paruus erat Excubiae somnum superant labor otia vincit Tunc Dea vana venus vinaque spreta iacent Hic ducis assumit partes hic militis arma Iste mucrone potens hic eques ille pedes Alter bombardis inimicas dissipat aedes Eminus hic hastis cominus hic gladijs Si cupis a longé globulis terrere superbos Hic discas hostes perterebrare tuos Tartaglia arte sua multos ad tartara mittit Transtulit hunc nuper Lucar arte sua Non lucrum quaerit Lucar non munera magna Laudem non fraudem doctus habere studet Sed pro regina pro relligione fideque Pro Christo Angligenas instruit arte sua G. B. Cantabrigiensis IN DEI NOMINE AMEN The first booke of Nicholas Tartaglia his Colloquies concerning the Arte of shooting in great and small Peeces of Artillerie translated out of Italian into English by Cyprian Lucar Gentleman who hath also augmented the volume of the said Colloquies for the benefite of his Readers with the Contents of euery Colloquie and with the Corollaries and Table that are in the same volume The first Colloquie How a Gunners Quadrant should be made and vsed and how a Peece of Artillerie doth shoote more ground when it is eleuated at the mouth than it will do when it lieth leuel and how Pellets doe make long and short Ranges according as the Peeces which shoote them are eleuated and howe a Table of Randons maye bee made for any Peece and how he which hath a true Table of Randons for a Peece shal be thereby able to make with that Peece a perfect shoote at any marke within the reach of his said Peece and teach any vnskilfull Gunner to do the same and how hee that wanteth such a Table shall neuer learne to shoote well at any marke without point blanke and how the outer sense telleth truth in particuler things but not in vniuersall things Interlocutors Francesse Maria Duke of Vrbine Nicholas Tartaglia DVKE What reasons are they which as you say in your booke dedicated vnto me you haue found out concerning the knowledge of shooting in Gunnes Nicholas The proportion order of shootes not only at marks far of but also at marks hard by with what Peece you will and with what sort of pellet you will Duke Speake more plainely and giue me an example thereof for I doe not vnderstand what you say Nicholas I am content to shewe vnto your Excellencie an example of my said inuention but first I must speake of that materiall instrument which I haue deuised set foorth in a picture at the beginning of my said booke dedicated vnto you the which instrument is made of a square peece of wood or of mettall like vnto this figure B A C and containeth a quadrant that is to say How a Gunners quadrant may be made one fourth part of a circle like vnto the figure H I G K which is to be described with a paire of compasses vpon the center H I meane one foote of the compasse ought to bee fixed in the point H the inward angle of the said square and the other moueable foote of the compas must describe I G K the crooked side or arke of that quadrant also another croked line equidistant from the first as is the line E F ought to be drawne with the said compasses but for this purpose the compasses may not bee opened so wide as they were before and all the space which is betweene the two croked lines that is to say betweene the arke I G K and the arke E F must be deuided into 12. equal parts drawn by the edge of a ruler from the point H the center of that Quadrant so as euery of the same diuisions which I call points may be perceiued to looke or lie right vpon that center H as they doe in this figure IN the same maner euery of the aforesaid partes or points should bee diuided into 12. A Type of the Gunners quadrant other equal parts Although I haue not diuided this figure into so many parts because they would heere marre the same but a Square of an ordinarie bignesse as before I haue said may be so diuided as that al the whol Square shall containe 144. equall parts which I call minutes These minutes are to be marked with more shorter lines than are the lines of the points to this end that they may be more easily nūbred by the halfe or midst of the points depicted with the greater lines that we may also know how that euery point containeth twelue minutes This done a pinne of yron or of lattin is to bee fixed precisely in the pointe H the center of the quadrant and vpon that pinne a moueable threede of silke or of some other thing with a plummet at the end of the same must hang downe like vnto the perpendicular H M D. The vse of the Gunnets quadrant This Instrument will help vs to iudge of all the variable positions or eleuations that may happen in any Peece of artillerie whatsoeuer And nowe concerning the same positions or eleuations this is to bee noted that the first position of euery Peece is to bee vnderstoode when it is laid leuell for then the longest legge of the said instrument being put into the mouth of the said Peece and rightly extended towards the bottome of his concauitie the threede and plummet which is fixed in the center of that instrument will fall precisely vpon the line H F K as it doth in the figure next following A peece lying leuell And a Peece shall bee said to bee mounted one point when the longest legge of our said instrument beeing in the mouth of the said Peece the saide threede and plummet doth fall precisely vpon the diuision of the first point as it doth in the figure nex following A Peece mounted at one point or 12. mintes Also a Peece shall be said to be eleuated two points when the said threede and plummet doth fall precisely vpon the diuision of the second point and when the said threede plummet doth fall precisely vpon the third point then the Peece is eleuated at three points and so we must say of the fourth fift and sixt points But when a Peece is mounted at the sixt point then the said Peece is mounted to the greatest eleuation that it may be at I speake this of a Peece of Artillerie because the morter peeces may be eleuated vnto all the other points following I meane euen vnto the 12. point This which wee haue spoken of points ought also to bee vnderstood of minutes that is to say when a Peece is so mounted that the said threed and plummet falleth Precisely vpon the diuision of the first minute that Peece shal be said to bee mounted one minute And when the said threed and plummet shall fall vpon the diuision of two minutes it shall bee said to bee mounted at two minutes In like sort it shall
