paruus erat Excubiae somnum superant labor otia vincit Tunc Dea vana venus vinaque spreta iacent Hic ducis assumit partes hic militis arma Iste mucrone potens hic eques ille pedes Alter bombardis inimicas dissipat aedes Eminus hic hastis cominus hic gladijs Si cupis a longé globulis terrere superbos Hic discas hostes perterebrare tuos Tartaglia arte sua multos ad tartara mittit Transtulit hunc nuper Lucar arte sua Non lucrum quaerit Lucar non munera magna Laudem non fraudem doctus habere studet Sed pro regina pro relligione fideque Pro Christo Angligenas instruit arte sua G. B. Cantabrigiensis IN DEI NOMINE AMEN The first booke of Nicholas Tartaglia his Colloquies concerning the Arte of shooting in great and small Peeces of Artillerie translated out of Italian into English by Cyprian Lucar Gentleman who hath also augmented the volume of the said Colloquies for the benefite of his Readers with the Contents of euery Colloquie and with the Corollaries and Table that are in the same volume The first Colloquie How a Gunners Quadrant should be made and vsed and how a Peece of Artillerie doth shoote more ground when it is eleuated at the mouth than it will do when it lieth leuel and how Pellets doe make long and short Ranges according as the Peeces which shoote them are eleuated and howe a Table of Randons maye bee made for any Peece and how he which hath a true Table of Randons for a Peece shal be thereby able to make with that Peece a perfect shoote at any marke within the reach of his said Peece and teach any vnskilfull Gunner to do the same and how hee that wanteth such a Table shall neuer learne to shoote well at any marke without point blanke and how the outer sense telleth truth in particuler things but not in vniuersall things Interlocutors Francesse Maria Duke of Vrbine Nicholas Tartaglia DVKE What reasons are they which as you say in your booke dedicated vnto me you haue found out concerning the knowledge of shooting in Gunnes Nicholas The proportion order of shootes not only at marks far of but also at marks hard by with what Peece you will and with what sort of pellet you will Duke Speake more plainely and giue me an example thereof for I doe not vnderstand what you say Nicholas I am content to shewe vnto your Excellencie an example of my said inuention but first I must speake of that materiall instrument which I haue deuised set foorth in a picture at the beginning of my said booke dedicated vnto you the which instrument is made of a square peece of wood or of mettall like vnto this figure B A C and containeth a quadrant that is to say How a Gunners quadrant may be made one fourth part of a circle like vnto the figure H I G K which is to be described with a paire of compasses vpon the center H I meane one foote of the compasse ought to bee fixed in the point H the inward angle of the said square and the other moueable foote of the compas must describe I G K the crooked side or arke of that quadrant also another croked line equidistant from the first as is the line E F ought to be drawne with the said compasses but for this purpose the compasses may not bee opened so wide as they were before and all the space which is betweene the two croked lines that is to say betweene the arke I G K and the arke E F must be deuided into 12. equal parts drawn by the edge of a ruler from the point H the center of that Quadrant so as euery of the same diuisions which I call points may be perceiued to looke or lie right vpon that center H as they doe in this figure IN the same maner euery of the aforesaid partes or points should bee diuided into 12. A Type of the Gunners quadrant other equal parts Although I haue not diuided this figure into so many parts because they would heere marre the same but a Square of an ordinarie bignesse as before I haue said may be so diuided as that al the whol Square shall containe 144. equall parts which I call minutes These minutes are to be marked with more shorter lines than are the lines of the points to this end that they may be more easily nūbred by the halfe or midst of the points depicted with the greater lines that we may also know how that euery point containeth twelue minutes This done a pinne of yron or of lattin is to bee fixed precisely in the pointe H the center of the quadrant and vpon that pinne a moueable threede of silke or of some other thing with a plummet at the end of the same must hang downe like vnto the perpendicular H M D. The vse of the Gunnets quadrant This Instrument will help vs to iudge of all the variable positions or eleuations that may happen in any Peece of artillerie whatsoeuer And nowe concerning the same positions or eleuations this is to bee noted that the first position of euery Peece is to bee vnderstoode when it is laid leuell for then the longest legge of the said instrument being put into the mouth of the said Peece and rightly extended towards the bottome of his concauitie the threede and plummet which is fixed in the center of that instrument will fall precisely vpon the line H F K as it doth in the figure next following A peece lying leuell And a Peece shall bee said to bee mounted one point when the longest legge of our said instrument beeing in the mouth of the said Peece the saide threede and plummet doth fall precisely vpon the diuision of the first point as it doth in the figure nex following A Peece mounted at one point or 12. mintes Also a Peece shall be said to be eleuated two points when the said threede and plummet doth fall precisely vpon the diuision of the second point and when the said threede plummet doth fall precisely vpon the third point then the Peece is eleuated at three points and so we must say of the fourth fift and sixt points But when a Peece is mounted at the sixt point then the said Peece is mounted to the greatest eleuation that it may be at I speake this of a Peece of Artillerie because the morter peeces may be eleuated vnto all the other points following I meane euen vnto the 12. point This which wee haue spoken of points ought also to bee vnderstood of minutes that is to say when a Peece is so mounted that the said threed and plummet falleth Precisely vpon the diuision of the first minute that Peece shal be said to bee mounted one minute And when the said threed and plummet shall fall vpon the diuision of two minutes it shall bee said to bee mounted at two minutes In like sort it shall
place of equalitie the pellet doth range with more difficultie and more sooner beginneth to decline downewardes to the grounde and declineth in a greater quantitie than when it is shot out of a peece somewhat eleuated that is to say it goeth then as the Gunners terme it much lesse in a right line than when it is shot out of a peece eleuated wherefore in this question the effects of shootes made in that place of equalitie will bee of lesse force and to a lesse effect than in any place of eleuation Obiection But here your Excellencie may say with good reason that although it is manifest by these demonstrations that in equall distances a shoote out of a peece lying leuell will do a lesse effect than a shoote out of a peece eleuated yet it is doubtfull whether a shoote out of a peece eleuated will doe a greater effect than a shoote out of a peece lying leuel in vnequall distances because in our question this is to be considered whether the peece which is on the plaine at the foote of the hill be more distant from the Fort than the other Peece which is on the toppe of the hill For such a difference may bee much greater than the difference of his shoote in a right line or the difference of his effects in equall distances and then the peece from the toppe of the said hill will doe a more greater exploite than the Peece which is on the plaine at the foote of the said hill To this doubt I aunswere thus Answere The distance from the Fort to the peece which is on the plaine may so much differ from that distance which is betweene the saide Forte and the saide peece which lieth vppon the toppe of the hill that the same will come to passe which was of you doubted Duke To make me vnderstand your meaning giue me an example by a figure Nicho. That I may shewe vnto you my meaning herein by a figure I wil suppose that the pellet of a Culuering doth waie 20 pound waight A Culuering which lying leuel shooteth about 200. paces will at the eleuatiō of 45. degrees or of 6. points or of 72. min. shoote about 800. paces and that the Culuering according to that experience which was made at Verona as I haue declared in the beginning of my booke of nwe science dedicated vnto your Excellencie in the place of equalitie that is to say lying leuell will shoote in a right line about 200. paces and that such a culuering at the eleuation of 45. degrees that is to say at the 6. point or at 72. minutes of our Quadrant by the reason alleaged in the last proposition of my seconde booke of our nwe science wil shoote in a right line about 800. paces Duke Doe you say that a Culuering being eleuated at 45. degrees or at the 6. point or at 72 minutes wil shoote about 800. paces and that the same Peece lying leuel wil shoot but about 200. paces Nicho. By reason I am taught so to say Duke It seemeth to mee that there is a great difference betweene those shootes Nicho. It commeth so to passe because that eleuation of 6 points doth differ much from the place of equalitie and according as the Peece is eleuated from minute to minute According as a Peece is eleuated from minute to minute or from point to point so from minute to minute and from point to point the pellet of that Peece doth augment his range in an insensible croked line so from minute to minute the pellet of that peece doth augment his raunge in a right line it doth also the like in the points but that is in a greater quantitie For the peece being eleuated to the first point of the Quadrant shootes more farther in a right line than when it is laid leuel Also the Peece eleuated to the second point of the said Quadrant shootes much farther in a right line than it doth when it is eleuated but at one point Likewise the Peece beeing eleuated to the thirde point shootes farther in a right line than it doth at the second point so successiuely the Peece being eleuated to the fourth point shootes farther than at the third point and at the fifth point farther than at the fourth point and at the sixt point as is aforesaid farther than at the fifth point and if the Peece should by degrees bee eleuated aboue the sixt point the pellet woulde flie more farther in a right line that is to say the Peece eleuated to the seuenth point would shoote farther in a right line than at the sixt point and at the eight point farther than at the seuenth point and at the ninth point farther than at the eight point and at the tenth point farther than at the ninth point and at the eleuenth point farther than at the tenth point and at the twelfth point farther than at the eleuenth point And at this twelfth point the pellet will flie wholie in a right line The pellet which is shot out of a peece mounted at 90. degrees or at 12. points flieth in a more perfect right line than whē it is shot out of a peece mounted at any other degree or point Note that Tartaglia calleth that a right line which is insensibly croked and that a crooked line which is euidently crooked to this end that the common people may the better vnderstand him and it will be a perpendicular aboue the horison And this pellet shot out of a peece mounted at the twelfth point will flie in a more perfect right line than any of the former pellets did because in truth the going or violent mouing of a bodie equallie heauie which is without the perpendicular of the horison can neuer haue any part perfectly right as it hath bin sayd in our said second booke of our nwe science Duke Why do you call that a right line which is not perfectly right Nicho. That the common people may the better vnderstand me I call that a right line which is insensiblie crooked and I call that a crooked line which doth euidently appeare to bee crooked Duke Proceede on Nicho. Now to returne to our purpose I say that if the distance betweene the said fortresse and the Peece lying on the plaine at the foote of the hil be 760. paces and that the distance betweene the same fortresse and the peece lying on the toppe of the said hill be but 130 paces in this case the said Culuering which is planted on the toppe of the hill will doe a greater exploit against the walles of that fortresse than that Culuering shall do which is planted on the plaine at the foote of the said hill the cause hereof is for that the said Culuering lying leuell doth shoote about 200. paces in a right line as before hath bin said Then for so much as the distance betweene that Culuering and the Fortresse is but 130 paces as it hath bin supposed the pellet of that Culuering
