part Mâ—lpâ—meno the twentieth part Erates the seventh part Terpomene the fourth part Polyhymnia took away 30 Vrania 220 and Calliope 300. so there vvere left me but 5 Appls hovv many had he in all at the first I ansvver 3â—60 There are an infinite of such like questions amongst the Greek Epigrams but it would be unpleasant to expresse them all I will onely adde one more and shew a generall rule for all the rest Of a Mans Age. A Man vvas said to passe the sixth part of his life in childe-hood the fourth part in his youth the â—hird part in Manhood and 18 yeares besides in old age what might his Age be the ansvver is 72 yeares vvhich and all others is thus resolved multiply 1 ◠¼ and â…“ together that is 6 by 4 makes 24 and that againe by 3 makes 72 then take the third part of 72 vvhich is 24 the fourth part of it vvhich is 18 and the sixth part of it vvhich is 12 these added together make 54 vvhich taken from 72 rests 18 this divided by 18 spoken in the Question gives 1 which multiplied by the summe of the parts viz. 72 makes 72 the Ansvver as before Of the Lion of Bronze placed upon a Fountaine with this Epigramme OVt of my right eye if I let vvater passe I can fill the Cisterne in 2 dayes if I let it passe out of the left eye it vvill be filled in 3 dayes if it passe out of my feet the Cistern vvill be 4 dayes aâ—filling but if I let the vvater passe out of my mouth I can fill the Cistern then in 6 houres in vvhat time should I fill it if I poure forth the vvater at all the passages at once The Greeks the greatest talkers in the vvorld variously apply this question to divers statues and pipes of Fountaines and the solution is by the Rule of â— by a generall Rule or by â—lgebra They have also in their Anthologie many other questions but because they are more proper to exercise than to recreate the spirit I passe them over as before with silence PROBLEM LXXVII Divers excellent and admirable experiments upon Glasses THere is nothing in the world so beautifull as light and nothing more recreative to the sight than Glasses vvhich reflect therefore I vvill novv produce some experiments upon them not that vvill dive into their depth that vvere to lay open a mysterious thing but that vvhich may delight and recreate the spirits Let us suppose therefore these principles upon which is built the demonstration of the apparâ—nces which are made â—n all sort of Glasses First that the rayes or beames vvhich reflect upon a Glasse make the Angle of incident equall to the Angle of Reflection by the first Theo. of the Catoptick of Euc. Secondly that in all plain Glasses the Images are seen in the perpendicular line to the Glasse as far within the glass as the
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
of Rockets in each of vvhich you may place 6 9 â—2 or 20 small Rockets Novv give fire at A. by help of a piece of primer going from one Lance to another all the Lances vvill instantly at once be lighted and as soone as the Lance at A is consumed it vvill fire the Channell vvhich is made in the ledge of the frame vvhich runnes under the Pots of fire and as the fire goes along burning the Pots vvill be cast forth and so the rank of Pots upon the sides of the frame AB.BC. and CD being spent the soucisons vvill begin to play being fiered also by a Channel vvhich runnes under them upon the ledges AD HIâ—G and RE. then when the Soucisons are spent upon the last ledge RE. there may be a secret Channel in the ledge CD which may fire the Box of Rockets at K. and may fire all the rest one after another which Boxes may be all charged with severall Fire-Workes for the Rockets of the first Box may be loaden with Serpents the second with Stars the third with Reports the fourth with Golden raine and the fifth with small flying Serpents these mounting one after another and flying to and fro will much inlighten the Aire in their ascending but when these Rockets discharge themselves above then will there be a most pleasant representation for these fires will dilate themselves in divers beautifull formes some like the branching of Trees others like fountaines of water gliding in the Aire others like flashes of lightning others like the glittering of starres giving great contentment and delight to those which behold them But if the worke be furnished also with Balons which is the chiefest in recreative Fire-works then shall you see ascending in the Aire but as it were onely a quill of fire but once the Balon taking fire the Aire will seeme more than 100. foot square full of crawling and flying Serpents which will extinguish with a volley of more than 500 reports and so fill the Aire and Firmament with their rebounding clamour The making of which with many other rare and excellent Fire-workes and other practises not onely for recreation but also for service you may finde in a book intituled Artificiall Fire-workes made by Mr. Malthas a master of his knowledge and are to be sold by VVilliam Leake at the Crowne in Fleet-street between the two Temple-Gates Conclusion In this Booke we have nothing omitted what was materiall in the originall but have abundantly augmented it in sundry experiments And though the examinations are not so full and manifold yet by way of brevitie we have expressed fully their substance to avoid prolixitie and so past by things reiterated FINIS Printed