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
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
declared in the precedent Colloquie I will heere saye vnto him that is desirous to learne that this action may be performed with smooth yron wedges which I would haue so made as euery of them should be a foote in length and at one end thinne like an edge of a knife and at the other end an inch thicke For when one of these wedges shall bee thrust into a peece charged with powder and pellet and the thin end of the wedge put in vnder the pellet it must needes bee a let to the moouing of the pellet and make the pellet sticking fast within the peece by reason it cannot by any meanes passe ouer the thicke end of the wedge to breake the peece although it was charged with no more powder than his ordinary charge Also if you will charge any greate peece of Artillerie with a full charge of suche gunpowder as I doe teache you to make in the 16. chapter of mine Appendix and haue marked their with the number of 13 you shall breake the peece Also you may breake any great peeece of Artillerie in what part thereof you will after this manner Lay the Peece in a furnace vpon yron wedges or vpon stones of ½ foote in height and make a good fire of coales vnder and rounde about that part of the peece where it shall be broken Then bloe the fire with a paire of belloes till you haue made the peece very hotte and after you haue so done take the peece out of the fire and with an yron hammer strike hard vpon the hot part of the peece and by so doing you shall breake the same peece in that verie place Likewise you maie breake any great peece of Artillerie thus Make in the ground a ditch somewhat longer than the peece which shall be broken and in the bottome of this ditch cut a trenche so long as that parte of the peece which shal be made hot Fill this trench with coales and laie the peece which shall be broken vpon yron wedges or stones of halfe a foote in height in the ditch so as the peece in that part which shall be made hot and broken may lie directly ouer the said trench then hauing couered the Peece in that part which shal be made hot and broken all ouer with coles made a wall of stones or some other thing round about it I meane the Peece so as men may worke vpon it put fire to the said coles and with belloes bloe the fire till you haue made the Peece very hot this done lift the Peece vp out of the ditch and with an yron hamer strike hard vppon the hot part of the Peece tyll you haue broken it there which you shall quickly doe The 23 Colloquie How it may be knowne whether a Peece which was neuer discharged or shot in will shoote right vppon a marke or wide or a scue from the marke vnto which the leuel shal be giuen And how if a Peece of Artillerie be more thicker vppon the one side than vppon the other the concauitie of the peece is not right in the middest of the mettall And how if a peece be more thicker vpon the one side than vpon the other the same peece will not shoote his pellets foorth right but alwayes awry towardes the thicker side of the mettall And how you may know the thinnesse and thicknesse of the mettall in any part of the concauitie in the peece Interlocutors Gunfounder Nicholas Tartaglia GVnfounder Is it possible that I may perceiue whether a Peece which is newly laid vpon his carriage was neuer shot in wil shoote right wide or ascue Nich. Your question in substance is no more than this that you would knowe whether the concauitie of that Peece doth lie right in the midst of the mettall or no if it doe not lie in the midst of the mettall that you would vnderstande how or towards what part of the Peece that concauitie doth goe which as I thinke may without any difficultie be done For I consider that this is a thing which by diuers wayes may be searched out and knowne But to shewe you a way by which it may speedilie and easily be done you must geue me some respite to think thereon Gunfounder Thinke a while of it for I haue asked this doubt of many which by their profession are Engenars and haue not found any of them able to resolue mee therein Nicho. Then I measure or cause some other to measure aduisedlie the distance betweene the point A the ende of the staffe or ruler Note and the mettall of that Peece in the same place and suppose that the sayd distance is precisely so much as is the short line E. Then I doe remoue those staues or rulers to an other place or side of the Peece and for your better vnderstanding hereof I doe remoue them to the opposite part of that Peece as it doth appeare by the other figure and in that place I measure or cause some other to measure the distance that is betweene the saide point A the ende of the staffe and the mettall of the Peece the which I will suppose to be as much as the length of the line F. Nowe I say if the line F be equall to the line E the mettall of that Peece is of equall thicknesse as well in the vppermost part as in the loermost part of that Peece But because in this case I doe sensibly finde the line F to be longer than the line E therefore I conclude that the mettall of the Peece is more thicker aboue than it is beloe and that it is so much more thicker as the line F is longer than the line E. After this sort and maner I must proceede to the right side and to the left side and to all the other partes or sides rounde about the Peece noting alwaies the distances by lines for by those lines Note I shall know exactly the thicknesse and thinnesse of the mettall round◠about the concauitie of that Peece and by the reasons before alledged I shall also know◠towardes what way or side the said Peece wil shoote his pellets which is the thing that wa◠proposed Gunfounder You haue tolde me of a good and speedie way which pleaseth me well The 4 Corollarie ALthough the concauitie in a Peece of Artillerie doth lie right in the middest of the mettall of that Peece yet may the said concauitie be taper bored wherefore to know whether or no a Peece of Artillery is taper bored you must prepare a Rammer head equall in height and compasse to the concauitie in the Peece and that being done thrust the said Rammer head into the said concauitie for if it will not go downe vnto the touchhole the Peece is taper bored in that very place where the Rammer head stickes To know how much the Peece is taper bored make the like proofe with a Rammer head of a lesse height compasse than the first was by