will strike the walles of that Fortresse neare about 70 paces before it would end his range in a right line but the Culuering which is planted on the plaine at the foote of the hill being distant from those walles 760 paces in a diametral line and eleuated to 45 degrees that is to say to the 6 point of our quadrant doth shoote about 800 paces in a right line and therefore it will strike those walles onely about 40 paces before it would ende his way in a right line or be sensibly perceiued to decline In the question proposed in this Colloquie the pellet which at his hitting would haue gon most farthest not meeting with an obiect to resist it shall do the greatest exploit vpon that obiect which resisteth And so that pellet which at his hitting would haue gon most farthest not meeting with an obiect to resist it shall doe the greatest exploit vpon that obiect which resisteth by the reasons alleaged vppon the fourth proposition of our first booke of our nwe science Therefore insomuch as the pellet of that Culuering which is planted on the top of the hill at the hitting of those walles had to flie more farther about 70 paces in a right line and that the pellet of that Culuering which is planted on the plaine at the foote of the hill at his hitting had to flie more farther but onely about 40 paces in a right line I conclude in this case by those reasons that the pellet of that Culuering which is planted on the top of the hill shall do a greater exploit against those walles than the pellet of that Culuering which is planted on the plaine at the foote of the hil and eleuated to the sixth poynt of our quadrant And if the pellet of this Culuering mounted to the sixt poynt be of a lesse force the pellet of that peece mounted at any other poynt vnder the 6 poynt is of much lesser force But if the distance from the said Fortresse vnto the Artillerie on the plaine had bin 600 paces in a diametrall line Note and that from the Fortresse vnto the Artillerie on the toppe of the hill it had bin 150 paces the Artillerie on the plaine mounted to the 6 poynt would haue stroken those walles with more force than the Artillerie vpon the top of the hill could haue done for the pellets shot out of the Artillerie on the plaine will beate those walles about 200 paces before the full ende of their ranges in a right line and the pellets of the Artillery on the top of the hil will beate those walles 50 paces before the end of their full course in a right line And therfore the difference of the saide effects that is from 50. paces to 200. paces which they make before they do sensibly decline is about 150. paces and therefore the said Culuering not onely at the eleuation of the sixt poynt of our quadrant but also at the eleuation of the fift point doth make that effect to be more greater But concerning this I will not stand to make any demonstration for that I will not be tedious vnto you Then if in so great a height as in the last case we haue supposed the Culuering vpon the plaine being mounted to the sixt point and also to the fift point will do a more greater exploit than the Culuering vpon the toppe of the hill such great effects will much more euidently follow in the first case which was proposed by your Excellencie where the hill and also the Fortresse were supposed to be of equall height and each of them to be 60 paces in height and the distance from the foote of one hill to the foote of the other or frō the top of the one hil to the top of the other to be 100 paces the Diametrall or Diagonall line that is to say the distance from the saide Fortresse to the place at the foote of the hill where the Artillerie is supposed to stand on the plaine by the 47 proposition of the first booke of Euclide to be about 116 paces leauing out the Fraction which should be added vnto that number and therefore the pellet shot out of the Culuering which is planted on the toppe of the hill will strike those walles about 140 paces before the full end of his range in a right line the pellets of the Artillerie which is planted on the plaine at the foote of the hill and mounted to the 6 point wil strike those walles about 684 paces before the full end of their ranges in a right line Note And because here is so great a difference in that one of those pellets doth hit the fortresse 140 paces before the full end of his range in a right line and the other pellet doth hit the same fortresse 684 paces before the full end of his range in a right line therefore in this question it is a plaine and euident thing that the Culuering planted on the plaine at the foote of the hill mounted to the 6 point 5 point or to any other point of eleuation wil do a greater exploit against the said fortresse than that Culuering will doe which is planted on the top of the hill Duke You haue answered well to this Question The third Colloquie How a pellet doth neuer range in a right line except it be shot out of a peece right vp towards Heauen or right downe towards the center of the world and by how much more swifter a heauie bodie driuen violently through the aire flyeth by so much in that mouing it is made the more lighter and how the more lighter a bodie is the more easilie wil the aire beare it and by how much a heauie bodie violently mouing doth go more swifter by so much it doth worke the more greater effect in all thinges which resist the same and by how much the swiftnes thereof doth more decrease by so much in that mouing the waight thereof which draweth the said heauie bodie towards the ground doth more increase and the more swifter a pellet flyeth in the aire the more lighter it is contrariwise the more sloer a pellet flieth the more heauier it is and howe the one part of a right line cannot be more or lesse right than the other part and how the more swifter a pellet flieth the lesse crooked is his range And how we be oftentimes deceaued by iudging according to the sence of seeing and how a peece is said to shoote at point blanke when it lying leuell or equidistant to the horison is discharged and howe the waigt of the pellet draweth the pellet out of his way and right passage perpendicularly towardes the grounde when it is shot out of a peece lying leuell and also when it is shot out of a peece eleuated or imbased except it be shot right vp towards Heauen or right downe towardes the center of the worlde Interlocutors Francesse Maria Duke of Vrbine Nicholas Tartaglia DVke By your arguments you
will cause it to shoote so much ground as is in the said space Then hauing placed your Quadrant or Semicircle by the mouth of your peece mooue it vp or downe till you shall espie through the sights or channell of the Quadrant or Semicircle the said marke and note what degree is touched with the line and plummet of the Quadrant or Semicircle that done put downe the mouth of the peece more loer by so many degrees than it was before I meane if you did mounte the peece foure degrees to shoote so much grounde as is betweene the peece and the marke and did note three degrees for the degrees touched with the said line plummet of the Quadrant or Semicircle then the mouth of the peece must be put downe or as some terme it imbased three degrees and so will the peece being laid right vppon the marke and mounted but at one degree strike the marke in the valley although in the precedent chapter the said peece was mounted at seuen degrees to shoote a like distance at a marke vppon a hill and at foure degrees to shoote a like distance vppon a plaine ground Heere this is to be noted that a pellet shot from an heigth into a loe place can doe no more harme than kill one person or make one hole in the place where it falles because as Luigui Collado hath written the pellet so shot doth more offend through his owne naturall waight than by the expulsiue power of the gunpowder which did expell it out of his peece The 67 Chapter How you may certainely know by the Gunners Semicircle whether a ship vppon the Sea or an Armie vppon the land or any other thing seene a farre of doth come towardes you stande still or goe from you and how you ought to discharge your great ordinance of diuers sortes against a ship or an Armie comming towardes you A Long distance being betweene you and a ship vpon the Sea or an armie of men moouing a farre of may oftentimes through the weaknesse of your sight deceiue you and make you not to discerne well whether that ship or armie doth stand still goe frō you or come towardes you therefore it will be very profitable as I thinke for you to learne how you may be alwaies certaine thereof for to follow your enemies when they shall flie from you and make preparation of defence when you shall see them come to assault you For this purpose you shall ascende into some high place from whence you may behold the ship or armie a farre of and hauing put a Semicircle to your eye mooue it vp or downe till you shall see through the sights or through a channell made in the said Semicircle that part of the ship or armie which is nearest vnto you Then your Semicircle remaining vnmooueable note diligently the part of the Semicircle touched with the hanging line and plummet of that Semicircle and after a while making the said line to hang againe directlie vppon the saide part which was touched with it when you did espie thorow the saide sightes or channell the ship or armie looke againe whether you can espie thorow the same sights or channell the part of the ship or armie which was first espied for if at your second looking you shall behold againe through the said sights or channell the very same part of the ship or armie which you did first espie you may boldly affirme that the said ship or armie mooued not betweene the time of the first and second looking And if your visuall line passing through the said sights or channell shall not at your second looking extend to the said part then it is certaine that the said ship or armie doth goe from you But if your saide visuall line passing through the said sights or channell shall at your seconde looking extende ouer the said part of that ship or armie then you may boldly say that the said ship or armie commeth towards you After all this you must measure by the helpe of your Semicircle how farre the said ship or armie is from you and finding by your measure that the said ship or armie is within the reach of your peeces you ought to shoote out of Culuerings Sakers Minions Faucons and Fauconets whole yron shot at the same ship or armie and when the armie shall come very neere vnto you chaine shot cliue shot dice shot baules of wild fire and such other like spoiling shot The 65 Chapter How you may make a perfect shoote in a darke night at any marke that may be seene in the day time and how a lighted candle may be carried in the night time so as no light shall be seene but at your will and pleasure IN the day time mount your peece to reach the appointed marke and at that very time place the mouth or concauitie of the peece right vppon the saide marke and then hauing put the longest legge of your Semicircle into the mouth of the saide peece note exactlie what degree vppon the Semicircle is touched with the line plummet hanging vppon the said Semicircle for that degree being written in your memoriall will shew you alwaies how much the said peece lying in that place must be mounted to reach the said marke After this let fall a line and plummet downe vnto the grounde from the middle part of the mouth of the peece and thrust a pin of wood or yron into that point of ground which was touched with the plummet last mentioned Likewise from the middle part of the breeche or taile of the peece let that line and plummet hang downe againe vnto the grounde and thrust an other pyn of wood or yron into the same very point of grounde which was last touched with the said plummet Finally draw a straight line vppon the ground right ouer both those pinnes and make each end of this line to reach two yardes at the least beyonde the pyn next vnto it This line lyeth directly vnder the middle parte of the mouth of the peece and also vnder the middle part of the taile of the peece and right vppon the marke and is named therefore the line of direction Now when you will shoote in a darke night with that peece at the saide marke charge the peece with his duetie in powder and with a fit pellet and plumme the middle of the mouth of the said peece and the middle of the taile of the said peece right vppon the said pynnes set in the said line of direction that you may by so doing lay the mouth of the peece right vppon the appointed marke Then the longest legge of your saide Semicircle being put into the mouth of the peece koyne the peece vp and downe till the line and plummet hanging vppon the Semicircle shall fall exactlie vppon the same degree that it touched before when it was mounted in the day time to strike the said marke Al this being done you ought to consider of other things that are