or sold by William Leak at the Crovvne in Fleetstreet neere the Temple these Books following YOrk's Heraldry Folio A Bible of a very fair large Roman letter 4â— Orlando Fâ—riosâ— Folio Callu learned Readings on the Scat. 21. Hen. 80. Cap 5 of Sewerâ— Perkins on the Laws of England Wiâ—kinsons Office of Sheâ—â—â—fs Vade Mecum of a Justice of Peace The book of Fees Peasons Law Mirrour of Justâ—ce Topicks in the Laws of England Sken de significatione Verborum Delaman's use of the Horizontal Quadrant Wilby's 2d set of Musique 345 and 6 Parts Corderius in English Dâ—ctor Fulk's Meteors Malthus Fire-workes Nyes Gunnery Fire-workes Câ—to Maâ—or with Annotations by Wil. Austin Esquire Mel Helliconium by Alex. Rossâ— Nosce teipsum by Sr John Davis Animadversions on Lilâ—iâ—s Grammer The History of Vienna Paris Lazarillo de Tormes Hero and Lâ—ander by G. Chapman and Christoph. Marlow Alâ—ilia or Philotas loving folly Bishop Andrews Sermons Adams on â—eter Posing of the Accidence Amâ—dis de Gaule Guillieliam's Heraldry Herberts Travels Baccâ—s Tales Man become guilty by John Francis Senâ—â—t and Englished by Henry Earl of Monmouth The Ideot in 4 books the first and second of Wisdom the third of the Mind the fourth of Sâ—â—tick Experiments of the Ballance The life and Reign of Hen. the Eighth written by the L. Herbet Cornwallis Essays Paradoxes Clenards greek Gâ—ammar 80 Aâ—laluciâ— or the house of light A discourse written in the year 1651 by SN a modern Speculator A Tragedy written by the most learned Hugo Grotius called Christus Patience and translated into Engl. by George Sand The Mount of Olives or Sollitary Devotions by Henry Vaughan Silurist VVith an excellent discourse of Man in glory written by the Reverend Anselm Arch Bishop of Canterbury The Fort Royall of Holy Scriptures by I. H. PLAYES Hen. the Fourth Philaster The wedding The Hollander Maids Tragedie King no K. The gratefull Servant The strange Discovery Othello the Moor of Venice The Merchant of Venice THE DESCRIPTION AND USE OF THE DOVBLE Horizontall Dyall WHEREBY NOT ONELY THE Houre of the Day is shewn but also the Meridian Line is found And most ASTRONOMICALL Questions which may be done by the GLOBE are resolved INVENTED AND WRITTEN BY W. O. Whereunto is added The Description of the generall HOROLOGICALL RING LONDON Printed for WILLIAM LEAKE and are to be sold at his Shop at the signe of the Crown in Fleetstreet between the two Temple Gates 1652. The description and use of the double Horizontall Diall THere are upon the Plate two severall Dyals That which is outermost is an ordinary diall divided into houres and quarters and every quarter into three parts which are five minutes a piece so that the whole houre is understood to contein 60 minutes And for this dyall the shadow of the upper oblique or slanting edge of the style or cocke doth serve The other diall which is within is the projection of the upper Hemisphaere upon the plain of the Horizon the Horizon it self is understood to be the innermost circle of the limbe and is divided on both sides from the points of East and West into degrees noted with 10.20.30 c. As far as need requireth And the center of the Instrument is the Zenith or Verticall point Within the Horizon the middle straight line pointing North and South upon which the style standeth is the Meridian or twelve a clock line and the other short arching lines on both sides of it are the houre lines distinguished accordingly by their figures and are divided into quarters by the smaller lines drawn between them every quarter conteining 15 minutes The two arches which crosse the houre lines meeting on both sides in the points of intersection of the sixe a clocke lines with the Horizon are the two semicircles of the Ecliptick or annuall circle of the sun the upper of which arches serveth for the Summer halfe yeere and the lower for the Winter half yeer and therefore divided into 365 dayes which are also distinguished into twelve moneths with longer lines having their names set down and into tenths and fifts with shorter lines and the rest of the dayes with pricks as may plainly be seene in the diall And this is for the ready finding out of the place of the Sun
South the intersections of the parallel of the sun with the Horizon is after 6 in the morning and before 6 in the evening and the Diurnall arch lesser then 12 houres and by so much lesser the greater the Southerne Declination is And in those places of the Ecliptick in which the sun most speedily changeth his declination the length also of the day is most aâ—tered and where the Ecliptick goeth most parallel to the Equinoctiall changing the declination but little altered As for example when the sun is neer unto the Equinoctiall on both sides the dayes increase and also decrease suddenly and apace because in those places the Ecliptick inclineth to the Equinoctiall in a manner like a streight line making sensible declination Again when the sun is neere his greatest declination as in the height of Summer and the depth of Winter the dayes keep for a good time as it were at one stay because in these places the Ecliptick is in a manner parallel to the Equinoctiall the length oâ— the day also is but little scarce altering the declination And because in those two times of the yeer the sun standeth as it were still at one declination