any great peece of Artillerie leuell to mount all manner of great peeces vnto any eleuation to imbase the mouth of any peece for to shoote at markes in vallies The vse of a gunners Semicircle to measure heigthes depths and distances to leuell all maner of groundes and to doe all such things as may be done by a Gunners Quadrant Moreouer for mensuration of Altitudes Latitudes profundities according to the Rules following The vse of a Geometricall square I doe exhort you to prepare a Geometricall square of a conuenient biggenesse and to make it of mettall or of Cypresse like in euery respect vnto his Type heere placed Sauing that I woulde haue you to diuide the Quadrant in your Geometricall square into ninetie equall partes called degrees and euery side of your said square into 1200 equall partes and the Index of your Square into 1697 and 191 â—394 of like equall parts which in this side of Paper for want of roome I could not doe The 112 Chapter To take the heigth of the Sunne with a Quadrant drawne within your Geometricall square SET your Geometricall square plumbe vpright vppon his side or ende V X and sette his side Y X right against or towardes the Sunne This doâ—e rayse vppe and downe the Index of the square vntill the Sunne shall shine duely through his two sight holes and then looke what degree in the edge of the Quadrant is touched with the fiduciall line of the sayde Index for the degree to touched doth shew exactly the degrees of the Sunnes heigth at that present time The 113 Chapter How you may measure at one station in a Sunne shining day with your Geometricall square and also with an Haulbert or any other staffe perpendiculerly erected the altitude of any Tower or other thing whose shadow length is knowne SET your Geometricall square vpright vppon his side or end V X and with the Quadrant drawne vppon the said square take the heigth of the Sun as you haue been taught in the last Chapter This done when the Sunne is 45 degrees in heigth the fiduciall line of the index wil lie directly betweene the right and contrary shadowe I meane vppon the line V Y and then the shadowes of all things perpendicularly eleuated are equall to their bodies Wherefore after you haue measured the length of the shadowe which a Tower doth giue you may note that measure for the altitude of the same Tower If the Sunne be aboue fortie fiue degrees in heigth the Index will fall vppon the right shadow of the square and forasmuch as then the shadowes of all bodies perpendicularlie erected are shorter than their bodies you must now multiplie all the partes in one side of the square in the measure of the shadowe which the Tower to bee measured doth giue and diuide the product thereof by the part of right shadowe touched with the fiduciall line of the Index and take the quotient number for the heigth of the said Tower But if the Altitude of the Sunne bee lesse than fortie fiue degrees the said Index will fall vppon the contrary shadowe of the square and seeing that then the shadowes of all bodies perpendicularly erected are longer than their bodies you shall multiplie the part of contrary shadowe touched with the fiduciall line of the Index in the length of the shadowe which the Tower to bee measured doth make and hauing diuided the product thereof by all the partes in one side of the square take the quotient number for the altitude of the said Tower How by the knowen length of a shadow which a Halberte or staffe perpendiculary erected doth giue in a Sunne shining day you may know the heigth of any Tower or other thing which giueth at the same time a shadow that may be measured IN a Sunne shining day pitch vpright a Halberte of a knowne length by the Tower or other thing whose Altitude you woulde knowe This done measure the length of the Halberts shadowe and also the length of the shadow which the said Tower doth giue For as the altitude of the erected Halbert is in proportion to his shadowe so the desired altitude of the Tower is in proportion to his shadowe Therefore multiply the length of the Halbert in the length of the shadow which the Tower giueth diuide the product thereof by the length of the shadow which the Halbert doth giue and take the quotient number for the Altitude of the said Tower Example The Tower to be measured giueth a shadowe of 125 feete in length the erected Halbert of eight feete in length doth make a shadow of twelue feete in length therefore multiplie eight in 125 and the product therof will be 1000 which diuided by twelue yeeldeth in the quotient 83 foote and foure ynches for the altitude of the said Tower Shadow Altitude 12 8 125 83 and â— The 114 Chapter How you may measure with your Geometricall square at one station any approchable altitutde also how you may with Arithmeticall skill measure the Hipothenusall distance betweene your said station and the top of the said altitude SET your Geometricall square plumbe vpright vppon his side or ende V Z. This done mooue the Index of the square vp and downe till you may see through his two sightes the top of the altitude to be measured then noting well what equall part in the side of the square is touched with the fiduciall line of the said Index looke whether the saide part is in the side of right shadow or in the side of contrary shadowe For if the said equall part be in the side of right shadowe which happeneth when the space betweene the base of the altitude to be measured and your standing is shorter than the said altitude you must multiplie the measure of the space betweene your standing and the base of the said altitude in all the partes that are in one side of the square and diuide the product by the equal part touched with the fiduciall line of the Index in the side of right shadowe and then adding the heigth of the center of your square aboue the base of the thing to be measured vnto the quotient thereof take the totall summe of that addition for the measure of the said approchable altitude Example S T is a Tower whose altitude I will measure R T is the space betweene the approchable base of the said tower my standing which space is 40 feete Q or V the heigth of the center of my square aboue the said base is 5 feet V Z X Y is the square set plumbe vpright vpoÌ„ his side V Z and V P is the fiduciall line of the Index which pointing directlie from mine eie at the center of the square to the top of the saide Tower toucheth the 800 parte in the right shadow therefore I multiple 40 feete the space betweene R and T in 1200 the whole number of partes in the whole side of the square and thereof commeth 48000