way vppon a Beame called a Stater with a small and light waight great things of a very heauie waight I neede not rehearse because euery man will confesse that it is a pointe of vanity to vse many things when a fewe things wil serue our turne as this Latin sentence doth declare Frustra fit per plura quod fieri potest per pauciora Therefore I aduise those that ought to haue vnderstanding in the science of waights to note well this which followeth Foure seuerall waights wil way any quantitie from one pound waight vnto 40 pounds in waight if the first of those foure waightes be of one pounde the seconde of 3 poundes the thirde of 9 poundes and the fourth of twenty seuen poundes in waight As for example a quantitie of 6 pounds in waight will be iustly wayed if you put the saide quantitie and the waight of 3 pounds in one scale and the waight of 9 pounds in the other Scale Also you may way a quantitie of 21 pounds in waight if you will put the saide quantitie and the waight of 9 poundes in one Scale and the waight of three pounds and the waight of 27 pounds in the other Scale In like manner with fiue waights that is to say with the said waight of 1 pound with the said waight of 3 pounds with the said waight of 9 pounds with the said waight of 27 pounds and with a waight of eighty one pounds you may way any quantitie from one pound waight vnto 121 poundes in waight Also with 6 waights I meane with the waight of one pound with the waight of three poundes with the waight of nine poundes with the waight of twenty seuen poundes with the waight of eightie one poundes with a waight of two hundred fourty and three poundes you may way any quantitie from one pounde vnto 364 poundes in waight When you doe way any quantitie in an vnknowne paire of ballance An admonition I counsell you to way the quantitie first in one scale of the same ballance and after in the other scale of the same ballance For as a quantitie wayed in a true payre of Ballances will be of one and the same waight in both the scales of that ballance so a quantitie wayed in a false payre of Ballances will be of more waight in one scale than in the other scale of false Ballances And besides all this it is needefull for you to know that some false Ballances are so subtillye made that their beames will lie in an equall heigth and beare the tunges of the same false Ballances vpright betweene their cheekes when their scales doe hang emptie But if you will way your thinges with a Stater To make and vse a long Stater make first a playne and smoothe beame of yron in fashion like a Pyramis or foure square Taper in length one yarde and in thicknesse about â…“ parte of an ynche and then vppon a strong pinne of yron called the first Axeltree set ouertwharte and very fast in the great ende of the Beame hang a pendant hooke of yron that winding and moouing to all sides may claspe and holde faste all the ropes of the scale in which the thinges that shall be wayed must lie Moreouer fixe an other strong Axeltree of yron in the sayde Beame as a parallel to the first and distant from the same about â— 21 parte of the Beames length Also you must set the tung of the Stater Squirewise vppon the beame right ouer this seconde Axeltree and put the cheekes of the tung vppon the endes of the seconde Axeltree so as they may easilie mooue vp and downe vppon the same And it is expedient that these cheekes shoulde haue in their vppermost ende a ringe or hooke by which the Stater may bee alwayes hanged vp when neede shall require Next after this you must lay in the scale of the Stater depending by ropes from the first Axeltree so much of knowne waight as being reckoned with the waight of the scale and the waight of the ropes belonging to the Scale will make both endes of the Beame to lie without any declyning in an equall heigth Which is perceaued by the tung of the Stater when it doth stande right vp betweene his cheekes Furthermore to this waight which hath made both endes of the Beame to stande precisely equidistant to the Horizon and is supposed by me to contayne fiftie poundes you shall adde tenne poundes of more wayght and that being done you shall hang a ringed poyze of tenne poundes in waight vppon that parte of the Beame which is marked in the Figure following with B F. Now the sayde poyze hanged vppon B F the longer parte of the beame must bee mooued to and fro vntill the tung of the Stater shall bee perceaued to stande very vpright beetweene his cheekes to this ende that the parte of the Beame which is then touched with the ring of the poyze may bee exactly marked with a small notch or with a fine line When you haue made there such a notch or such a lyne lay tenne poundes of more wayght in the scale and because the tung of the Stater will now enclyne towardes A the greater ende of the beame remooue the sayde poyze towardes F vntill the tung of the Stater standing vpright betweene his cheekes shall shewe agayne equalitie of wayght and then as before you haue beene taught to doe make an other notch or drawe an other lyne vppon that part of the beame which is touched with the ringe of the poyze For the space betweene these two notches or lynes will exactly shewe a distinction and separation of tenne poundes in wayght Vnto which if you adde the first wayght which is supposed to bee fiftye and the seconde wayght which was tenne the totall summe of the whole wayght which the ringed poyze doeth counterpeyse in the notch or lyne last made amounteth to seuenty poundes Finally you must marke vppon the beame the space that is betweene the two notches or lynes so manye tymes as the beame will receaue the same For the notch or lyne in each of those spaces is a distinction of tenne poundes in wayght so that if you will diuide euery of those equall spaces into tenne equall partes and euery of these tenne equall partes into sixteene equall partes the beame will not onely shewe the places of poundes in wayght but also the place of euery ounce that is in each of the sayde poundes For euery of those equall spaces doe geue equall increase and looke what proportion the supposed waight of 50 pounds which made both endes of the beame to lie in an equall heigth beareth to the ringed poyze the same proportion doth B F the longer parte of the beame beare to A B the shorter parte of the beame And because B F the longer parte of the beame is twenty times so much in length as A B the shorter parte of the beame and that the ringed poyze wayeth tenne poundes multiplie
more swiftly and in a more righter way than a like pellet will doe which is shot out of the same Peece with his due charge in powder and the pellet shot out of a peece with more powder shall strike aboue that place where the other pellet shot with lesse powder will strike And because the bullet shot out of a peece which is charged with more powder than his due charge flieth more swiftly than that bullet doth which is shot with a lesser quantitie of powder also flieth in a more righter way than the other therfore it did strike aboue that place where the other bullet did hit Prior. I doe not well vnderstand this which you haue tolde me I meane that the bullet shot with a lesse quantitie of powder will not flie in so right a way as that bullet wil doe which is expelled with a more quantitie of powder Will you not graunt that a bullet shot out of a Peece charged with his due charge and quantitie of powder doth flie right vppon that place or marke vnto which the leuel is giuen within a conuenient distaunce Nicholas I doe also denie that a bullet will flie in a right line vnto the marke at which the leuell is giuen A pellet will not flie in a right line vnto the marke at which the leuel is giuen except it be shot right vp towardes heauen or right down towards the cēter of the worlde as you may also reade in the seconde and third Colloquie of this booke And of the very same matter I did once dispute with the Duke of Vrbine of famous memorie the father of the Duke of Vrbine that nowe is I meane that a bullet shot out of any peece of Artillery by any maner of meanes doth neuer goe nor can goe in any small part of his way vppon a perfect right line except it bee shot straight vp towardes heauen or straight downe towardes the center of the worlde Prior. I perceiue that you say true because if the bullet at the first shoote had gon right vppon the marke then by recharging the peece afterwardes with a more quantitie of powder the other bullet coulde not by any reason haue strooken aboue the marke but in the very same place where the pellet or bullet which was shot out of the Peece with lesse powder did strike before And of purpose I haue deuised this question because it seemed a strange thing vnto me that the bullet did ascende aboue the right line by charging the Peece with more powder and therefore to morrowe in the euening I will dispute better with you of this matter which doth like mee well The 7. Colloquie When the leuell sight which is set vppon the mouth of the peece is precisely so high as the leuell sight which is set vppon the taile of the peece and he which will shoote at any marke seeth with his eye the same marke by the extreames or vppermost partes of the said sights then the pellet wil alwaies strike somewhat vnder that marke And when it is said that both the leuell sights are of an equall height you must vnderstand thereby that the extreames or toppes of the sayde leuell sights are equally distant from the loest part or ground of the concauitie in the peece for the height of the leuell sightes and also the lonesse or shortnesse of the leuell sights must alwaies be measured from the loest part or ground of the concauitie in the Canon of the peece And when the leuell sights vpon a peece are of an equall height and he that shoots doth see his mark by the tops of those leuel sights then by how much more farther the said marke is from the peece by so much the pellet will strike more vnder the mark And when the leuell sight which is set vpon the mouth of the peece is more higher than the leuell sight which is set vppon the taile of the peece and he which shootes doth see his marke by the toppes of those leuel sights the pellet wil strike more vnder that marke than it will do when both the leuell sights are of an equal height And when our visual line in seeing our marke doth cut the line in which the pellet flieth then the leuel sight at the mouth of the peece is more shorter than it should be And when our visual line in seeing our mark doth not cut nor touch the line in which the pellet flieth then the leuel sight at the mouth of the peece is not so short as it should be And when our visual line in seeing the marke doth touch or cut the line in which the pellet flyeth and the marke at which we shoote is in the saide touch poynt or in the saide poynt of intersection then the leuell sight at the mouth of the peece hath his due length and conuenient shortnesse and the pellet wil strike in the middest of the marke but when the saide marke shall be within that touch point or point of intersection then the pellet will hit somewhat vnder that marke and when the saide marke shall bee without that touche poynt or poynt of intersection then the pellet will hit aboue the saide marke And when a pellet in his range shal cut the visual line and ascend aboue the same lyne then the same pellet in his descending will cut the same line againe And when our visuall line doth cut the line of the pellet then of necessitie it shall cut the same line in 2. places and the first of these 2. places cannot be very far from the peece but the other place of intersection must of necessitie be very far from the peece I meane in the end of the pellets violent range And when a pellet in his range shal cut the visual line ascend aboue the same lyne then the gunner may with that pellet strike 2 sundry markes in 2 seueral places Interlocutors L. Gabriel Tadino Prior of Barletta Nicholas Tartaglia PRior Yesterday in the euening you concluded and by good naturall reason shewed that a pellet shot out of a peece doth not in any part of his waie goe in a right line except it be shot right vp towards heauen or right downe towards the center of the worlde now I demaund of you whence it commeth that a pellet shotte out of a peece at a marke within point blanke Whē the leuel sight at the mouth of the piece is precisely so high as the leuell sight at the taile of the peece and he which will shoote at any marke seeth with his eie the same marke by the vppermost parts of the said sights thē the pellet will alwaies strike sōwhat vnder that marke doth strike somtimes in the very middest of the marke and somtimes vnder the marke and sometimes aboue the marke Nich. All this commeth to passe by reason of the leuell sights that are vpon the peece For if the leuel sight at the mouth of the peece be precisely so high as the leuel