place of equalitie the pellet doth range with more difficultie and more sooner beginneth to decline downewardes to the grounde and declineth in a greater quantitie than when it is shot out of a peece somewhat eleuated that is to say it goeth then as the Gunners terme it much lesse in a right line than when it is shot out of a peece eleuated wherefore in this question the effects of shootes made in that place of equalitie will bee of lesse force and to a lesse effect than in any place of eleuation Obiection But here your Excellencie may say with good reason that although it is manifest by these demonstrations that in equall distances a shoote out of a peece lying leuell will do a lesse effect than a shoote out of a peece eleuated yet it is doubtfull whether a shoote out of a peece eleuated will doe a greater effect than a shoote out of a peece lying leuel in vnequall distances because in our question this is to be considered whether the peece which is on the plaine at the foote of the hill be more distant from the Fort than the other Peece which is on the toppe of the hill For such a difference may bee much greater than the difference of his shoote in a right line or the difference of his effects in equall distances and then the peece from the toppe of the said hill will doe a more greater exploite than the Peece which is on the plaine at the foote of the said hill To this doubt I aunswere thus Answere The distance from the Fort to the peece which is on the plaine may so much differ from that distance which is betweene the saide Forte and the saide peece which lieth vppon the toppe of the hill that the same will come to passe which was of you doubted Duke To make me vnderstand your meaning giue me an example by a figure Nicho. That I may shewe vnto you my meaning herein by a figure I wil suppose that the pellet of a Culuering doth waie 20 pound waight A Culuering which lying leuel shooteth about 200. paces will at the eleuatiō of 45. degrees or of 6. points or of 72. min. shoote about 800. paces and that the Culuering according to that experience which was made at Verona as I haue declared in the beginning of my booke of nwe science dedicated vnto your Excellencie in the place of equalitie that is to say lying leuell will shoote in a right line about 200. paces and that such a culuering at the eleuation of 45. degrees that is to say at the 6. point or at 72. minutes of our Quadrant by the reason alleaged in the last proposition of my seconde booke of our nwe science wil shoote in a right line about 800. paces Duke Doe you say that a Culuering being eleuated at 45. degrees or at the 6. point or at 72 minutes wil shoote about 800. paces and that the same Peece lying leuel wil shoot but about 200. paces Nicho. By reason I am taught so to say Duke It seemeth to mee that there is a great difference betweene those shootes Nicho. It commeth so to passe because that eleuation of 6 points doth differ much from the place of equalitie and according as the Peece is eleuated from minute to minute According as a Peece is eleuated from minute to minute or from point to point so from minute to minute and from point to point the pellet of that Peece doth augment his range in an insensible croked line so from minute to minute the pellet of that peece doth augment his raunge in a right line it doth also the like in the points but that is in a greater quantitie For the peece being eleuated to the first point of the Quadrant shootes more farther in a right line than when it is laid leuel Also the Peece eleuated to the second point of the said Quadrant shootes much farther in a right line than it doth when it is eleuated but at one point Likewise the Peece beeing eleuated to the thirde point shootes farther in a right line than it doth at the second point so successiuely the Peece being eleuated to the fourth point shootes farther than at the third point and at the fifth point farther than at the fourth point and at the sixt point as is aforesaid farther than at the fifth point and if the Peece should by degrees bee eleuated aboue the sixt point the pellet woulde flie more farther in a right line that is to say the Peece eleuated to the seuenth point would shoote farther in a right line than at the sixt point and at the eight point farther than at the seuenth point and at the ninth point farther than at the eight point and at the tenth point farther than at the ninth point and at the eleuenth point farther than at the tenth point and at the twelfth point farther than at the eleuenth point And at this twelfth point the pellet will flie wholie in a right line The pellet which is shot out of a peece mounted at 90. degrees or at 12. points flieth in a more perfect right line than whē it is shot out of a peece mounted at any other degree or point Note that Tartaglia calleth that a right line which is insensibly croked and that a crooked line which is euidently crooked to this end that the common people may the better vnderstand him and it will be a perpendicular aboue the horison And this pellet shot out of a peece mounted at the twelfth point will flie in a more perfect right line than any of the former pellets did because in truth the going or violent mouing of a bodie equallie heauie which is without the perpendicular of the horison can neuer haue any part perfectly right as it hath bin sayd in our said second booke of our nwe science Duke Why do you call that a right line which is not perfectly right Nicho. That the common people may the better vnderstand me I call that a right line which is insensiblie crooked and I call that a crooked line which doth euidently appeare to bee crooked Duke Proceede on Nicho. Now to returne to our purpose I say that if the distance betweene the said fortresse and the Peece lying on the plaine at the foote of the hil be 760. paces and that the distance betweene the same fortresse and the peece lying on the toppe of the said hill be but 130 paces in this case the said Culuering which is planted on the toppe of the hill will doe a greater exploit against the walles of that fortresse than that Culuering shall do which is planted on the plaine at the foote of the said hill the cause hereof is for that the said Culuering lying leuell doth shoote about 200. paces in a right line as before hath bin said Then for so much as the distance betweene that Culuering and the Fortresse is but 130 paces as it hath bin supposed the pellet of that Culuering