they are called the summer solstice and winter solstice And in the mean space the neerer every place is to the Equinoctiall the greater is the diversity of dayes Wherefore we may hereby plainly see that the common received opinion that in every moneth the dayes doe equally increase is erroneous Also we may see that in parallels equally distant from the Equinoctiall the day on the one side is equall to the night on the other side VI. Vse To finde how far the sun riseth and setteth from the true east and west points which is called the suns Ampâ—itude ortive and occasive Seek out as was shewed in III Vse the imaginary circle or parallel of the suns course and the points of that circle in the horizon on the East and West sides cutteth the degree of the Amplitude ortive and occasive VII Use. To finde the length of every day and night Double the houre of the sunnes setting and you shal have the length of the day double the hour of the sunnes rising and you shal have the length of the right VIII Vse To finde the true place of the sun upon the dyall that is the point of the instrument which answereth to the place of the sun in the heavens at any time which is the very ground of all the questions following If the dyall be fixed upon a post Look what a clock it is by the outward dyall that is look what houre and part of houre the shadow of the slanting edge of the style sheweth in the outward limbe Then behold the shadow of the upright edge and marke what point thereof is upon that very houre and part in the inner dyall among the parallels that point is the true place of the Sunne at the same instant If the dyal be not fixed and you have a Meridian line noâ—ed in any window where the Sunne shineth place the Meridian of your dyal upon the Meridian line given so that the top of the stile may point into the north and so the dyal is as it were fixed wherefore by the former rule you may finde the place of the Sunne upon it If the dyal be not fixed neither you have a Meridian line but you know the true houre of the day exactly hold the dyal even and parallel to the Horizon moving it till the slanting edge of the stile cast his shadow justly upon the time or houre given for then the dyal is truly placed as upon a post Seek therefore what point of the upright shadow falleth upon that very houre and there is the place of the Sun But if your dyal be loose and you know neither the Meridian nor the time of the day First by the day of the moneth in the Ecliptique finde the suâ—s parallel or dâ—urnall arch for that day then holding the dyal level to the horizon move it every way untill the slanting shadow of the style in the outward limbe and the upright shadow in the Sunnes diurnal arch both shew the very same houre and minute for that very point of the Sunnes parallel which the upright shadow cutteth is the true place of the Sun on the dyal at that present But note that by reason of the thicknes of the style and the bluntnesse of the angle of the upright edge the Sun cannot come unto that edge for some space before and after noone And so during the time that the Sunne shineth not on that upright edge the place of the Sunne in the dyal cannot be found Wherefore they that make this kinde of double dyal are to be careful to file the upright edge of the style as thinne and sharpe as possible may be That which hath here bin taught concerning the finding out the Suns true place in the dyal ought perfectly to be understood that it may be readily and dexteriously practised for upon the true performance thereof dependeth all that followeth IX Vse To finde the houre of the day If the dyal be fastned upon a post the houre by the outward dyal or limbe is known of every one and the upriâ—ht shadow in the Suns parallel or diurnal arch will also shew the very same houre But if the dyall be loose either hold it or set it parallel to the Horizon with the style pointing into the north and move it gently every way untill the houre shewed in both dialls exactly agreeth or which is all one finde out the true place of the Sun upon the dyall as was taught in the former question for that point among the houre lines sheweth the houre of the day X Vse To finde out the Meridian and other points of the Compasse First you must seek the truâ— houre of the day by the last question for in that situation the Meridian of the dyall standeth directâ—y north and south and the east pointeth into the east and the west into the west and the rest of the points may be given by allowing degrees 11. 1 â— unto every point of the compasse XI Vse To finde out the Azumith of the sun that is the distance of the Verticall circle in which the sun is at that present from the Meridian Set your diall upon any plain or flat which is parallel to the horizon with the Meridian pointing directly north or south as was last shewed then follow with your eye the upright shadow in a streight line till it cutteth the horizon for the degree in which the point of intersection is shal shew how far the suns Azumith is distant from the east and west points and the complement thereof unto 90 shal give the distance thereof from the meridian XII Vse To finde out the Declination of any Wall upon which the sun shineth that is how far that wall swerveth from the north or south either eastward or westward Take aboard having one streight edg