which you shoote Prior. By what reason can it do so Nicholas By this reason When the leuell sight at the mouth of the Peece is shorter than the leuel sight which is on the breech of the Peece then alwayies by the fift petition of Euclide our visuall line doth of necessitie meet with the right line which proceedeth straight foorth according to the vndermost part of the concauitie in the Peece and for that the way in which the pellet flieth for a good space togeather is neare vnto it or not farre from it although it bee not straight nor goeth in truth by the saide line which proceedeth straight foorth according to the vndermost part of the concauitie in the canon of that Peece And therefore that intersection may be in such a place where the same visuall line will also cut the line or way in which the pellet flieth And this commeth to passe when the leuell sight at the mouth of the Peece is more shorter than it should be in respect of the leuell sight which is on the breeche of the Peece And that intersection may be also in such a place wher the said visual line wil not cut nor touch the said line or way in which the pellet flieth And this hapneth whē the leuel sight at the mouth of the Peece is not sufficiētly enough more shorter than the leuel sight which is on the breech of the Peece Also that intersection may bee in such a place where the visual line wil touch the line or way in which the pellet flieth When our visual line in seeing the marke doth touch or cut the line in which the pellet flieth and the marke at which wee shoote is in the said touch point or in the said point of intersection then the leuel sight at the mouth of the Peece hath his due length and conuenient shortnesse and the pellet will strike in the middest of the marke But when the saide marke shall be within that touch point or point of intersection then the pellet will hit somewhat vnder that marke and when the said marke shal be without that touch point or point of intersectiō the the pellet wil hit aboue the said mark this happeneth when the leuel sight at the mouth of the peece hath his due and conuenient shortnesse in respect of the leuel sight which is on the breech of the Peece and then if by chaunce our visual line shall cut the said line or way of the pellet and by chaunce the marke vnto which the leuel is giuen shall be precisely in the point of that intersection without doubt the pellet will strike precisely in the midst of that marke but if by chaunce the said marke shall be within that intersection that is to say more towardes the peece then the pellet wil alwaies hit somwhat vnder the mark I meane vnder the midst of it and by how much the more remote or farther of the same mark shal be from that intersection that is to say more towards the Peece by so much the pellet will hit more vnder the middle part of that mark But if by chaunce the same mark shal be somwhat without that intersectiō that is to say somewhat more higher thā that intersectiō then the pellet wil hit aboue the marke for a certaine space by how much the more remote or farther of the same marke shal be frō that intersection by so much the pellet wil hit more aboue the marke Pri In this matter I do not wel vnderstand you Nich. Let vs suppose by the figure folowing Example that a Peece of Artillery hath vpon it 2 leuell sights marked with these letters C and D that D the leuel sight is shorter thā the leuel sight C that F G is the line which proceedeth straight foorth according to the order of the vndermost part or ground of the concauitie in the Peece that H I is the line or way in which the pellet flieth that our visual line proceeding straight foorth by the tops or vppermost points of the two leuel sights C and D doth of necessity as hath bin before said cut the line FG and therefore let vs suppose that our said visual line doth also cut the said line H I in the point K as it doth in the figure folowing Now I say that if the marke to which the leuel is giuen be precisely in the point K the pellet will strike precisely in the middle of that mark And if by chaūce the said marke be within that intersection that is to say towards the Peece as if I should say in the point M the pellet will alwaies strike somewhat vnder the midst of that mark because in al that space the pellet rangeth alwaies vnder our visual line And by how much the said mark is more remote or farther frō the point K that is to say Note by how much more nearer M is to the peece by so much the pellet wil strike more loer neuertheles such lonesse in such a case can neuer be equal to the difference that is betweene the extreame or vppermost part of the leuell sight which is vppon the mouth of the peece I meane betweene the point D and the center of the said concauitie or hollonesse in the peece the which difference is about one halfe part of the thicknesse of the peece in the breech and therefore when the marke to which the leuell is giuen lieth betweene the Peece and that intersection the Gunner is subiect to a small error by reason of the leuel sights But when such a marke is somewhat without that intersectiō as if I should say in the point L the pellet will strike aboue the marke because for a long way or space the pellet flieth aboue the visuall line And therefore by how much the saide marke is more farther from the point K by so much the stroke of the pellet in a long way will hit the more higher When a pellet in his range shal cut our visual line ascend aboue the same line then of necessitie the same pellet in his descēding will cut the said line againe When our visual line doth cut the line of the pellet then of necessitie it must cut the same in two places the first of those two places can not bee very far from the peece but the other place of intersection must of necessitie be very far from the peece I meane in the end of the pellets violent range And it is true that the pellet going farre in his croked or naturall way returneth to cut againe our visual line because our visual line C D K L doth infinitely proceede straight foorth and the pellet doth not infinitely proceed in the way H K I but in time beginneth to decrease and encline towards the center of the worlde and finally finding no resistance directeth it selfe in his naturall way towards the said center of the worlde and so by going farre it doth of
within the marke that is to say betweene the Peece and the marke as it doth appeare by the reasons alleaged in the seuenth Colloquie and because for a very long way together by how much the marke at which you shoote is more beyond the said intersection by so much the pellet will hit more aboue that marke therefore by remoouing the same marke somewhat father of from your standing that marke will be likewise somwhat more remooued from that intersection and by so much as the marke shall bee remooued more farther of euen vnto a certaine limite by so much the pellet will hit more higher or more aboue the said marke the same in effect will followe if the Schioppetiero or Gunner will goe backe more farther of from the marke And all this which I haue tolde you must bee intended when the pellet hits aboue the marke through the fault of the two leuell sights and not through the fault of him which shootes Admonition for if it be by default of him which shootes I meane if he in discharging the Handgunne doth make any moouing and that thereby the pellet doth strike aboue vnder or wide of the marke our reasons extend not to helpe that inconuenience but to amend those faultes which may be committed by the meanes of the two leuell sights which are set vpon the handgunne Note Also you must vnderstand that the said marke may be so much transported and set so farre of from his first place that not only the pellet will hit more nearer to the marke than it did at the first shoote but also strike the same marke as it doth appeare by the reasons alleaged in the end of the seuenth Colloquie that is to say if by happe the marke shall bee transported and set so farre of as that it be put in the same place where our visual line makes a second intersection in the way of the pellet without doubt the pellet will hit in the very middest of the marke as it hath been said before in the 7 Colloquie And if by chaunce the marke bee not put in that place of the second intersection but neare vnto it then the pellet will not hit so precisely in the very middest of that marke but neare vnto it that is to say if the marke shall be put somewhat within the place of that intersection the pellet will strike somewhat aboue the marke and if the marke be put somewhat without that intersection Note the pellet will strike somewhat vnder the marke as all this may easily be perceaued by the reasons and picture in the ende of the seuenth Colloquie And the sayd marke may bee also transported so much from the said second intersection as that the pellet can not come to touch it which by naturall reason is easie to be perceiued Schioppetiero I doe well vnderstand your reasons and make great account of them The 28 Colloquie The reasons and causes why a Schioppetiero which doth shoote in a Handgunne at a marke lying leuell with his eye and through the fault of his leuell sights doth shoote vnder the marke shall by remouing the said marke more farther from him and shooting at it againe strike sometimes more vnder the same marke than he did before and sometimes betweene the marke and the place where the pellet did hit at the first and sometimes precisely in the marke and sometimes aboue the marke Interlocutors Schioppetiero Nicholas Tartaglia SChioppetiero By occasion of the aforesaid question an other thing commeth to my remembrance which is this I shoote in my handgunne at a marke lying leuell with the mouth of my Peece and for that the pellet doth hit vnder the marke through the fault of the two leuell sights I doe remoue the same marke farther of from me or goe backe from the said marke now if I shall shoote againe at that marke lying in a right line with my Peece whether or no will the pellet at the second shoote hit more higher or more loer than it did at the first shoote Nicho. In this case there may be diuers alterations because the leuel sight before at the mouth of the Peece may be of equall height with the leuell sight behinde at the breech of the Peece and the said leuell fight before may bee more higher and also more shorter than the leuell sight behinde Note If then by chaunce the leuell sight before vppon the mouth of the Peece shall bee of equall heigth or longer than the leuell sight behinde vpon the taile of the Peece according to the reasons alleaged in the beginning of the seuenth Colloquie by how much more farther the marke is remooued frō you by so much the pellet wil strike more loer But if the leuell sight before shall be more shorter than the leuell sight behind and that by chaunce it is so much shorter than the other as that your visuall line doth cut the way of the pellet as is declared in the ende of the seuenth Colloquie in that case the pellet must needes at the seconde shoote strike higher than it did at the first shoote and yet that may be vnder the marke that is to say betweene the said marke the place where the pellet strooke at the first bloe and it may bee also precisely in the midst of the marke Note it may bee also aboue the marke For alwaies when the leuell sight before is so much shorter than the leuell sight behinde as that your visuall line doth cut the way of the pellet as before hath been sayd and that in such a case a Shioppetiero or Gunner doth shoot at a marke lying leuell with his Peece through the fault of the two leuell sights and not through any fault in himselfe doth hit vnder the marke it is manifest that the intersection which the visuall line makes in the way of the pellet by the reasons alleaged in the ende of the seuenth Colloquie shall be beyonde the marke that is to say the marke shall be betweene the sayd intersection and him that doth shoote And therefore if the place to which the marke shal be remooued be within that intersection of necessitie the said second bloe will be vnder the marke and yet it will be more nearer to the marke than the first bloe was that is to say it will be between the marke the first bloe But if the marke be remooued to the very place of the intersection the pellet at the second shoote will hit precisely in the middest of the marke that is to say in the marke which lyeth in a right line with the mouth of the Peece But if the marke be remooued by chaunce beyond the said intersection the pellet at the second shoote must needes strike aboue the marke and it will strike so much more aboue the marke vnto a certaine limite as the marke is more remooued beyonde the saide intersection as in the ende of the precedent Colloquie hath been sayde But if the leuell
Italian Authors Nicholas Tartaglia Vannuccio Biringuccio Girolamo Ruscelli Girolamo Cataneo Francesco Ferretti Cosimo Bartoli Gio Francesco Peuerone Abel Fullone Luigi Collado Latin Authors Daniel Santbech Sebastian Munsterus Ioan Baptista Porta Hieronymus Cardanus Ioan Iacobus Weckerus Anton Maria. Gemma Frisius Hermannus Witekindus Thomas Finck Ioan Demerlierius Christian Vrstisius English Authors M. Robert Recorde Doctor of Phisike M. William Cunningham Doctor of Phisike M. Leonarde Digges Gent. M. Thomas Digges Gent. M. Peter Withorne Gent. The first Chapter The properties office and duetie of a Gunner A Gunner ought to be a sober wakefull lustie hardie patient prudent and quick sprited man he ought also to haue a good eysight a good iudgement and perfect knowledge to select a conuenient place in the day of seruice to plant his Ordinance where he may doe most hurt vnto the enemies and be least anoyed by them and where his Ordinance may not be surprised by the enemie A Gunner ought to be skilfull in Arithmeticke and Geometrie to the ende he may be able by his knowledge in those artes to measure heights depthes breadthes and lengthes and to drawe the plat of any peece of ground and to make mines countermines artificiall firewoorkes rampiars gabbions or baskets of earth and such like things which are vsed in time of warre to be made for offensiue and defensiue seruice A Gunner ought also to procure with all his power the frendship and loue of euery person and to be carefull for his owne safetie and for the preseruation of all those that shal be about him Also he ought to be no surfeter nor a great or sluggish sleeper but he must gouerne him selfe in al times as a wise modest sober honest and skilfull man ought to doe that through want of vnderstanding he may neuer leese his credite nor an vniuersall victorie which oftentimes by the meanes of good Gunners well managing their peeces is gotten Also a Gunner ought at the receite of his charge to make an Inuitorie of al such things as shall be committed to his charge as well to render an account as to consider the want of such necessaries as to the Artillerie apperteineth And when a Gunner shall