will strike the walles of that Fortresse neare about 70 paces before it would end his range in a right line but the Culuering which is planted on the plaine at the foote of the hill being distant from those walles 760 paces in a diametral line and eleuated to 45 degrees that is to say to the 6 point of our quadrant doth shoote about 800 paces in a right line and therefore it will strike those walles onely about 40 paces before it would ende his way in a right line or be sensibly perceiued to decline In the question proposed in this Colloquie the pellet which at his hitting would haue gon most farthest not meeting with an obiect to resist it shall do the greatest exploit vpon that obiect which resisteth And so that pellet which at his hitting would haue gon most farthest not meeting with an obiect to resist it shall doe the greatest exploit vpon that obiect which resisteth by the reasons alleaged vppon the fourth proposition of our first booke of our nwe science Therefore insomuch as the pellet of that Culuering which is planted on the top of the hill at the hitting of those walles had to flie more farther about 70 paces in a right line and that the pellet of that Culuering which is planted on the plaine at the foote of the hill at his hitting had to flie more farther but onely about 40 paces in a right line I conclude in this case by those reasons that the pellet of that Culuering which is planted on the top of the hill shall do a greater exploit against those walles than the pellet of that Culuering which is planted on the plaine at the foote of the hil and eleuated to the sixth poynt of our quadrant And if the pellet of this Culuering mounted to the sixt poynt be of a lesse force the pellet of that peece mounted at any other poynt vnder the 6 poynt is of much lesser force But if the distance from the said Fortresse vnto the Artillerie on the plaine had bin 600 paces in a diametrall line Note and that from the Fortresse vnto the Artillerie on the toppe of the hill it had bin 150 paces the Artillerie on the plaine mounted to the 6 poynt would haue stroken those walles with more force than the Artillerie vpon the top of the hill could haue done for the pellets shot out of the Artillerie on the plaine will beate those walles about 200 paces before the full ende of their ranges in a right line and the pellets of the Artillery on the top of the hil will beate those walles 50 paces before the end of their full course in a right line And therfore the difference of the saide effects that is from 50. paces to 200. paces which they make before they do sensibly decline is about 150. paces and therefore the said Culuering not onely at the eleuation of the sixt poynt of our quadrant but also at the eleuation of the fift point doth make that effect to be more greater But concerning this I will not stand to make any demonstration for that I will not be tedious vnto you Then if in so great a height as in the last case we haue supposed the Culuering vpon the plaine being mounted to the sixt point and also to the fift point will do a more greater exploit than the Culuering vpon the toppe of the hill such great effects will much more euidently follow in the first case which was proposed by your Excellencie where the hill and also the Fortresse were supposed to be of equall height and each of them to be 60 paces in height and the distance from the foote of one hill to the foote of the other or frō the top of the one hil to the top of the other to be 100 paces the Diametrall or Diagonall line that is to say the distance from the saide Fortresse to the place at the foote of the hill where the Artillerie is supposed to stand on the plaine by the 47 proposition of the first booke of Euclide to be about 116 paces leauing out the Fraction which should be added vnto that number and therefore the pellet shot out of the Culuering which is planted on the toppe of the hill will strike those walles about 140 paces before the full end of his range in a right line the pellets of the Artillerie which is planted on the plaine at the foote of the hill and mounted to the 6 point wil strike those walles about 684 paces before the full end of their ranges in a right line Note And because here is so great a difference in that one of those pellets doth hit the fortresse 140 paces before the full end of his range in a right line and the other pellet doth hit the same fortresse 684 paces before the full end of his range in a right line therefore in this question it is a plaine and euident thing that the Culuering planted on the plaine at the foote of the hill mounted to the 6 point 5 point or to any other point of eleuation wil do a greater exploit against the said fortresse than that Culuering will doe which is planted on the top of the hill Duke You haue answered well to this Question The third Colloquie How a pellet doth neuer range in a right line except it be shot out of a peece right vp towards Heauen or right downe towards the center of the world and by how much more swifter a heauie bodie driuen violently through the aire flyeth by so much in that mouing it is made the more lighter and how the more lighter a bodie is the more easilie wil the aire beare it and by how much a heauie bodie violently mouing doth go more swifter by so much it doth worke the more greater effect in all thinges which resist the same and by how much the swiftnes thereof doth more decrease by so much in that mouing the waight thereof which draweth the said heauie bodie towards the ground doth more increase and the more swifter a pellet flyeth in the aire the more lighter it is contrariwise the more sloer a pellet flieth the more heauier it is and howe the one part of a right line cannot be more or lesse right than the other part and how the more swifter a pellet flieth the lesse crooked is his range And how we be oftentimes deceaued by iudging according to the sence of seeing and how a peece is said to shoote at point blanke when it lying leuell or equidistant to the horison is discharged and howe the waigt of the pellet draweth the pellet out of his way and right passage perpendicularly towardes the grounde when it is shot out of a peece lying leuell and also when it is shot out of a peece eleuated or imbased except it be shot right vp towards Heauen or right downe towardes the center of the worlde Interlocutors Francesse Maria Duke of Vrbine Nicholas Tartaglia DVke By your arguments you