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
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
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
making diuers proues after this sort you shal know how much the Peece in euery place of his concauitie is taper bored Such a Peece as is so taper bored that his concauitie is wyder at the mouth than at the touchhole is to be misliked because the Gunner may put into it a pellet which though it shall seeme to be a fit pellet will sticke fast in the Peece and by reason it will not go downe vnto the powder breake the Peece if it be not shot out in such or like sort as in the 27 chapter of mine Appendix you are taught to doe the same Also such a Peece is to be misliked because the pellet that shall goe downe to the powder is so small that it will swarue in the deliuerance randge a lesse ground than it would haue done if it had bin fit for the mouth of the Peece But such Peeces as are not taper bored from their mouthes downewards towards their touchholes till within a foote or a foote and a halfe of their touchholes are not as some say to bee misliked because such Peeces are thereby more stronger and by that meanes their pellets will goe more closer vnto the powder yet this can not be denied that the ladles for such peeces must bee rounder bent and that as the spunge which is fit for the mouth of one such Peece will not goe within his concauitie downe to the touchhole or bottome so the spunge which is fit for one such Peece at the bottome will be too loe for the rest of his concauitie The 24 Colloquie The cause and reason why the mouth of a hot Peece of Artillerie falling into a sandie grounde did drawe a great quantitie of the said sand into the concauitie of that Peece Interlocutors Gunfounder Nicholas Tartaglia GVnfounder I will aske an other question of you which is this one time as I prooued certaine Peeces at Lio At Lio which is a place with in a mile of Venice there is a Hauen vnto which yeerely on the Ascention day as William Thomas in his booke intituled The History of Italy saith the Duke of Venice with the Senate in their best aray vse to goe for to throw a ring into the water thereby to take the Sea as their Espowse it chaunced after I had charged and discharged one Peece manie times together that the mouth of the same Peece fell into a very sandie grounde and that so soone as the mouth of the sayde Peece was within the said ground a great quantitie of the same sand was drawne into the concauitie of that Peece nowe I aske of you the cause of that effect Nicho. A Gunner did once aske me the like question as it wil appeare in the 21 Colloquie of this booke for as your Peece drew into the concauitie thereof a great deale of sande so his Peece drew into the concauitie of the same a little dogge Therefore I will answere your question as I did answer his that is to say a Peece which is discharged oftentimes together must needes waxe hot and so soone as it waxeth warme it is made thereby somwhat attractiue euen as a cupping or boxing glasse and by so much it is made more attractiue as it is made more hot Therefore it is no maruaile that your said Peece drew sande into his concauitie Gunfounder I doe like well of this your answere The 25 Colloquie How that leuell sight which is well placed vpon a handgunne to shoote at a marke lying leuell with the mouth of the same Gunne and in a conuenient distance from the said Gunne will not serue well to shoote at a marke set on a height in a like conuenient distance from the said Gun And how he which will shoote in such a Gunne that hath such a leuell sight at a marke lying leuell with his Gunne and in a conuenient distance from his standing ought to take his leuell at the middle of that marke And also how hee which will shoote in such a Gunne that hath such a leuell sight at a marke set on a height in a like conuenient distance from his standing ought to take his leuell at the loest part of that marke Interlocutors Schioppetiero This worde Schioppetiero doth here and in all other places of this booke signify him that doth vse to shoote in an Harchibuse Caliuer or any other Handgunne Nicholas Tartaglia SChioppetiero I haue a Handgunne with a leuell sight so well placed that if I doe shoote in the said Peece at a marke lying leuell with the mouth of the same and in a conuenient distance from my Peece most commonly the pellet will strike in the middle of that marke although the said marke be a very small thing Now I aske of you whether or no that leuel sight being so well placed will serue mee to shoote at a marke or some other little thing espied on a height in a like conuenient distance Nich. It is a manifest thing that the said leuell sight will not serue you so well to shoote at a marke espied on a height in a like conuenient distance Schioppetiero Wherefore Nicho. Because if you shoote at a marke lying leuell in a conuenient distance most cōmonly your pellet strikes in the middle of the marke and of necessitie at the end of that distance and in that place your visuall line doth touch or cut the line or way in which the pellet must goe And because in shooting at markes espied on a height the pellet doth goe much more by a right line or by a lesse croked line than the pellet which is shot at a marke lying leuell with the Peece as hath bin sayd before in the second Colloquie therefore by how much the pellet shot at a marke on a height doth go more righter than the pellet which is shot at a mark lying leuel by so much doth that way of the pellet come more nearer or sooner to meete and cut your said visuall line than the way of the pellet which is shot at a marke lying leuell Then making that intersection more nearer by shooting at a marke on a height the thing at which you shoote will be beyond that intersection and so the said thing or marke being at the sayde first distance beyond that intersection it is impossible by reason of your said leuel sight that the pellet shall in that case strike in the middest of the marke Schioppetiero I do not well vnderstand your reasons neither will I trouble you to make me vnderstand them for I thinke you should haue much a doe with me to make me perceiue them But do you conclude that if I shoote at a marke espied on a height at the same first distance that the pellet will strike aboue that marke or vnder that marke Nicho. I conclude that there the pellet will strike aboue the marke for alwayes when the visual line doth cut the way of the pellet and that the marke or thing at which you shoote is