be appoynted to doe an exployte he ought to want neither a fire stone nor a tyndar box with a good steele nor flintstones nor tindar nor gunmatches nor a flaske full of good touchpowder to kindle his gunmatch and fire when neede shall require Also when a Gunner shall be appoynted to doe an exployte he must lay his powder twenty paces from his Peeces in such a place where no fire water or hurt may come vnto it through any person or by reason of any winde weather or otherwise and keeping his powder alwayes couered he must not be vnmindfull of this that it is a very dangerous thing for a Gunner to trust many because a generall hurt and death may thereuppon followe Also a Gunner that hath a charge ought to haue alwayes in a readinesse all necessarie things for his artillerie that is to say wheeles axeltrees ladles rammers spunges gunpowder pellettes tampions chaineshot crossebarres sustian canuas or paper for cartredges and firewoorkes fourmes for ladles and cartredges needles threed to sowe and binde the cartredges and firewoorkes artificiall torches candles lantornes mattockes shouels crowes of yron handaxes leuers enguines for the mounting and imbasing of ordinance ropes little handbaskets glwe or payst horsecollers horses or oxen to drawe his peeces all manner of cartware carters to guyde and keepe his horses and oxen and a sufficient number of Gunners and assistants to charge discharge mount imbase wadde ramme make cleane scoure and coole his peeces when they are ouer heated and to haue for this purpose vineger and faire colde water Also a Gunner ought alwayes to haue a gunners staffe or a partisant or a halbert sticking by him for a part of his defence and he ought to put into the cocke of his Gunners staffe a gunmatch or wrappe about the lower end of his staffe partisant and halbert a good gunmatch which may geue fire vnto his peeces of artillerie when neede shall require Also a Gunner ought not to sleepe much at any time of the day or night when he is appoynted to serue in the fielde or in any other place nor to eate or drinke in any other roome than where his peeces of artillerie are planted because in his absence the same peeces may be choked poysoned and harmed by diuers wayes and that he may many times vppon a sudden haue good occasion to discharge all his peeces And it is requisite for a Gunner to fixe vppon the tayle of the carriage of his peece a chest to holde his necessary things and to defende him from small shot when he shal serue in a place where no baskets of earth are set to defend him Also a Gunner ought to haue a ruler and a payre of compasses to measure the heigth length of euery peece his concauitie and the length depth and widenesse of euery ladle whereby he may know whether his peece is laden with too much powder or is charged with a lesse quantitie of powder than it ought to haue A Gunner ought to knowe the names length and waight of all manner of peeces and be able to tell readilie how much gunpowder is a due charge for euery peece how manie times in one day euery peece may without harme be shot of how many Gunners and assistants or labourers ought to attend vppon euery peece how many horses or oxen will drawe euery peece what sorte of peeces doe commonly carry pellettes of lead what sorte of peeces doe shoote Pellettes of yron what sorte of peeces are vsually laden with pellettes of stone and what sorte of peeces haue chambers and how euery kinde of peece should be charged with his powder tampion pellet and wadde Also a Gunner must be skilfull to make Saltpeeter to refine and sublime Saltpeeter to make diuers sortes of gunpowder to make coles for gunpowder to purifie brimstone for Saltpeeter to make cartredges to amend and make good agayne euery sorte of gunpowder which by any manner of meanes hath lost his vertue and force and tell how much Saltpeter ought to be put into the sayd vnforceable gunpowder to make it so strōg as it was before and how many times the saltpeeter which shall be put into the sayde gunpowder ought to be refined Also a Gunner in time of seruice ought to forbyd with meeke and courteous speeches all manner of persons other than his appoynted assistantes to come neere his peeces to the ende that none of his peeces may be choked poysoned or hurt and he ought not for any prayers or rewarde to lende any peece of his gunmatch to another person because it may be very hurtfull to him in time of seruice to lacke the same Also a Gunner before he goeth to doe any exployte ought to consider of all thinges which shal be needeful for him to
foure foote wide within the stakes This done wreath about the stakes of each gabbion or basket so many of the said Osiar twigges or pliant roddes as will suffice to make euery basket extende one foote in heigth aboue the head of the taulest gunner After you haue so done fill vp the said baskets with earth which must be throwne into each basket by a little and little at a time and cause a man standing within euery basket to treade well and ramme downe all the same earth as it shall be so cast in But when gunners shall serue vppon a platfourme where no baskets of earth are set to defende them they may shadow themselues with cables or bigge ropes with wet strawe or wet hay with dead bodies of enemies with mattresses shippe sailes or canuas hanged stiffe vp so as the enemie shall not see any marke or man vppon the platfourme to shoote at and with a line drawe vp the nearer or loost end of the same mattresses ship sailes or canuas so often as they shall haue cause to shoote at their enemies This deuise as some men doe thinke will be also profitable for those that shall in time of warre stand vppon the walles of a cittie towne or forte because they may put vp at their pleasure the canuas looke vnder the same with more safety than through the loope or looke holes in the wall at which the enemis are alwayes readie to shoote If for defence in seruice you will make a double Gabbion which at the least ought to be eight foote in widenesse and 25 feete and 1 7 of a foote in compasse digge at the ende of euery foote in measure vppon that compasse a whole foote ½ foote or somwhat more in deepenesse and set vpright in euery of the said holes a staffe often foote in length and in compasse so bigge as a mans arme This done wreath pliant twigges of Osiar or of nut trees or of oke or of willoe about all the same erected staues vp to their tops while you are so occupied cause an other man with a woodden beetle to beate downe your worke close togeather whereby it will be more able to resist the violent bloe of a pellet Also in the very middest of the Gabbion driue a strong peece of oke into the ground lay other peeces of tymber ioyned fast togeather ouerthwarte the gabbion from one of his sides to the other After all this fill vp the said gabbion with good clay or with blacke small and wet earth well rammed downe or with greene turfes digged out of meddowes or with bagges full of earth or fine sande or with bagges of wooll which is the best thing of al for this purpose and take heed that you do put no stone into any gabbion among those things which do fill it vp The 49 Chapter Rules by which Rabinets Bases Fauconets forreine ordinance that are not so high as the Faucon Faucons Minions Sakers Culuerings Basiliskes Cannons and all peeces which do shoote stone pellets may for proofe and also for seruice be duely charged with that sort of corne gunpowder which is marked in the 16 Chapter of this Appendix with the figure of 1 and by which you may tell what roome a due charge of such corne gunpowder will fill vp in the concauitie of any great peece that shooteth pellets of lead or pellets of yron 1 YOu may prooue all sorts of great peeces with three shoots in this maner following Charge euery Rabinet Base Smeriglio Rebadochino Fauconet Faucon Minion Passauolante Moiane Saker Culuering which is fortified with mettal as it ought to be for the first shoote of proofe with the whole waight in gunpowder of his pellet for the second shoote of proofe with 5 4 in gunpowder of the waight in his pellet for the third and last shoote of proofe with 3 2 in gunpowder of the waight in his pellet As for example if a peece which shal be prooued doth shoote a pellet of 12 pounds in waight you must charge the said peece for the first shoote of proof with 12 poundes in gunpowder for the second shoote of proofe with 15 poundes in gunpowder and for the third shoote of proofe with eighteene poundes in gunpowder 2 Charge euery Cānon Basilisk for the first shoot of proof with ⅔ in gūpowder of the waight in his pellet for the second shoot of proof with ⅚ partes in gūpowder of the waight in his pellet and for the third and last shoote of proofe with the whole waight of his pellet in gūpowder As for example if any Peece named in this second rule shall be prooued with a fit pellet of 45 poundes in waight you must charge the said peece for the first shoote of proofe with thirtie poundes in gunpowder and for the second shoote of proofe with 37. poundes and ½ pound in gunpowder and for the third and last shoote of proofe with 45 pounds in gunpowder 3 Charge euery cannon periero of the olde making for the first shoote of proofe with ⅓ in gunpowder of the waight in his stone pellet for the second shoote of proofe with 7 18 partes in gunpowder of the waight in his stone pellet and for the third and last shoote of proofe with 4 9 partes in gunpowder of the waight in his stone pellet As for example if a cannon periero of the old making shall be prooued with a fit stone pellet of 36 poundes in waight you must charge the said cannon periero for the first shoote of proofe with 12 poundes in gunpowder for the second shoote of proofe with 14 poundes in gunpowder and for the third shoote of proofe with 16 poundes in gunpowder 4 Charge euery cannon periero of the nwe making for the first shoote of proofe with ½ in gunpowder of the waight in his stone pellet for the second shoote of proofe with 5 ◠parts in gunpowder of the waight in his stone pellet for the third and last shoote with ¾ parts in gunpowder of the waight in his stone pellet As for example if a cannon periero of the nwe making shall be prooued with a fit stone pellet of 36 poundes in waight you must charge the said cannon periero for the first shoote of proofe with 18 poundes in gunpowder for the second shoote of proofe with 22 poundes and ½ pounde in gunpowder and for the third and last shoote of proofe with 27 poundes in gunpowder 5 Also you may prooue any great peece of artillerie by these rules following charge and discharge thrise togeather for proofe euery Smeriglio Rebadochino Base Rabinet Fauconet Faucon Minion Saker Passauolante and demie Culuering loer than ordinarie with the whole waight in corne gunpowder of his leaden pellet 6 Charge discharge thrise togeather for proofe euery ordinary demie Culuering demie Culuering of the biggest sort whole Culuering not so high as ordinary whole ordinarie demie Culuering and whole Culuering of the biggest sort which is not so well fortified
the ladle is pulled out remayne in the lowest ende of the same peece After you haue in this sorte laded the peece with his due charge in gunpowder thruste harde with a rammer twise togeather no more except you doe charge a Cannon all the sayd gunpowder home vnto the lowest ende of the peece that it may not lie dispersed or loose nor be too harde rammed downe in that place Also thruste a bigge wad of toe hay strawe or of vntwisted ropes into the peece home vnto the charge in gunpowder for to sweepe and keepe togeather all the sayd charge in gunpowder and to cause the pellet that shal be shotte out of the same peece to range farre Then putting a fitte pellet into the concauitie of the peece which fitte pellet as our English Gunners doe say ought alwayes for diuers reasons to be ¼ of an ynch lesse or shorter in his diameter than the heigth of the sayde concauitie driue with a rammer the pellet home vnto that wadde and if the peece shall shoote downewardes at a marke A fitte pellet as our english Gunners doe say is ¼ of an ynche lesse or shorter in his diameter than the heigth of the concauitie in his peece But among the Gunners in high Germany this is a general rule that the diameter of a fitte pellet ought to be neither more nor lesse than 20 21 of the diameter in the mouth of his peece As for example a fitte pellet for a peece of seuen ynches in diameter must be 6 ynches ⅔ of an ynche in diameter thruste an other bigge wadde of toe hay strawe or of vntwisted ropes into the peece home vnto the said pellet for to keep the pellet within the peece to stay the pellet there that it may not role out before the peece shal be discharged moreouer put good dry gunpowder into the touchhole and about the touchhole of the peece like a trayne and be not ignorant that after all this is done the peece is charged and that you standing vppon one side of a peece so charged and touching the trayne of gunpowder by the touchhole of the peece with a lintstocke or with a fiered Gun-match which some Gunners doe tie to the ende of a sticke of three or foure foote in length and some Gunners doe set fast in the cockes of their staues and some Gunners doe winde about the staffe ende of an halbert or partisant may safely discharge the same peece Also if you will in time of seruice charge any of the sayd peeces of Artillerie with cartredges doe thus Put first