bee sayd of all the rest euen to the greatest eleuation that is to say to the eleuation of the sixt point or of 72. minutes as this figure next following doth manifestly shewe The other minutes from thence to the end are for morter peeces A peece mounted at 6. points or 72. minutes How a peece doth cast more ground when it is eleuated at the mouth then it will do when it lyeth leuell How pellets do make long and short ranges according as the peeces which shoote them are eleuated Duke What will you infer vpon this Nicholas Hereupon I will first infer that a peece of Artillery mounted at one point shootes more farther than it will doe when it lyeth leuell and that a piece mounted at two points will shoote more farther than at one point and a piece mounted at three points will shoote more farther than at two points Also a piece being mounted at 4. pointes will shoote much more farther than it will do at 3. points Likewise a peece mounted at 5. points will shoote somwhat farther than at 4. points And a peece mounted at 6. points shootes a pellet of leade a little farther than it doth at 5. points For reason teacheth vs that the range of a pellet shot out of a peece mounted at 5 points and the range of a like pellet shot out of the same peece mounted at 6. points doe so little differ as that vpon any small aduauntage happening either by force of powder or by any other meanes the peece being mounted at 5. points will shoote so far as it can doe when it is mounted at 6. points and perchaunce farther but when one doth mount such a peece so as they doe mount morter peeces that is to say at 7. points with out doubt by mounting the peece at 7. points he shall not shoote so far as he did when that peece was mounted at 6. points also at the 8. Point he shall not shoote so far as he did at the 7. point Likewise at the 9. point he shal shoote much shorter than he did at the 8. point at the 10. point he shall shoote lesse ground than at the 9. point so at the 11. point he shall shoote much shorter than at the 10. point finally at the 12. and last point he shall not shoote so far by a great deale as hee did at the 11. point But in this last eleuation it may be thought that by naturall reason the pellet should returne backe againe into the mouth of the peece yet by many accidents which do commonly happen in that instant when the peece is discharged the Pellet will not precisely returne into the very mouth of the peece but fall downe neare vnto the same Duke This is to be graunted as all that which you haue besides spoken but what will you infer vpon this Nicho. I will secondarily infer that I haue found out in what kind of proportion or order the said shootes do increase by euery eleuation and that not onely from point to point of our said instrument but also from minute to minute euen to the end of the eleuation of the 6. point or of 72. minuts yea that with euery sort of pellet whether the same be of leade yron or stone Likewise I haue found out in what proportion the shootes do decrease when peeces are eleuated beyond the said 6. point as morter peeces are eleuated Howe a Table of randons may bee made for any peece of Ordinance How he which hath a table of randoms for a peece shall be therby able to make with that peece a perfect shoote at anye marke within the reach of his said peece teache any vnskilfull gunner to doe the same and how he that wāteth such a table shall neuer learn to shoote well at anye marke without point blanke and that not onely from point to point but also from minute to minute euen to the end of all the 12. points or of the 144. minutes Duke What profite will come by this your Inuention Nicho. The profite of this inuention is such as that by the knowledge of one onely shoot out of any peece of ordinance whatsoeuer each man may make a table of al the shootes that such a peece will shoote at any eleuation that is to say from point to point and from minute to minute in our said instrument the which table shall be of such vertue and propertie as that any person hauing the same with him shal not onely know how to shoote but also be able to teache euery vnskilfull Gunnar to shoote in such sort of gunnes at any marke so many paces and so far of from him as he will so that the marke be not farther than such peeces will reache and this notwithstanding he which is so taught lacking such a table cannot learne any part of this inuention fot this secrete shal be knowne onely to him that hath such a table and to none other Duke If he that hath such a table wil not shoote himselfe but cause one other person to shoote shall not that other person learne this secrete Nicho. No most excellent Lord but that other person may be likened vnto the seruants of Appotecaries which continually compound medicines according as they are appointed by Phisitions to doe and learne not thereby to be Phisitions Duke This seemeth to me a thing incredible because you say in your said booke that you did neuer shoote in any gunne and for that he which will iudge of thinges in which he hath had no proofe or experience is oftentimes deceiued The eie is that which giueth vs a true testimonie of things imagined The outer sense reileth truth in particular things but not in vniuersall things for vniuersall thinges are subiect onely to vnderstanding and not to any sense For the eie is that which giues vs a true testimonie of thinges imagined Nich. It is true that the outer sense doth tel vs the truth in particuler things but not in vniuersal things for vniuersal things are subiect only to vnderstāding not to any sense Duke You haue said enough if you can make me to see this which I do not beleeue you shal work a wonder Nich. Al things happening by nature or art are thought to be wonders when no reason is giuen for the same but your Excellencie shall find my sayings herein to be true if you will cause them to bee tried with a Peece of Artillerie Duke I must goe now vnto Pesaro but at my returne from thence I will cause all this which you haue told mee to be proued The second Colloquie Where a Peece of Artillerie which is eleuated at the mouth will doe a greater exploite than a Peece which lieth leuell and where a Peece which lieth leuell will doe a greater exploit then a Peece which is eleuated how a Peece which lieth leuel wil neuer shoot so far in an insensible croked line as it wil do when it is somwhat eleuated
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
C D M L do not touch the said line or way of the pellet H I K. And let the point M be that place of the visual line which commeth most neerest to the said way or line of the pellet Now I say if the marke vnto which the leuell is giuen happeneth to bee in the point M the pellet will strike vnder that marke I meane it will strike in the point N. But it wil strike at that place N more neerer to that marke than in any other place therefore if that marke were more without from the point M as if I should say in the point L or within betweene the Peece and that point M as if I shoulde say in the point O the pellet woulde alwayes strike more vnder the marke But it is true that it is more subiect to error without than within that point M as it appeareth to be by the figure folowing Prior. You haue said enough For I do well vnderstand you in this matter The 9. Colloquie When the leuell sight which is vpon the mouth of the peece shal be by so much loer or shorter than the leuell sight which is vpon the breech of the saide peece as that our visuall line passing by the extreames or toppes of those leuell sights in taking the leuell of things doth