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
gunpowder which in this our age doth commoÌ„ly charge euery cannon periero is more stronger than the gunpowder which did charge in time past the Cannoni perieri of the old making Morter pâ—… 13 The thicknesse of mettall at the breech of euery motter peece ought to be so much as the Diameter in the mouth of his chamber the thicknesse of mettall at the trunnions in euery morter peece ought to be so much as the semidiameter of the mouth in the chamber and the thicknesse of mettall at the necke of euery morter peece ought to be â— part of the Diameter in the mouth of the chamber 14 The Diameter at the mouth of the chamber in euery morter peece ought to bee equall to the semidiameter in the mouth of the morter peece the length of euery chamber in a morter peece ought to be so much as once and a halfe the Diameter of the chamber The vse 〈◊〉 morter pâ—… Note 15 Morter peeces are commonly vsed in the night time to shoot pellets of stone baules of wildefire cases filled full of stones pellets of lead or square peeces of yron Note And when an expert gunner will shoote in a morter peece he putteth no wadde vppon the powder in the peece nor giueth fire to the same peece in any other place than at his mouth with a gunmatch The 40 Chapter To measure the thicknesse of mettall in any part of a peece of artillerie MEasure first with a paire of calleper coÌ„passes or with an ynch rule the whole thicknes of the peece Likewise measure with a paire of other coÌ„passes I mean straight coÌ„passes or with an ynch rule the Diameter or which is all one the heigth of the concauitie in the Peece then subtracting the heigth of the said concauitie froÌ„ the whole thicknesse of the Peece in that part which was so measured take half of the remainder for the thicknes of the mettal in that measured part of the peece Or for lacke of a payre of calleper compasses put a girdle or string that will not stretch round about the outside of the Peece in that part which is to be measured measure exactly so much of that girdle or string as went about the peece this done multiplie that measure by seuen and deuide the product by 22 and so the quotient wil giue you the true measure of the whole thicknesse of the Peece in that part which was measured the rest of this worke you must doe as you did when you measured the whole thicknesse of the Peece with a paire of Calleper compasses The 41 Chapter How euery great peece of Artillerie hath trunnions for three causes and how Gunfounders may learne to set the trunnions of euery great peece in their due places EVery great Peece of artillerie hath trunnions for thre causes of which the first is to hold vp the Peece vppon his carriage the second is to make a Peece when it resteth vppon them in his carriage to moue easilie vp and downe and at the will of the Gunner to lie sometimes leuell and sometimes mounted And the thirde cause is that they set in their due places and well laid vppon a fit carriage wil make their Peece in his discharge to lie fast and steadie without any mouing forwardes or backwards downeward or towardes any side wherein the whole inportance of the shoote doth rest When the trunnions of a Peece are set to high that is to say more nearer to the mouth of their Peece thaÌ„ they should be then the Peece in which the trunnions are so set will be so heauie at his taile as that the Gunner shall not without great paine and strength lift it vp And when the trunnions of a peece shall be set too loe that is to say more nearer to the touchhole than they should be then the mouth of their Peece by meanes of the vnequall and great waight which is between the said mouth and the said trunnions will in his discharge fall downe towards the ground wherefore I will not wrap vp here in silence the rules by which gunfounders may alwaies set the trunnions of euery great Peece in their due places Diuide the length of the Peece into seuen equall partes and in the third part measured from the touchhole towards the mouth of the Peece set the trunnions so as â…” partes of the circumference of the Peece in that place where the trunnions shall be set may bee seene aboue vppon the Peece betweene the two trunnions Also a Gunfounder skilfull in the arte of numbring may by the helpe of the golden rule set the trunnions of euery great Peece in their due places after this maner hee may multiplie the length of the Peece in which the trunnions shall be set by three and hauing diuided the product thereof by seuen note the quotient number for the measure of the space between the loest end of the peece his concauitie and the place where the trunnions must be set As for example if a Gunfounder would know in what part of a peece which is 144 ynches in length the trunnions of the same Peece should be set he must multiplie 144 the length of the Peece by three whereof will come 432 which diuided by seuen yeeldeth in the quotient 61 ynches and 5 7 of an ynch for the space betweene the loest end of that peece his concauitie and the place where the trunnions of the same Peece ought to stand The 42 Chapter How great peeces of artillerie may be cast of lead how the thicknesse of a leaden peece round about the concauitie so farre as the due charge of gunpowder for the same peece will reach ought to be once a halfe so much as the height of a pellet that is fit for the same peece how the thicknesse of a leaden peece at his necke round about the concauitie ought to be â…” partes of the heigth of the said pellet how any one peece of what weight soeuer it is may be drawne by the strength of many men from one place to another And how olde rustie yron serueth to make gunne pellets better than nwe yron VVHen a citie or towne shall be besieged that hath in it no yron or brasse peeces of artillerie for offensiue and defensiue seruice then the inhabitants of that Cittie or Towne may in time of need cause great peeces of artillery to be cast of lead whereof there is no lacke within any Cittie or Towne of England for such peeces of lead wil beare well the ordinary charge of powder and pellet if from the touchhole so farre as the due charge of gunpowder for the same peece will reach the thicknesse of the mettall round about the concauitie of the peece bee once and a halfe the heigth of his pellet and that the thicknesse of the mettall round about the concauitie at the necke of the peece bee â…” partes of the heigth of the said pellet An Admonition But these peeces being made very hot with