a cartredge into the mouth of the Peece and then with a rammer thruste it into the lowest end of the Peece his concauitie and next driue a woodden tampion with a rammer into the same concauitie home to the cartredge then ioyne a good bigge wadde of hay strawe toe or of vntwisted ropes vnto the sayd tampion and put a fitte pellet into the Peece close vnto the sayd wadde and when a Peece so charged shall shoote downewardes at a marke thruste an other like bigge wadde into his concauitie harde vppon the pellet This done put a long pricker into the touchhole of the Peece so charged and with the same pricker pearce diuers holes thorow the cartredge lying within the Peece or which in mine opinion is a better deuise cut cleane away before you doe put the cartredge into the hollow Cylinder a peece of the outside of the cartredge in that parte which shall lie directly vnder and next vnto the touchhole Finally fill the touchhole of this Peece with good and dry corne gunpowder and make about the touch-hole a little trayne of powder and considering that the tampion within the sayd Peece if the powder lying behinde the same tampion should happen to be moyste must be drawen out with a long yron worme An admonition or cutte in peeces with a long yron cheesell which will be a perillous worke to doe I counsel you to discharge the sayd Peece within a conuenient time after it shal be so charged with a tampion The 52 Chapter How without a Ladle you may lade any Fauconet Faucon Minion Saker Culueringe Cannon or other like made Peece with his due charge in loose gunpowder PVt a long straight and smoothe staffe into the bottome of euery Fauconet Faucon Minion Saker Culueringe Cannon and euery other like made Peece that shall be charged and hauing thruste the staffe downe close by the mettall into the concauitie of his Peece so farre as it may goe marke with a knife or with some other conuenient thing that parte of the staffe which is touched with the lippe or outmost edge of the Peece his mouth Then drawing the sayd staffe out of his Peece measure along vppon the same staffe with a compasse beginning at the sayd marke and proceeding downewardes in a straight line towardes that end of the staffe which was at the bottome of the sayd concauitie the iust length of the roome which a due charge in gunpowder will fill vp in the sayd concauitie You may see in the 49 Chapter of this Appendix what roome a due charge in gunpowder will fill vp in any Fauconet Faucon Minion Saker Culuering Cānon or any other like made Peece and make an other visible marke vppon the staffe at the end of the same length and for a distinction call it the lowermost marke After this throe Gunpowder into the Peece with your handes vntill by estimation the Peece hath receaued thereof a due charge and with a rammer as you haue beene taught in the precedent Chapter thruste the same gunpowder downe into the bottome of the Peece and to the ende you may be guyded by the sayd staffe to throwe no more gunpowder into the Peece than is requisite and to take out the excesse when you haue throne too much gunpowder into the Peece put the sayd staffe agayne into the Peece home vnto the gunpowder and looke where the lowermost marke vppon the same staffe is For as the Peece lacketh a parte of his due charge in gunpowder if the sayd lowermost marke shall now be within his mouth and hath more than his due charge in nwe gunpowder if the sayde lowermost marke shall be without his mouth So if you haue throwen into the Peece his due charge in gunpowder the sayd lowermost marke will now neither be within the mouth of the Peece nor without the mouth of the Peece but touch exactly the outmost edge or lippe of the Peece his mouth The 53 Chapter How you may duely charge any Chamber peece of Artillery and how you may charge any Cannon Periero PVt into euery chamber so much powder as his peece requireth for a due charge and with a rammer beate a tampion of softe wood downe vppon the gunpowder Moreouer put a bigge wadde into the peece at that ende where the mouth of the chamber must goe in and after the wadde thruste into the peece at the
I may discouer vnto you the force of all other peeces of artillerie  Poynt blanke Vtmost randon  Vtmost randon Poynt blanke Faucon 320 Yards 1280 Yards Faucon 1280 Yards 320 Yards Saker 360 Yards 1440 Yards Saker 1440 Yards 360 Yards The 61 Chapter How you must mount your peece when you will shoote vnto the farthest end of the vtmost randone NIcholas Tartaglia in his Epistle set at the beginning of his booke named La noua scientia declareth that euery great Peece of Artillery ought to be mounted at 45 degrees when it shall shoote vnto the farthest ende of his vtmost randon But William Bourne in his Treatise of shooting in great Ordinance wryteth that it is needefull for vs to consider well of the winde before we doe mount any peece to shoote vnto the farthest ende of his vtmost randon because as he sayth when we will shoote with the winde vnto the farthest ende of the vtmost randon we must mount our peece at 45 degrees and in a windie day against the winde sometimes at 36 degrees sometimes at 37 degrees sometimes at 38 degrees sometimes at 39 degrees sometimes at 40 degrees according as the winde is in bignesse and in a fayre calme day at 42 degrees The 62 Chapter How you may mounte any great peece of Artillerie with a ruler as well as with a quadrant or semicircle vnto the number of tenne degrees and how such a ruler ought to be made and how such a ruler ought to be vsed when a peece of Artillerie is by it mounted or imbased THe measure of the length of the peece that shal be mounted by a ruler being doubled reduce into ynches after this multiplie the sayd number of ynches by 22 and diuide the product by 7 and diuide againe the quotient number of that diuision by 360 then take the last quotient for the number of ynches and partes of an ynch that wil make a degree vppon a ruler for that peece which was so measured As for example I wil mounte a peece of 6 foote long at one degree with my ruler therefore 6 foote the length of that peece being doubled maketh 12 foote which reduced into ynches make 144 ynches This number of 144 multiplied by 22 produceth 3168 which diuided by 7 yeeldeth in the quotient 452 and 4 7 then doe I diuide that quotient of 452 and 4 7 by 360 and so the quotient of this last diuision which is 1 and ◠3 ◠5 sheweth that this peece of 6 foote in length being mounted by my ruler 1 ynche and ◠3 9 5 of an ynche lyeth iustly of the same heigth that it would doe if it should be mounted at one degree of a quadrant or semicircle Now to know how much the sayde peece must be mounted for 2 degrees of a quadrant or semicircle I multiplie 1 and ◠3 9 5 by 2 and thereof commeth 2 and ⅓ ◠5 wherefore I say if the sayde peece be eleuated by the ruler 2 ynches and ⅓ ◠5 of an ynche that it lieth mounted at two degrees Likewise by multiplying the sayd number of 1 and ◠3 9 5 by 3 the product therof which is 3 and ⅔ 7 5 expresseth that the sayd peece must be mounted 3 ynches and ⅔ 7 5 of an ynch for 3 degrees And after this order I may knowe how to mount the sayde peece with a ruler vnto any other degree to which the peece wil be mounted with a ruler for you ought not to be ignorāt of this that a peece of artillerie cannot be mounted with a ruler aboue 10 degrees because the degrees are taken out of a circumferēce and not out of a straight line The ruler with which peeces of artillerie may be mounted is made in fashion like vnto the picture drawē in the margent marked as common rulers are with ynches halfe ynches quarters of ynches halfe quarters of ynches and with more lesser partes of an ynch Also in the middest of this ruler almost from one end to the other there is a slitte or open place within which a plate of brasse or lattin hauing in it a little hole pearced thorow is so placed that the said hole may as need shall require be mooued vp and downe in that slitte and be set right against any ynch or parte of an ynche marked vppon the same ruler And although as it seemeth to me a peece may be more easilie and more iustly mounted vnto any degree by a quadrant and also by a semicircle than by a ruler yet wil I not let passe to shewe in this place how you must vse the ruler to mounte a peece by it Wherefore when you wil mount a peece by a ruler to shoote at any marke put first the true disparte of the peece to be mounted vppon the peece his mouth as you haue beene taught in the 57 Chapter of this Appendix then knowing at what degree the peece must be mounted to reach the marke set the hole which is in the mouable plate of the ruler right against the number of ynches and partes of an ynche that will make iustly the same degree and hauing so done set the ende of the ruler vppon the tayle of the peece so as the ruler may stande vppon the peece squirewise vntill you haue done your woorke After this the mouth of the sayde peece being layde right vppon the marke koyne the breeche of the peece vp and downe vntil you may see thorow the sayd hole in the plate the top of the disparte and the marke and when you haue so done geue fire to the peece that you may strike the sayde marke The 63 Chapter How you may by the helpe of wedges lay the concauitie of any great peece of Artillerie right against a marke how by the helpe of wedges you may make a perfect shoote at a marke lying vnder the mouth of your Peece and how by the helpe of wedges you may cause your Peece to strike in the marke after it hath at one shoote shotte vnder the marke and at an other shoote shotte aboue the marke PRepare of yron or of strong and harde wood two sortes of wedges for euery great peece of Artillery that is to say three wedges of one sorte and three wedges of an other sorte Make euery wedge of the one sort iust so thicke as ⅓ parte of the heigth in the disparte of his peece and let euery wedge of the other sorte be no thicker than ⅙ parte of the sayde heigth This done lay the vppermost parte of mettall at the tayle of the peece and the vppermost parte of mettall ouer the mouth of the peece in an equall heigth and in a right line with the marke and then put vnder the tayle of the peece one of his sayde wedges of the thicker sorte which as Luigi Collado affirmeth will cause the concauitie of that Peece without any more woork to lie right against the sayd marke But when you purposing to shoote at a marke lying vnder the mouth
second shoote against the said marke in euery respect as it did lie at the first shoote and afterwards raise vp the dispart vppon the mouth of your peece till you shall see by the vppermost part of mettall in the taile of the peece and the toppe of that dispart the place where the pellet strooke at the first shoote This done imbase the mouth of that peece till the said vppermost part of mettall and the toppe of the same dispart doe lie in a right line with the marke and then giuing fire to the peece you shall see that by this meanes the peece will shoote into the marke To amend a loe shoote Also when a pellet shot at a marke within point blanke doth strike somewhat vnder his marke you may amend the said loe shoote in this maner Recharge your peece and after you haue for the second shoote laid it against the marke in euery respect as you did lay it for the first shoote set vpright vppon the vppermost part of mettall in the taile of the peece a waxe candle of such a length as that you may see by the toppe of the saide candle and the toppe of the dispart vppon the mouth of the peece the loe place where the pellet before did hit Then hauing mounted the mouth of your peece till the toppe of the saide waxe candle and the toppe of the dispart vppon the mouth of your peece doe lie in a right line with the saide marke giue fire to the peece and so you shall shoote into the marke To amende a shoote wide vppon your right hand But when a pellet shot at a marke within point blanke shall strike wide vppon your right hand then to amend that wide shoote recharge the peece which shot that pellet and laying it for the second shoote against the marke as it did lie at the first shoote remoue the leuell sight vppon the taile of your peece somewhat towards your left hand so as the top of your nwe leuell sight and the toppe of your peece his dispart may be perceaued to lie in a right line with the place where the pellet before did strike This done mooue your peece to and fro till you shall see that the top of your nwe leuell sight and the toppe of your peece his dispart do lie in a right line with the marke for an end of this worke giue fire to your peece which now without faile will shoote his pellet into the marke To amende a shoote wide vppon your left hand You may amend a shoote wide vppon your left hand as you haue been taught to amend a shoote wide vppon your right hand sauing for the amendment of a shoote wide vpon your left hand you must alwaies remoue the leuel sight vppon the taile of your peece somwhat towards your right hand The 73 Chapter To make an engine which will make a great spoile and a merueilous slaughter PLace a great peece of Artillerie within a brode yron hoope and lay a great number of Caliuers or Muskets in the said hoope rounde about the said peece according to the figure next folowing and when need shall require charge and discharge all the same peeces togeather This engine discharged out of a ship at men in a Gallie Foyst or any other like vessell as Girolamo Ruscelli writeth will make a great spoile and a merueilous slaughter The 74 Chapter Instructions for all those that are vnskilfull to handle and vse an Harchibuse Caliuer or Musket 1 EVery person vnskilfull to handle and vse an Harchibuse Caliuer or Musket ought first to learne to handle and carry soldier like the saide peece and the Flaske and touch boxe belonging to it the alowed bore of a caliuer in Ao. DniÌ„ 1588 the alowed bore of a musket in Aº DniÌ„ 1588. 