only touch and not cut the way of the pellet then the distance from the mouth of that peece to the saide contingent or touche point is so much grounde as that peece can cast leuel and then if the marke vnto which the leuell is giuen shal be in that contingent or touch point the pellet will strike precisely in the middest of that marke And when the marke shall happen to be either without or within that touch point the pellet will strike vnder the marke but more vnder when the marke is without the said touch point than it will do when the marke is within the same touch point Interlocutors L. Gabriel Tadino Prior of Barletta Nicholas Tartaglia PRior Now go forward in the last part of the proposed matter that is to say whē the leuel sight at the mouth of the Peece shall haue his due conuenient shortnes in respect of the leuel sight which is on the breech of the Peece Nicho. When the leuel sight at the mouth of the peece shal be by so much loer or shorter thā the leuel sight on the breech of that Peece as that our visuall line passing by the extreames or tops of those leuel sights in taking the leuel of things doth only touch not cut the way of the pellet as by the figure following it doth appeare to do in the point M the distance frō the mouth of that Peece to the said touch point which in the figure following shall bee the line H M may with reason be said to be so much ground as that Peece can cast leuel And then if the mark vnto which the leuel is giuen shal by chance be found to be in that touch point the pellet wil strike precisely in the middle of that mark But whē the said mark shal happē to be without the same touch point that is to say without the point M the pellet will alwaies strike somwhat vnder that marke I meane so much more vnder the middle of that mark as the same marke shal be more remote or farther from the touch point be it without or within that touch point And it is true that the same marke being within that is to say Note towardes the Peece the Pellet cannot strike very loe because that lonesse can neuer be equall to the height of the leuel sight which is vpon the breeche of the Peece which may be about the one halfe of the thicknesse of the peece in the breech as hath been said in the ende of the seuenth Colloquie and therefore in such a case the stroke is subiect to a small error in respect of that which may happen when the marke is without or beyonde that touche point as any man of a meane capacitie may consider Obiection Prior. Wherefore do you attribute vnto the distance which is betweene the Peece and the same touch point that it is all the ground which the Peece can shoote leuell and doe not attribute the same to the distance betweene the Peece and the point of the intersection in which point if the marke bee set the pellet will likewise strike in the middle of the saide marke euen as it doth when the marke is in the touch point as hath been declared in the seuenth Colloquie Answere Nicho. Because the Point of intersection hauing no determinate place may be in very many places according as by very many wayes the leuel sight on the mouth of the Peece may be need Our visual line passing by the extreames of the leuel sights may cut the line of the pellet in very manie places But when our visuall line passing by the extreames of the leuel sights doth only touch and not cut the said line of the pellet the said touch point cannot bee but in one onely place lesse more shorter than the leuell sight on the breech of the Peece But the touch point cannot be but in one place only the which place is more farther from the mouth of the Peece than any other place whatsoeuer where our visuall line may meete with the line of way in which the pellet flieth Then that being a more longer or farther concourse and lesse variable than any of the other concourses which doe cut the same I thinke for this reason that such a dignitie ought more worthily to bee giuen to that touch point than to any of the points of intersection Prior. Your sayings do agree with reason and this matter with the other two matters which haue been spoken of before are three good lessons The 10. Colloquie When one or both of the leuell sights shall not be precisely set in the very middest of the vppermost part or outside of the peece then that peece will alwaies shoote his pellet wide of the marke vnto which the leuel was giuen by those sights Also when the concauitie or hollownesse of a peece is not bored or cast right in the middest of the mettall then that peece will shoote his pellet wide of the marke vnto which the leuel shal be giuen And how the middle part of the concauitie in a peece may be iustly knowne and how the leuel sights may be rightly placed vpon the outside and vppermost part of a peece right ouer the middle point of the concauitie in the peece Interlocutors L. Gabriel Tadino Prior of Barletta Nicholas Tartaglia PRior You haue heeretofore made mee to vnderstande the cause why a pellet shot at a marke vnto which leuell is giuen doth sometimes strike in the middest of that marke and sometimes aboue that marke and sometimes vnder that marke nowe I woulde knowe why the pellet doth sometimes strike muche wide of the marke vnto which the leuel is
giuen Nicho. This may happen by two causes the one of them is by reason of the leuell sights for when one of those sightes or both of them shall not be precisely set in the middest of the vppermost part or outside of the Peece Note that Peece is forced thereby to driue his pellet wide of the marke For if the leuell sight on the breech of the Peece shall be set without the same point of the middest as for example towards our right hand the same Peece also will driue his pellet wide vpon the same right side of the marke vnto which the leuell was giuen Note And if the leuell sight on the breech of the Peece shall be set without the same point of the middest and towardes our left hande the same Peece vvill also strike vvide from the marke tovvardes the same left side Prior. It seemeth to mee that this should be contrary to that vvhich you haue said I meane if the leuell sight on the breech of the Peece be set vvithout the point of the middest and tovvards the right side that the peece will shoote his pellet wide of the marke towardes the left side Nicho. It is not so my Lorde but it is as I haue told you and to the ende that this may bee proued to be true by reason I doe suppose for example sake that the peece in the figure folowing hath on his breech a leuell sight noted with this letter C set somewhat without the point of the midst towards the right hand and that the leuell sight D which is at the mouth of the Peece is set iust in the point of the middest and that the point E