of your Peece within poynte blanke doe looke vppon that marke by the sayde two vppermost partes of mettall put vnder the tayle of your peece two of the sayde wedges of the thicker sorte and by so dooing you shall make a perfect shoote at the sayde marke Also as the sayde Luigi Collado writeth if your peece lying leuell dooth shoote vnder the marke and afterwardes the vppermost parte of mettall ouer his mouth being layde in an equall heigth with the vppermost parte of mettall at his tayle doth shoote somuch aboue the marke as before it did shoote vnder you may at the thirde and next shoote cause your sayde peece to strike in the sayd marke if you will for this thirde shoote lay againe the vppermost parte of mettall ouer his mouth in an equall heigth with the vppermost parte of mettall at his tayle and put afterwardes one of his sayde wedges of the thinner sorte vnder his tayle The 64 Chapter How to make a perfect shoote at any companie of horsemen or footemen passing by the place where Ordinance doth lie vppon a leuell grounde and also how to make a perfect shoote at any shippe sayling in a riuer by the place where Ordinaunce doth lie vppon a leuell grounde and also how to make a perfect shoote at any moouing thing passing by a place where Ordinance doth lie vppon an vneuen ground WHen any horsemen or footemen shall passe by a place where a great peece of Artillerie doth lie the Gunner must charge that peece duely with good gunpowder and with a fit pellet to this ende that the same peece may goe off so soone as fire is put vnto it Also the Gunner in this case must lay his peece truely disparted vppon a leuell grounde right against some marke in their way as for example against some tree bushe hillocke cloude or if it may bee vppon some turning way because in such a place they can not depart verie quicklie from the marke and in fine when the said horsemen or footemen shall come neare vnto that marke or be in that turning way the Gunner must discharge his saide peece at them Likewise when a Gunner will shoote at a ship sayling in a Riuer hee ought to plant his peece against some cloude or other marke lying from him on the farther side of the water and giue fire vnto his peece when the forepart of the shippe shall beginne to be betweene the mouth of the peece and the marke But when the peece which shall be discharged at a mouing thing doth lie in his carriage vppon an vneuen ground the Gunner must measure by the helpe of a Quadrant or Semicircle how many ynches the ground vnder one wheele of the peece his carriage is more higher than the ground vnder the other wheele of the same carriage or for want of a Quadrant and Semicircle he must goe to that wheele of the Peece his carriage which standeth vppon the loer grounde and hanging a line and plummet downe to the grounde from the middle and highest parte of that wheele measure exactly the space betweene the said plummet and the middest of the loermost part of the same wheele for this measure sheweth in like maner how much the ground is more higher vnder one wheele than vnder the other wheele And when hee hath so done he must lay his said peece according to that measure wide from the marke towardes the more higher side of ground I meane if it bee found by the first or second way to measure the said difference of heigthes that the grounde vnder the wheele on the North side of the peece his carriage doth lie sixteene ynches aboue the ground that is vnder the wheele vppon the Southside of the same carriage the Gunner to make a perfect shoote at the moouing thing ought to lay the mouth of his saide peece sixeteene ynches wide towardes the North from the vnmooueable marke that must guide him to shoote at the moouing thing The 65 Chapter How much a peece must bee eleuated for to shoote vpwardes at a marke vppon a hill without point blanke and by what meanes the mouth of a peece may be laid right vppon any marke VVHen you will shoote vpwards at a marke which is scituated vppon a hill without poynt blanke you must first measure with your Quadrant or Semicircle the space which is betweene your peece and the marke afterwardes mount that peece at so many degrees as will cause it to shoote so much ground as is in the saide space then place your Quadrant or Semicircle close by the mouth of your peece and mooue it vp or downe till you shall espie through the sightes or channell of the Quadrant or Semicircle the said marke That done note the degree which was touched in this last action with the line and plummet of the Quadrant or Semicircle and mount the peece againe more higher by so many degrees than it was before I meane if you did mount the peece at foure degrees to shoote so much grounde as is betweene the peece and the marke and did note three degrees for the degrees which were touched with the line and plummet of the Quadrant or Semicircle then must you mount the peece againe at three degrees more and so the said peece will lie mounted in the whole summe at seuen degrees for to shoote vpwardes to the marke vppon the hill And by so doing if the peece be layd right vppon the marke you shall vndoubtedly strike the same But if your peece doe not lie right vppon the marke when it is discharged it will strike wide of the marke so many times the measure of the widenesse that it lyeth at when it is discharged as the length of the peece is contained in the distance betweene the peece and the marke As for example if a peece of eight foote long be planted one ynch wide from the marke lying eight hundred foote distant from the peece I conclude that the said peece planted one ynch wyde from the marke will strike at the end of that distance one hundred ynches wide from the said marke To lay your peece right vppon the marke doe thus hang a line and plummet right ouer the taile of the peece in the middle part thereof and winde the peece vntill you standing behinde the same peece shall see that the middle part of the mouth of the peece doth lie directly betweene the marke and the line hanging at the taile of the peece For when the middle part of the mouth of the peece doth lie directlie betweene the marke and the said line then doth the peece lie right vppon the marke The 66 Chapter How much a peece ought to bee imbased for to shoote at a marke lying in a valley without point blanke TO shoote downewardes at a marke lying in a valley without point blanke measure first with your Quadrant or Semicirle the space which is betweene your peece and the marke and afterwardes mount that peece at so many degrees as