4 Also he ought to learne how he shall in a commendable maner charge his peece and how he shall afterwardes when need shall require lay it to his cheeke 5 Hauing learned to charge he ought also to know how hee should shoote in the saide peece at randon and likewise how he should shoote in that peece at a marke within the leuell of the same peece and how vppon a small stay in march or skirmish hee should charge and discharge speedily his peece 6 Also he ought to prooue before hee hath vrgent cause to vse his peece whether it bee good and meete for his purpose or like to breake 7 And in a skirmish made only for practise or sport let him take heed that hee doe not charge his peece with any bullet whereby any person may be maymed or put in hazard of his life or limmes 8 Also for diuers reasons which are not meete to be expressed in this booke let no person at any time vse to shoote out of his peece any pellet of lead after hee hath chawed it in his mouth and bitten it with his teeth The 75 Chapter How to mount a morter peece for to shoote out of the same fireworks or great stones ouer walles or other high places into cities townes or camps to burne and beate downe houses tents and lodgings within the same places IT behooueth him which will shoote out of a morter peece any fireworke or great stone for to haue it fall right downe vppon the appointed place to know these 3 things The waight of the shot how much ground his peece wil shoote at the best of the randon how far the place which he would burne or beate downe is from him The said three things being knowne he may easily by this example following learne to doe as he intended Example The peece will shoote the fireworke or the great stone at the best of the randon 800 paces and the place to be burned or beaten downe is distant from that peece 600 paces therefore that peece must be mounted for to doe this exploit at 48 degrees and ½ degree But if the fireworke or the great stone will flie at the best of the randon 900 paces and the place to bee burned or beaten downe bee distant from the peece sixe hundred paces then the saide peece must bee mounted at fortie one degrees and almost ½ of a degree And when the fireworke or stone will flie at the best of the raudon 1000 paces and the space betweene the peece and the said place doth containe 600 paces the said peece must be mounted at sixe thirtie degrees and ½ part of a degree but for the better vnderstanding hereof marke well this figure following â— for t to be burned or beaten downe The â—…etus or perpendiculer line A morter peece set vpright In the said figure there is a Quadrant and vppon the same with a moueable Hipothenuasa or Index a right angled triangle is fashioned The base of that triangle representing the space betweene the peece the marke ought to bee diuided into so many equal partes as the said distance betweene the peece and the marke doth containe paces Likewise the
you must instruct the Pyoners to vndermine deepe within harde grounde and to make the way of the myne three foote in breadth and sixe foote in heigth and to digge the sayd Ouen and place of greatest effect sixe or seuen foote in breadth and nine or tenne foot in heigth to this ende that the gunpowder laide in that place may make his vent vpwardes and that the ayre which is within the saide holloe place may ayde the gunpowder to open and ouerturne the ground which is right ouer it When the saide Ouen and place of greatest effect shall happen to be made in a stonie grounde where the stones are like to fall then you must vnderproppe them with holloe pypes of timber filled ful of good gunpowder and remember alwaies to obserue a meane in making the Ouen and place of greatest effect because it ought in no manner of grounde to be too bigge or too little The myne being finished according to your saide platte couer the ground or floore in the saide Ouen and place of greatest effect with boordes and hauing stroed vppon those boordes a sufficient quantitie of good gunpowder put so many barrelles without any heads or couers full of good and strong gunpowder vppon the same boordes as will execute the thing appointed to be done and in so doing perswade your selfe that the better and greater the quantitie of gunpowder which shal be laide in the saide Ouen place of greatest effect is the more greater will be the effect of the same Moreouer for to fire the said gunpowder when time shall require lay a gunmatch made of fine bumbase cotten that hath beene well sodde in vineger brimstone and saltpeeter well roled in gunpowder and well dried in the Sunne within a Trunke Pype or case of boordes which gunmatch and trunke must extende and reache in length from the gunpowder stroed vppon the boordes in the saide Ouen and place of greatest effect vnto the mouth and beginning of the myne and also somewhat without the same and hauing couered the saide gunmatch all ouer with a traine of dry gunpowder close vp the said trunke with a couer of boordes so as no soile or moysture may come vnto the gunpowder within the same Trunke Or if you will you may tie a peece of a gunmatch vnto the ende of a small line and when the saide ende of a gunmatch shal be a fire drawe the same by that line running on a pulley thorow a traine of gunpowder made within a Trunke vnto the barrels of gunpowder in the saide ouen and place of greatest effect But before you doe fire the gunpowder in the myne with a gunmatch after the doctrine last taught or in any other manner you must with earth rootes of trees blockes of timber stones and such like things walle fortefie and ramme vp the mouth of the saide Ouen or rather all that parte of the myne which C D and E in the figure next following doth represent so as no fire or aire may breath out of the said ouen and place of greatest effect by any other way than by the saide holloe Trunke For in so much as that parte of the myne which is noted in this figure next following with E lieth not right against the saide ouen and place of greatest effect and likewise for that the place of the myne which D in this figure following doth represent lieth not right against C and also for that the mouth of the myne which B representeth in the figure next following is not right against E and D it is certaine when the gunpowder in the saide ouen and place of greatest effect shall be set in a fire after the way of the myne from C to D is so stopped vp with earth rootes of trees blockes of timber stones and such like thinges that the saide gunpowder will with a great and horrible violence bloe and ouerturne all the ground and buildings ouer the same The 102 Chapter How a caue ought to be made rounde about a Castle or Forte that is besieged to the intent that they which are in the saide caue may heare and perceaue at all times whether or no the enemie doth woorke to vndermyne the same Castle or Forte WHen a Castle or Forte is besieged and the Captaine of that Castle or Forte doth feare that the enemie will vndermine the same place then the Captaine to auoid the hurte which may come by the saide myne ought to commaunde his Souldiers to make a deepe pitte within their Castle or Forte and from the bottome of the same to dyg a caue vnder the foundation of the walles of their saide Castle or Forte and also vnder the ditch which enuironeth the saide place vntill they shall come vnto the outside of the saide ditch and from thence to vndermine on the outside of the saide ditch as the ground will suffer them to woorke rounde about the saide Castle or Forte When the Souldiers haue brought out of the saide caue all the earth which was in the same they may fortefie the walles of their Castle or Forte with the same earth and laying sackes of wooll straightly bounde about with cordes in diuers places of the saide caue they ought to put vppon euery of the saide sackes a latten bason and cast into euery of the saide basons sixe or eight harde peason to this ende that they which are in the saide caue may heare and perceaue at all times by those peason whether or no the enemie doth worke to vndermine the same Castle or Forte for at euery stroke that the Pioners shall strike the peason in the saide basons will vndoubtedly make an audible iarre whereof the Captaine ought presently to haue warning that he may in conuenient time with countermines or by some other pollicie make the myne of his enemies to be of no effect Moreouer to knowe whether or no the enemies doe make any myne against you this may be done Sinke diuers deepe welles in diuers places towardes the suspected myne and hauing made diuers holes with a long auger in the sides of those welles cause vigilant and skilfull men to watch and harken continually at the saide holes or in the bottome of the saide welles whether or no the enemies doe vndermine towards you But if this way shall not like you take a drumme and set one ende of it flatte vppon a very plaine peece of ground neare vnto the head of one of the saide welles and then vppon the vpper ende or head of the drumme lay fiue or sixe haukes belles or such belles as are commonly set in collars for little dogges or for wante of such belles a conuenient number of drie beanes which will make a sounde at euery stroke geuen in the myne with any mattocke or pickaxe if the enemies doe vndermine within fourty or fifty paces of the saide drumme and that sound will be by so much more audible by how much more nearer to the drūme the enemies Pioners doe come Also you may
through the said channell D E that 1 the mark at your first standing doth lie right between you and the thing to which you measure Now without moouing of your Semicircle looke agayne through the said channel F G at some other thing lying sidewise in a right angle from 3 the mark of your 2 standing and goe in a right line towards the same thing last espied till the saide marke which hath here bin noted with the figure of 2 shall stand right betweene you and the thing to which you measure and there make a marke which in this example shal be the figure of 4. This done measure exactly the distāce betweene the marke 1 and the mark 2 cal it the first distance also measure exactly the distance betweene the marke 1 and the marke 3 call it the 2 distance Finally measure the distance between the mark 3 the mark 4 call it the 3 distance Now subtract the first distance from the third and reserue the remainder for your diuisor then multiplie the 3 distance by the second distance diuide the product by your reserued diuisor and so the quotient wil shew the true lēgth from the marke 3 vnto the ship tower or other thing to which you did measure At the figure of fiue there is a shippe lying at Rode in the Sea and from 6 7 8 and 9 a platfourme with ordinance vppon the lande I am required to measure vnto the said ship wherefore making my first standing at the place 1 I measure from thence vnto the place 2 which lyeth sidewise 200 yardes in a right angle from 1. Againe I measure from the saide place 1 vnto 3 the place of my seconde standing which lyeth 300 yardes in aright line with the said shippe behind my first standing Also I measure from the saide place marked with the figure of 3 vnto the place 4 lying 240 yardes sidewise in a right angle from 3 and scituated so as the said place 2 doth lie in a right line betweene it and the said ship then subducing 200 from 240 I keepe the remainder which is 40 for my diuisor and after this I multiplie 300 by 240 whereof commeth 72000 which diuided by 40 my said reserued diuisor yeeldeth in the quotient 1800 yardes for the longitude betweene 3 the place of my second standing and the said shippe The 118 Chapter How you may measure a short distance as the breadth of a towne ditch or narrow riuer without any Geometricall Instrument or arithmeticall knowledge STanding right vp with your bodie and necke vppon the side of a towne ditch or narrow riuer put your feete close together and behold with one eie a grasse leafe stone or other marke in the opposite side of the same ditch or riuer and in so doing pull down your hat or cap ouer your eie till you may see no other thing beyond the marke so espied After this keeping still your body and necke vpright your feete ioyned together and your one eie fast shut turne your selfe towards the plainest peece of ground that is about you and marke well that part of ground which you shall espie vnder your hat or cap most farthest from your station for the distance betweene the middest of your feete and the said farthest part of ground is equall to the breadth of the said riuer The 119 Chapter How you may at one station measure vppon an heigth with a Geometricall square a longitude vppon plaine SEt your Geometricall square very vpright vppon his side or ende X Y ouer the plaine where you will measure an vnknowne longitude This done mooue the Index of your said square vp or downe till you may espie through his sights the farthest ende of the desired longitude