is the marke vnto which the leuel is giuen by the said two leuell sights the which point E must needes bee wide towardes the left side from the line F G which is supposed to be the way of the pellet as it doth appeare to bee in the figure following Then this point or marke E being vpon the left side wide of the pellets way it followeth that the way of the pellet lieth wide from the same marke and towardes the right side thereof as by the figure following which is made for an example you may perceaue And such effect would much more solowe if D the leuell sight on the mouth of the Peece were also without the same pointe of the middest towardes the other side that is to say towardes the left side The second cause of such effect or inconuenience may come through the concauitie of the peece which often times is not bored or cast right in the middest of the mettall I meane that the same concauitie or hole is not in the verie middest of the mettall but makes one side of the peece to be more thinner or thicker than the other side so that although the two leuell sightes be well set and perfectly placed in the verie middell pointes vpon the vppermost part of the mettal yet that peece must needs shoot wide for notwithstanding the leuell sightes are placed in the verie middle points vpon the vppermost parte of the mettall yet they doe not stande right ouer the middell of the concauitie of that peece and for that cause such a peece shootes wide Wherefore to remedie this inconuenience it is necessarie to search aduisedly for the verie middle of the concauitie as well in the taile of the Peece as in the mouth of the same and to place the leuell sightes ouer the middle of the same concauitie for to amende that fault in the Peece You may see the type of this instrument which is made of two long rulers or staues in the 23 Colloquie of this booke How the leuell sights that are to be placed vpon the outside vppermost part of a Peece may be set in their due places right ouer the middle point of the concauitie in the same Peece To finde the middle of the same concauitie the Gunners vse as I haue been informed two long Rulers or small staues verie right and of equall breadth and doe put one of them right into the concauitie and downe to the bottome of the same and the other without vpon the Peece and they ioyne one part of that Ruler which is aboue the Peece to the Ruler that goeth into the mouth of the Peece in that part thereof which is without the mouth of the same and so where they finde the very middle of the concauitie to bee there right ouer the same vpon the outside and vppermost part of the Peece they doe place in the taile of the Peece and at the mouth of the Peece the two leuell sightes And this being a way speedy enough and of smal cunning it is not to be misliked although it may be otherwise done Prior. May not a way be deuised to set those leuell sightes in their due places without the helpe of those Rulers only by discharging the Peece oftentimes together Nicho. It may be so done That is to say if the Peece shall strike wide vpon the right side of the marke moue the leuell sight which is on the taile of the Peece somewhat towards the left part and if the Peece shall happen to strike wide towards the left side of the marke moue the same leuell sight which is on the taile of the peece somwhat towards the right side and goe on in so doing till the perfect place where that leuell sight must stand is found and then make a durable marke in that place if the leuell sight be a moueable thing so that at an other time you may haue no cause to seeke for that place againe Prior. I doe vnderstand you well and am satisfied for this euening The 11. Colloquie Howe there is a proportioned length for euery peece of Artillerie and howe when any kinde of peece is made more longer or more shorter than his proportioned length it will shoote alwaies lesse grounde And howe this is no generall rule that by howe much the Canon of a peece is more longer by so muche it shootes the farther and how it is a manifest error and a very vnprofitable thing to make very long Culuerings and how a Culuering doth shoote further than a Cannon and howe a Cannon may bee made to shoote farther than a Culuering and howe much the mettall of euery peece shoulde weigh and how long each peece ought to bee and how much each pellet which is shotte out of those peeces doth weigh and howe many Horses or Oxen must bee prouided to drawe each kinde of peece Interlocutors L. Gabriel Tadino Prior of Barletta Nicholas Tartaglia Seruant PRior What is the cause that by howe much the Canon of a Peece of Artillerie is more longer by so much it shootes the farther Nicholas This proposition is not generall I meane that by how much the Canon of a Peece is more longer by so much it shootes the farther Note You may know the proportioned length of eury great
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
before declared will be somewhat more than sixe fingers that is to say there will remaine 34 Zanantonio How must I order this number 34. which remaines for to make of it a conuenient fraction to be added vnto those six fingers Nicholas I haue not hetherto in any Authour which hath written of the extraction of Cubike rootes read any good rule which will teach you to make a true fraction after the Cubike roote is extracted out of a number which is no Cubike number and the cause thereof is except I be deceaued for that the right way to extract a Cubike roote was vnknowen vnto them I doe not say vnknowen as though the said Authors knew not how to extract a Cubike roote or that the rules which they haue set downe serue not for to extract a Cubike roote but I will say that their rules are not so true and plaine for that purpose as they shoulde be for if they were true plaine to extract the Cubike roote it would be thereby an easie matter to make a fraction of the number remayning after the nighest Cubike roote is extracted out of a number not Cubike By reading M. Records book called the whetstone of wit you may learne after the nighest cubike roote is extracted out of a number not cubike to make a fraction of the number remayning Zanantonio Is not that the right way to extract a Cubike roote which you haue alredie shewed vnto me Nicholas That is the very true and right way for to extract a Cubike roote Zanantonio In so much as you haue taught me to extract a Cubike roote I pray you teach me also how I shall make after the nighest Cubike roote is extracted out of a number not Cubike a fraction of the number remayning Nicholas You must at this time haue patience but I promise you I will shortly teach you and all others that will learne to doe the same and also other thinges Zanantonio