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
expressed in the first chapter of this Appendix and obserue the same before you do shoote for by so doing there is no doubt but that the pellet shot out of the saide peece will strike the appointed marke in any night how darke so euer it is Also if this doctrine be obserued at euery time when you will shoote at a marke you may without faile strike the saide marke so often as you will with diuers peeces from sundrie places in any darke night But to the end you may see at all times before you shoote whether or no the line and plummet hanging vppon the Semicircle falleth vppon the degree noted in your memoriall wheather or no the middle part of the mouth of the peece doth lie right ouer the line of direction I counsell you to prepare a close boxe of boordes like a lantorne to carrie a lighted candle and to haue a dore in the side of the boxe to open when you will see with your candle and to shut when you will haue no light seene Example A peece of artillery beeing planted in the day time at B and mounted by a Semicircle 3 degrees did strike D a marke in the wall of a forte and when the said peece was discharged at the same marke the middle part of the mouth of the peece and the middle part of the taile of the peece did lie directly ouer B C the woodden or yron pinnes which stande in the line of direction therefore when you will shoote in the night time from B to D you must mount this peece three degrees and plumme the middle part of the mouth of the peece and the middle part of the taile of the peece right ouer B C the wodden or yron pinnes in the line of direction and so doing you can not faile in your purpose The 69 Chapter How you may carrie in the night time a lighted Gunmatch so as it shall not bee seene nor bee wet with raine HAng at your girdle as you doe the sheath of your knife a hollow cane of eight or tenne ynches in length and let the Cane be open at both endes then put the lighted ende of the gunmatch into the Cane and as the gunmatch within the Cane shall burne and consume so put the lighted end of the same gunmatch more farther or loer into the Cane and by this meanes the lighted end of the gunmatch being within the Cane can not bee seene in the night nor be wet with raine The 70 Chapter In what distance peeces of Artillerie ought to be planted for batterie In what order peeces of artillery ought to be mounted for batterie In what sort peeces of artillery ought to bee discharged for batterie and in what measure a breach with battery ought to be and in what maner a peece made hot with many shootes ought to be cooled TO batter a wall of a Towne or fort lay your Cannons if you can at the distance of 80 paces from the wall which shall be beaten downe and in no wise without constraint more farther from that wal than 150 paces for when Cannons doe lie 300 or 200 paces of from the wall which shal be battred they are planted as Luigui Collado writeth in an inconuenient distance vnmeete place to batter Also lay the mouthes of your Cannons so as they may strike a foot one aboue an other in the wal vnto ¼ of the heigth in the said wal discharging them altogether at one instant continue the batterie till you haue made a breach so bigge as at the least nine men in a rancke may enter into it After a peece with manie shootes is made very hot it changeth his colour shooteth weaklie and then to saue it from breaking you ought to coole it within with a spunge wet in cold water or in two parts of cold water one part of vineger or in lie mingled with a little water and lay all ouer the peece or at the least from the touchhole to the mouth sheepes skinnes with long wooll on thē dipped in the said cold water or in 2 parts of cold water 1 part of vineger or in lie and a little water which lie stoppeth the powres of the mettall in the peece and causeth it to resist heate The 71 Chapter How a Gunner may outshoote other Gunners in one and the same peece at one and the same eleuation with pellets of one waight of one kinde with an equall waight of one the same kind of gunpowder WRappe the pellet in linnen or woollen cloth so as it may goe very stiffe and close vnto the gunpowder in the peece and by so doing you shall make the sayde pellets to randge more grounde than a like pellet which is not so wrapped in cloth will doe Likewise when a Gunner shall shoote with an other Gunner in one and the same peece at one and the same eleuation with pellettes of one waight and of one kinde with an equall waight of one and the same kind of gunpowder and in all pointes with like aduantage hee that shooteth last shall out shoote him which did first shoote in the saide peece by the reasons alleaged in the 4 Colloquie of the first booke of N Tartaglia his Colloquies and in the seuenth Colloquie of the second booke of N Tartaglia his Colloquies Also if a gunner after he hath laded a peece with his due charge in gunpowder will make a hole with a staffe of a conuenient length and bignesse thorow the very middest of the same gunpowder and likewise after he hath duely charged his saide peece with 2 waddes of hay strawe toe or of vntwisted ropes and a fit pellet wil fill the touchhole of the same peece with good gunpowder and make an other hole with his proyning yron thorow the same touch gunpowder downe vnto the hole which was first made in the saide due charge of gunpowder within the peece doubtlesse he shall by so doing shoote more ground than an other Gunner ignorant of this skil can doe in the same peece at one and the same eleuation with a like pellet and an equall charge of one and the same sort of gunpowder The staffe which shall make a hole in the middest of the peece his charge in gunpowder ought for euery Fauconet Faucon Minion Saker Culuering French demie Cannon demie Cannon lower than ordinarie and demie Cannon to bee in compasse three or foure ynches or there aboutes and the staffe which shall make a hole in the middest of the peece his charge in gunpowder for euery ordinarie demie Cannon demie Cannon of the eldest sort French double Cannon ordinarie double Cannon and double Cannon of the eldest and biggest sort ought to be in compasse fiue ynches or thereabout The 72 Chapter How you may amend high loe and wide shootes To amend an high shoote VVHen a pellet shot at a marke within point blanke hath strooke somwhat aboue that marke lay your peece for 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