Then note diligently the partes of the square cut with the fiduciall line of the Index And if the partes so cut be in the contrary shadow multiplie the whole number of partes in one side of the square by the number of feet or yards which are in the heigth betweene the center of your Instrument and that part of the plaine which lieth directly vnder the same center and diuide the product thereof by the partes cut in the side of your square and note the quotient for the true measure of the desired longitude When the partes so cut shall be in the right shadow multiplie the partes so cut in the heigth between the center of your Instrument that part of the plaine which lieth directly vnder the same center and hauing diuided the product thereof by the whole number of partes in one side of the square note the quotient for the true measure of the desired longitude But if the fiducial line of the said Index shall lie directly betweene the right shadow and the contrary shadowe when you espie through the said sights the farthest end of the desired longltude then the heigth betweene the center of your Instrument and the part of the plaine which lyeth vnder the same center is equall to the desired longitude Example Admit that B C is an vnkowne longitude between a ship a gallie tying at Rode in the Sea that to measure the same longitude I haue set my Geometricall square plumbe vpright vppon his side or end X Y in A the maine top of the ship directlie ouer B one ende of the said longitude and that when I saw through the sights vppon the Index the gallie at C the farthest end of the desired longitude the fiduciall line of the saide Index did cut fortie partes of contrary shadowe and that the center of my square is tenne yardes aboue the said B therefore I multiplie 1200 the whole number of partes in one side of the square by tenne the measure of the heigth betweene the center of my square and B and the product thereof being 12000 I diuide by fortie the partes cut in contrary shadowe and so the quotient yeeldeth three hundred for the number of yardes in the measure of the saide longitude This one example geueth light to the ingenious Reader to worke in mensurations of longitudes when the fiduciall line of the index shall cut partes in the right shadowe of the square and also when the same fiduciall line shall lie vppon the square directly betweene the right shadowe and the contrary shadowe wherefore I doe omit to set downe here more examples in so plaine a matter The 120 Chapter How you may measure with a Geometricall square at two stations any longitude in sight TO measure at two stations an vnknowne longitude which here shal be supposed to be A B lay your Geometricall square flat and leuell vppon a stoole or vppon a foote made of purpose to holde it vp Then setting the fiduciall edge of his Index vppon the line H I which passeth directly from H to the beginning of the equal parts marked vpon X Y a side of the square turne the square vpō the stoole or foote his Index remaining stedfast vpō the said line H I
till you may espie through the sights vppon the saide Index B the farthest ende of the said vnknowne longitude This done the square remaining vnmooueable turne the fiduciall edge of his Index to the line V Z which passeth directly from V to the beginning of the equall partes marked vppon Y Z an other side of the said square then looking againe through the said sights note some mark a good space from you the farther this mark is froÌ„ you the better it is for your purpose then pitchinge vp a staffe right vnder the center of your square in A conueye your square vnto the saide marke which heere I will call C and recon to be 40 yardes from A now the square being layde againe flat and leuell vppon a stoole or vppon a foote right ouer C as it was before at A put the fiduciall edge of the Index vppon the saide line H I and turne the square vppon the stoole the Index remayning vnmouable vppon the saide line H I till you may see through the sights vppon the same Index the staffe in A. After this the square remayning vnmouable turne the saide Index to and fro till you may see through his sights B the extreame parte of the desired longitude and note diligently what parte of contrary shadowe is then touched with the fiduciall edge of the Index for if you will multiplie the whole number of partes in one side of the square by the number of yards betweene A and C your two stations and diuide the product thereof by the parte of contrarie shadowe touched with the fiduciall edge of the saide Index the quotient will shewe you the true measure of the saide longitude Example Admitte that at C your seconde station the fiduciall edge of the Index did touche the 100 parte of contrary shadowe and that you did then see through the sightes vppon the same Index B the extreame parte of the desired longitude Then multiplie 1200 the whole number of partes in one side of the square by 40 the number of yardes betweene A and C your two stations and diuide the product thereof which is 48000 by 100 the parte of contrary shadowe touched with the fiduciall edge of the Index at C your seconde station and so the quotient will yeelde 480 yardes for the desired measure of the sayde longitude A B. The 121 Chapter How you may measure with a Geometricall Square any distance or breadth lying in a plaine leuel grounde with your eye or station how so euer the same breadth or distance is scituated BEing required to tell the distance or breadth betweene two Towers which for example may here be named Q and R measure first how farre either Tower is from you which you may doe by sundrie wayes before taught and then laying your Geometricall Square flatte and leuell vppon a stoole or vppon a foote made of purpose to beare it vp turne the Square about till you haue set H I a line vppon one side of the saide Square right against Q the Tower next vnto you For if R the other Tower were nearer to you than the Tower Q you shoulde first lay the line H K right against the same Tower R. This done the Square not being remooued turne the Index to and fro till you may see through his sightes the saide Tower R which in this example as before I haue tolde you is the fardest Tower from you Then opening your compasse to so many equall partes in the side of the Square as there are yards betweene the center of the Square the tower Q. which I will here suppose to be an hundred yardes set one foote of your compasse in the center of your Square and with the other foote of your compasse make a fine visible mark at M vppon the line H I and when you haue so done open your compasse againe to so many partes in the side of the Square as there are yardes betweene the center of your Instrument and the saide Tower R which I will likewise suppose to be an hundred and fiftie yardes and putting one foote of your compasse in the saide center make an other fine visible marke vppon the face of the Square with the other foote of your compasse at N close by the fiduciall edge of the saide Index which ought now to lie in that place where it stoode when you did last see through his sightes the sayde Tower R. Moreouer open your compasse to the space betweene those two markes M and N and lay your compasse so opened vppon the partes in the side of your Square and so you shall perceaue how many yardes are betweene the Tower Q and the Tower R. For looke how many equall partes are beetweene the two feete of your compasse so many yardes are beetweene the Tower Q and the Tower R and therefore if sixty one partes shall bee betweene the two feete of your compasse you may boldly affyrme that the distance or breadth betweene the Tower Q and the Towre R doth containe sixty and one yardes â—…derstande â—…teous reaâ—… that M â—…ght to stand 〈◊〉 this picture 〈◊〉 the ende of 〈◊〉 line which â—…tendeth 〈◊〉 the side 〈◊〉 the square 〈◊〉 the fiducial â—…ge of the â—…ex and N â—…ght to stand 〈◊〉 that end of 〈◊〉 sayde line â—…ch adioyâ—…th to the fiduciall edge of the index H ought to stand at the center of the square and I ought to stand at the lowest â—…de of the square where the equall partes begin and that betweene H M are 100 equall partes betweene M N 61 â—…uall partes and betweene H N 150 equall partes The 122 Chapter How you standing vppon the toppe of a hill or drie ditch may measure with a Geometricall Square the deepenesse of the same hill or ditch and the breadth of any drie ditch or valley TO measure the deepenesse and breadth of M N O a ditch or valley measure first his breadth MN as you may doe by sundrie wayes before taught which breadth shall here be supposed to be eighteene yardes Likewise measure by the precepts before geuen the length or depth of M O which here shall be supposed to be fifteene yardes this done square 15 the measure of the depth M O and the product thereof will bee 225. Likewise square 9 which is ½ of the measure of the breadth M N and the product thereof will be 81. Then subduce the square 81 from the saide square 225 and out of the remainder which is 144 extract the Square root which being 12 sheweth the number of yardes that are in P O the depth of the ditch or valley Also in this manner if you stande vppon the toppe of a hill you may measure the heigth of the same hill The 123 Chapter How you may drawe a platte of any peece of grounde which shall containe the true proportion and Symetrie thereof in such sorte that you may tel how farre any place in the platte is distante from other TO drawe a platte of
hole in the center of the protractor I doe turne the protractor to and fro keeping his center ouer the prick last made till I haue set it in euery respect as it did lie before vpon the prick of my first station and hauing made a pointe with a cole in the edge of the protractor at euery degree and parte of a degree noted in the table of my second station I put the protractor aside and drawe straight lines from the prick made for the place of my second station vnto euery of those pointes noting well the crossing of like lines That is to say where the line of the Beacon drawne from the pricke of my first station meeteth with the line of the Beacon drawne from the prick of my second station and where the line of the Tower drawen from the prick of my first station meeteth with the line of the Tower drawen from the prick of my second station and so of the rest for other intersections or crossinges in this woorke are not to be regarded Also to know how farre euery place in this plat is from other I diuide the space before the prick of my first station and the prick of my seconde station into so many equall parts as there are yardes which for example I here suppose to be 200 then drawing straight lines from euery one of these noted places vnto other and opening my compasse to one of the said equall partes I measure how many times it is contayned in euery of the sayde lines and say that the number of yardes in the length of them is as this Table following doth shewe A Table shewing the distance of euery place from the two stations and also the distance of euery place from other and therein this is to be noted that 1 signifieth the first station 2 the seconde station 3 the Beacon 4 the Towre 5 the house 6 the Church and 7 the Windemill FRom 1 to 2 200 yardes From 1 to 3 193 yardes and ¼ of a yarde From 1 to 4 350 yardes From 1 to 5 375 yardes From 1 to 6 425 yardes From 1 to 7 395 yardes and ◠of a yarde From 2 to 3 300 yardes From 2 to 4 391 yardes and ⅔ of a yarde From 2 to 5 362 yardes and ½ of a yarde From 2 to 6 358 yardes and ⅓ of a yarde From 2 to 7 283 yardes and ◠of a yarde From 3 to 4 166 yardes and ⅔ of a yarde From 3 to 5 218 yardes and 2 11 of a yarde From 3 to 6 316 yardes and ◠of a yarde From 3 to 7 340 yardes From 4 to 5 88 yardes and ◠of a yarde From 4 to 6 208 yardes and ◠of a yarde From 4 to 7 275 yardes From 5 to 6 120 yardes From 5 to 7 195 yardes and ⅚ of a yarde From 6 to 7 107 yardes and ¾ of a yarde In this manner by changing my stations I may make diuers plattes expressing the true proportion and distances of Cities Townes Hauens Castles Fortes Campes Mynes Hilles and all other notable places within a whole Region Laus Deo Gutta cauat lapidem non vi sed sape cadendo Sic homo fit sapiens non vi sed saepe legendo The ende of Lucar Appendix AT LONDON Printed by Thomas Dawson for Iohn Harrison the elder at the Signe of the Greyhounde in Paules Churchyarde And are there to be solde 1588. IN SPE Amendements of faults made in printing the three bookes of Colloquies Faultes Page Line Amendmentes BOdie mouing 12 43. and 44. bodie violently mouing 6160 28 50 6146 be loer 53 22 be more loer which conteine 33 64 50 which conteins 33 here and ende 70 44 here an ende is in our 74 9 is now in our Amendments of faults made in printing Lucar Appendix Faultes Page Line Amendments IN some other 10 18 into some other and doe it vnto 10 26 and doe vnto it that time 10 52 the time into the flowre 11 11 into flowre in a Cauldron 11 12 in the cauldron and vineger 14 10 or vineger or after 14 11 and after full of round 15 3 full of litle round their tinder 21 1 the tinder being well wette 21 21 being wett a whole foote 41 23 whole of a foote The 65 Chapter 57 14 the 68. Chapter said pellets 59 45 said pellet next mixture 66 37 mixture next and put 70 23 put peece and close 70 24 peece next and close by it 73 17 by them bloe the forts 93 4 bloe vp the forts before 119 21 betweene