If there be no other remedie I will haue patience till that time The 2. Corollary YOu may also in this sorte following double or treble a round pellet or any other sphericall bodie Drawe a rightline of what length you will and note that line with A B then crosse that line with another line which I would haue you to note with C D and call the poynt in which the saide lines doe crosse one another E. This done open your compasse to the length of the diameter of that Sphere which you will double or treble and with your compasse so opened marke vppon the line E D from E towards D the length of that diameter And when you will treble the said Sphere marke the length of that diameter thrise vpon the line E B from E towards B. But at this present you shal onlie double the said Sphere and therefore marke the length of the saide diameter vppon the line E B from E towards B no more times thā twise as I haue done in the points F G of the figure folowing Now deuide the line E F into two equall parts in the point H and deuide the line E H into two equall parts in the point L. likewise deuide the line L H into two equall parts in the point M. After this plasing one foote of your compasse in M and the other foote of the same in G you must describe a semicircle which in the figure folowing is marked with these letters N C G. Finally deuide the said line C D into two equall parts in the point O and then plasing one foote of your compasse opened to the widenesse of one of those partes last mentioned in O and the other foote of your compasse vpon the line E A drawe the archeline N R C and by so doing you may conclude that the space N E by the ninth proposition of the sixt booke of Euclide is double to the space E D as it doth appeare by the figure following The 11. Colloquie How Vitruuius hath erred in appointing a proportion for those stones which are put into the hole of the Enguine called Balista Interlocutors Zanantonio Nicholas Tartaglia ZAnantonio By what rule or way doth Vitruuius appoint a proportion for those stones which are put into the hole of the Enguine called Balista Nicholas I do now remember that the reason which you asked me in the precedent Colloquie is the very same which Vitruuius doth write of in the seuenteenth Chapter of his tenth booke where he concludes that if the stone which is shot out of the Balista doth way two pounde waight the hole at the head of the Balista must be fiue fingers and if such a stone doth way fower pound waight the said hole must be sixe fingers the which determination is like vnto mine in the precedent Colloquie in respect of the whole number that is to say of six and not of the fraction For the fraction 34 which remaines in that place telleth vs that the said hole must be somewhat more than six fingers and ¼ Zanantonio It may be that Vitruuius his booke was ill translated Nicholas It is so translated into Latin Zanantonio But looke I pray you whether his other determinations which folow in that place be iustly concluded Nicholas Without doubt there is some error in them but more in one than in another And I beleeue that this commeth so to passe for that hee was ignorant how to make a conuenient fraction of that which did remayne when he had extracted the Cubike roote out of a number not Cubike and for proofe thereof he concludes that if a stone which is to be shot out of that Balista doth way sixe pound waight that the hole at the head thereof must be seuen fingers and for the fraction which remaynes more than the said 7. fingers he puts downe 9. pointes in fourme like vnto a circle Zanantonio Who knoweth that the saide 9. pointes doe signifie the conuenient fraction or part of a finger which that hole should be more than the saide 7. fingers seeing we vnderstande not the signification of the said 9 points which is an auncient thing Nicholas When it is so it foloweth of necessitie that in euery place where 9. such points are put they represent one and the same fraction the which is otherwise for in the saide places there happens fractions of diuers denominations as for example the hole at the end of the Balista must be 7. fingers and about ◠◠parte of a finger for to receiue the said stone that is to say the said hole would be somewhat lesse than 7. fingers and 1 ◠parte of a finger Therefore in that place the said 9. points should signifie somewhat lesse thā 1 ◠part of a finger And for a stone of 10 pound in waight the saide Vitruuius concludes that the saide hole of the Balista would be 8. fingers high and more which he doth expresse by the saide 9. pointes but I by working according to the order set downe in the
foure foote wide within the stakes This done wreath about the stakes of each gabbion or basket so many of the said Osiar twigges or pliant roddes as will suffice to make euery basket extende one foote in heigth aboue the head of the taulest gunner After you haue so done fill vp the said baskets with earth which must be throwne into each basket by a little and little at a time and cause a man standing within euery basket to treade well and ramme downe all the same earth as it shall be so cast in But when gunners shall serue vppon a platfourme where no baskets of earth are set to defende them they may shadow themselues with cables or bigge ropes with wet strawe or wet hay with dead bodies of enemies with mattresses shippe sailes or canuas hanged stiffe vp so as the enemie shall not see any marke or man vppon the platfourme to shoote at and with a line drawe vp the nearer or loost end of the same mattresses ship sailes or canuas so often as they shall haue cause to shoote at their enemies This deuise as some men doe thinke will be also profitable for those that shall in time of warre stand vppon the walles of a cittie towne or forte because they may put vp at their pleasure the canuas looke vnder the same with more safety than through the loope or looke holes in the wall at which the enemis are alwayes readie to shoote If for defence in seruice you will make a double Gabbion which at the least ought to be eight foote in widenesse and 25 feete and 1 7 of a foote in compasse digge at the ende of euery foote in measure vppon that compasse a whole foote ½ foote or somwhat more in deepenesse and set vpright in euery of the said holes a staffe often foote in length and in compasse so bigge as a mans arme This done wreath pliant twigges of Osiar or of nut trees or of oke or of willoe about all the same erected staues vp to their tops while you are so occupied cause an other man with a woodden beetle to beate downe your worke close togeather whereby it will be more able to resist the violent bloe of a pellet Also in the very middest of the Gabbion driue a strong peece of