This number of two you must subtract from the other reserued quotient which was sixe and the remainder therof will be foure this remainder of foure must also be reserued Then measure the space betweene the first and seconde standing with what kinde of measure you wil and the number of that measure diuide by foure the remainder which you did last reserue and to the quotient thereof adde the heigth of your eie from the grounde and so you may conclude that the totall summe thereof is the altitude of the thing seene as for example suppose the space betweene your two standings to be 156 paces then diuide 156 by foure and thereof commeth thirtie nine to this thirtie nine adde the heigth of your eie from the grounde which you shall also suppose to be two paces and so the total summe being fortie one sheweth the heigth of A B. But to the end this kinde of mensuration may be the better vnderstood I will giue you an other example thereof which shall differ from the aforesayde example and in this example following I will suppose the side of the square to be diuided only into twelue partes Suppose againe that your first standing is in the place marked with C and that at the same standing the said line doth fall vppon the tenth parte of contrarie shadowe as it doth in the figure following and that at your second standing in the place marked with V the said line falleth vppon the eight part of contrary shadowe as likewise it appeareth to doe in the said figure and that the space betweene C and V containes 285 feete and that from your eye to the grounde that is to say from E to C or from X to V there are foure feete Now diuide twelue the whole number of partes of one side of the scale by 10 the part of contrarie shadowe touched with the said line at the first station and the quotient will be one and ⅕ the which you must reserue Then diuide againe the saide number of twelue by eight the part of contrary shadowe touched with the said line at the seconde station and the quotient will be one and ½ Out of this one and ½ subtract that one and ⅕ which was reserued and so there will remaine 3 20. By this 3 20 diuide 285 which is the number of feete in the distance betweene C and V and the quotient thereof will bee 950. To this 950 adde foure feete for the heigth of your eie from the ground or for the heigth of E aboue C or for the heigth of X aboue V and so the totall summe thereof being 954 feete is the true measure of the altitude A that is to say of the line betweene A and B which B is an inuisible point by imagination conceiued directly vnder the said A within the ground T. To make a demonstration hereof from your eye at the second station that is to say from X to your eye at the first station that is to say to E drawe the line X E and produce the same line in your imagination till it meete with the said line A B within the grounde T in the point F which is also an inuisible point conceiued by imagination to bee within the said ground and leuell with your eie I meane with X and E And because the triangle A E F is like vnto the triangle L P Q of the first station such proportion as the line or side A F hath vnto the line or side E F the same proportion hath the side P Q to the side Q L. Wherefor by the 13 and 21 definition of the seuenth booke of Euclide so many times as the said P Q is contained in the side Q L so many times the side A F is contained in the side E F. And because the side P Q containes ten partes of the one side of the scale and the side L Q containes twelue of those partes therefore the side L Q containes the side P Q once and ⅕ part thereof and so it followeth that the side E F containes the side A F once and ⅕ part thereof And now although you be ignorant of the altitude of A F of the distance betweene E and F yet you know that the said distance E F containes the heigth A F once and ⅕ part thereof Then reseruing this 1 and ⅕ go to your second standing where you shall finde the triangle X F A to be like vnto the triangle L P Q of the seconde standing and that so many times as the side P Q which is eight partes of the scale of contrarie shadowe is in the side L Q which is 12 the whole number of partes of one side of the scale so many times the heigth A F is contained in the distance X F and because the side P Q that is to say 8 parts is contained once and ½ in the side L Q that is to say in 12 partes therefore the heigth A F is likewise contained once and ½ in the distance X F. Therfore subtracting the distance E F from the distance X F that is to say 1 and ⅕ from 1 and ½ there will remaine 3 10 for the difference E X so as the said difference E X wil be 3 10 of the said heigth A F. And because the said difference E X is such as is the line V C by the 34 proposition of the first booke of Euclide and that the said line V C is supposed to containe 285 feete therefore it followeth that there are 285 feete in 3 10 of the heigth A F. By reason whereof the whole heigth of A F should be 950 feete as before hath been sayd Then ioyn 4 feete which is supposed to be the heigth of E C and of X V vnto the said number of 950 feete and so the totall summe thereof will be 954 feete which is the whole heigth of A B because the heigth of F B doth likewise containe 4 feete And therefore as the side P Q of the first standing is in proportion to the side or Hipothenusal line L P so is the heigth A F to the Hipothenusall distance A E. And because the side P Q is in proportion to the side or Hipothenusall line L P by the 47 proposition of the first booke of Euclide as 10 is to the nighest square roote of 244 which number of 244 is the summe that came by adding the square of 10 to the square of 12 therefore multiplie 950 feete by 15 and 19 30 which is the nighest square roote of 244 and diuide the product thereof by 10 and the quotient wil yeeld 1485 feete two ynches for the Hipothenusall distance A E. And forsomuch as the distance betweene E and F is so much as the heigth of A F and ⅕ parte more as before hath been prooued therefore take ⅕ of the heigth A F that is to say ⅕ parte of 950 feete which is 190 and adde the same summe of 190 to the
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
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
sight before be somewhat shorter than the leuell sight behind and that the shortnesse thereof bee so little as that it is not able to cause your visuall line to ioyn aloe with the way of the pellet yet in this case at euery remoouing of the mark the pellet wil hit vnder the mark and this notwithstanding the pellet at the second shoote may hit aboue that place and vnder that place and also in the very same place where the pellet did strike at the first shoote For if the marke at the first shoote be by chaunce set in the place where your visuall line passeth most nearest to the way of the pellet as hath been declared in the eight Colloquie and is afterwardes transported beyond that place without doubt the pellet will strike at the second shoote more vnder than it did at the first shoote The same followeth when the marke is set beyonde that place but when the marke is set at the first shoote within that place where your visuall line passeth most nearest to the way of the pellet that is to say more neare vnto you and is afterwardes remoued for the second shoote more nearer to that place the pellet will strike at the second shoote higher than it did at the first and yet that bloe will bee vnder the marke that is to say the pellet will strike betweene the first bloe and the marke But when the marke is remoued without that place where your visuall line passeth most nearest to the way of the pellet it may be remoued so little without that place as that the second bloe will be betweene the first bloe and the mark and it may be remoued so much without that place as that the second bloe will be vnder the first bloe and it may be so proportionally remoued without the saide place as that the second bloe will hit precisely in the place of the first bloe and all this will appeare very plainely to him that doth consider well of the figure in the eight Colloquie But when the leuell sight before hath his due and conuenient shortnesse in respect of that leuel sight which is behind the which thing happeneth very seldome times that is to say that the visuall line doth precisely touch and not cut the way of the pellet then if in such a case any Schioppetiero or Gunner shall shoote at any marke vppon a right line by meanes of the said two leuell sights and not through his owne fault shall strike with the pellet vnder the marke it may be by that which hath been spoken and declared in the ninth Colloquie that the said marke is both within and without the touch of those two lines for the marke being so within or without that touche the pellet alwayes strikes vnder the marke as may bee easily perceaued by the figure in the ninth Colloquie But when the first bloe is much vnder the marke it may bee adiudged that the marke is without the sayde touche for the marke being within the sayd touche the pellet can not hitte very loe by the reasons alleaged in the said ninth Colloquie And if the marke being without the sayde touche be set more without the same touche certainelie the second bloe will bee muche vnder the first bloe But when the marke being set within the said touch is remoued to a place more farther it may happen that the marke in the second place is within that touche and it may bee in the very touche and it may bee also without that touch If the marke then in the seconde place bee set within that touche the second bloe will bee aboue or higher than the first bloe and yet it will be vnder the marke that is to say it will bee betweene the marke and the first bloe But if by chaunce the marke in the seconde place bee set in the verie point of the touche the seconde bloe will bee preciselie in the middest of the marke But if the marke in the seconde place bee set without the sayd touche it may bee so much without the same as that the seconde bloe will bee loer than the first bloe and it may bee also so little without that touche as that the seconde bloe will bee higher than the first and yet it will bee vnder the marke that is to say betweene the marke and the first bloe And it may bee so proportionallie without as that the seconde bloe will strike precisely in that place where the first bloe strooke Schioppetiero Your reasons haue done me much good for I beginne now to vnderstand them and where I had thought to haue made an ende of my questions your argumentes haue brought new doubtes into my minde so that if I shall not be tedious vnto you I will desire you to resolue me in them Nicholas Proceede for by so doing you shall not be tedious vnto mee The 29. Colloquie The cause why a Schioppetiero or a Gunner when he standes neare vnto a marke lying leuell with his eie is more apt with euery sort of leuel sights to strike that marke or to make a faire shoote at the same than when he standes more farther from the said marke And how hee which will shoote at a little marke lying very neare vnto him ought to take his leuell at such a height as that the mouth of his Peece may couer the same marke Interlocutors Schioppetiero Nicholas Tartaglia SChioppetiero I perceiue by your arguments before alleaged that your opinion is if the leuell marke at which I shoote be not set in the point where my visuall line meetes with the way of the pellet that I cannot strike the said marke in the middest the which thing on the one part as I consider must needes bee true by naturall reason so on the other part my long experience causeth mee to thinke otherwise of the same But before I doe tell you in what part that agreeth not with my experience I will desire you to open this doubt vnto mee whence commeth it that euery Schioppetiero and euery Gunner generally the more nearer he standes vnto a marke lying leuell with his Peece the more apt hee is with euery sorte of leuell sightes to strike in the marke or to make a faire shoote Nicholas To open your doubts concerning all sorts of differences which may happen in the two leuell sights I will first beginne with this when by chaunce the leuell sight before is precisely of the same height that the leuell sight behinde is of I meane when the leuell sight before is equally so high as the leuell sight behinde then by how much he that shootes stands more nearer to the marke by so much he shall be more apt to strike in the marke or to make a faire shoote and this commeth to passe through two causes The first of them is for that alwayes as before hath been said in the seuenth Colloquie that Handgunne or Peece will shoote vnder the leuell marke and the bloe will be by so much