oke into the ground lay other peeces of tymber ioyned fast togeather ouerthwarte the gabbion from one of his sides to the other After all this fill vp the said gabbion with good clay or with blacke small and wet earth well rammed downe or with greene turfes digged out of meddowes or with bagges full of earth or fine sande or with bagges of wooll which is the best thing of al for this purpose and take heed that you do put no stone into any gabbion among those things which do fill it vp The 49 Chapter Rules by which Rabinets Bases Fauconets forreine ordinance that are not so high as the Faucon Faucons Minions Sakers Culuerings Basiliskes Cannons and all peeces which do shoote stone pellets may for proofe and also for seruice be duely charged with that sort of corne gunpowder which is marked in the 16 Chapter of this Appendix with the figure of 1 and by which you may tell what roome a due charge of such corne gunpowder will fill vp in the concauitie of any great peece that shooteth pellets of lead or pellets of yron 1 YOu may prooue all sorts of great peeces with three shoots in this maner following Charge euery Rabinet Base Smeriglio Rebadochino Fauconet Faucon Minion Passauolante Moiane Saker Culuering which is fortified with mettal as it ought to be for the first shoote of proofe with the whole waight in gunpowder of his pellet for the second shoote of proofe with 5 4 in gunpowder of the waight in his pellet for the third and last shoote of proofe with 3 2 in gunpowder of the waight in his pellet As for example if a peece which shal be prooued doth shoote a pellet of 12 pounds in waight you must charge the said peece for the first shoote of proof with 12 poundes in gunpowder for the second shoote of proofe with 15 poundes in gunpowder and for the third shoote of proofe with eighteene poundes in gunpowder 2 Charge euery Cānon Basilisk for the first shoot of proof with ⅔ in gūpowder of the waight in his pellet for the second shoot of proof with ⅚ partes in gūpowder of the waight in his pellet and for the third and last shoote of proofe with the whole waight of his pellet in gūpowder As for example if any Peece named in this second rule shall be prooued with a fit pellet of 45 poundes in waight you must charge the said peece for the first shoote of proofe with thirtie poundes in gunpowder and for the second shoote of proofe with 37. poundes and ½ pound in gunpowder and for the third and last shoote of proofe with 45 pounds in gunpowder 3 Charge euery cannon periero of the olde making for the first shoote of proofe with ⅓ in gunpowder of the waight in his stone pellet for the second shoote of proofe with 7 18 partes in gunpowder of the waight in his stone pellet and for the third and last shoote of proofe with 4 9 partes in gunpowder of the waight in his stone pellet As for example if a cannon periero of the old making shall be prooued with a fit stone pellet of 36 poundes in waight you must charge the said cannon periero for the first shoote of proofe with 12 poundes in gunpowder for the second shoote of proofe with 14 poundes in gunpowder and for the third shoote of proofe with 16 poundes in gunpowder 4 Charge euery cannon periero of the nwe making for the first shoote of proofe with ½ in gunpowder of the waight in his stone pellet for the second shoote of proofe with 5 ◠parts in gunpowder of the waight in his stone pellet for the third and last shoote with ¾ parts in gunpowder of the waight in his stone pellet As for example if a cannon periero of the nwe making shall be prooued with a fit stone pellet of 36 poundes in waight you must charge the said cannon periero for the first shoote of proofe with 18 poundes in gunpowder for the second shoote of proofe with 22 poundes and ½ pounde in gunpowder and for the third and last shoote of proofe with 27 poundes in gunpowder 5 Also you may prooue any great peece of artillerie by these rules following charge and discharge thrise togeather for proofe euery Smeriglio Rebadochino Base Rabinet Fauconet Faucon Minion Saker Passauolante and demie Culuering loer than ordinarie with the whole waight in corne gunpowder of his leaden pellet 6 Charge discharge thrise togeather for proofe euery ordinary demie Culuering demie Culuering of the biggest sort whole Culuering not so high as ordinary whole ordinarie demie Culuering and whole Culuering of the biggest sort which is not so well fortified
the ladle is pulled out remayne in the lowest ende of the same peece After you haue in this sorte laded the peece with his due charge in gunpowder thruste harde with a rammer twise togeather no more except you doe charge a Cannon all the sayd gunpowder home vnto the lowest ende of the peece that it may not lie dispersed or loose nor be too harde rammed downe in that place Also thruste a bigge wad of toe hay strawe or of vntwisted ropes into the peece home vnto the charge in gunpowder for to sweepe and keepe togeather all the sayd charge in gunpowder and to cause the pellet that shal be shotte out of the same peece to range farre Then putting a fitte pellet into the concauitie of the peece which fitte pellet as our English Gunners doe say ought alwayes for diuers reasons to be ¼ of an ynch lesse or shorter in his diameter than the heigth of the sayde concauitie driue with a rammer the pellet home vnto that wadde and if the peece shall shoote downewardes at a marke A fitte pellet as our english Gunners doe say is ¼ of an ynche lesse or shorter in his diameter than the heigth of the concauitie in his peece But among the Gunners in high Germany this is a general rule that the diameter of a fitte pellet ought to be neither more nor lesse than 20 21 of the diameter in the mouth of his peece As for example a fitte pellet for a peece of seuen ynches in diameter must be 6 ynches ⅔ of an ynche in diameter thruste an other bigge wadde of toe hay strawe or of vntwisted ropes into the peece home vnto the said pellet for to keep the pellet within the peece to stay the pellet there that it may not role out before the peece shal be discharged moreouer put good dry gunpowder into the touchhole and about the touchhole of the peece like a trayne and be not ignorant that after all this is done the peece is charged and that you standing vppon one side of a peece so charged and touching the trayne of gunpowder by the touchhole of the peece with a lintstocke or with a fiered Gun-match which some Gunners doe tie to the ende of a sticke of three or foure foote in length and some Gunners doe set fast in the cockes of their staues and some Gunners doe winde about the staffe ende of an halbert or partisant may safely discharge the same peece Also if you will in time of seruice charge any of the sayd peeces of Artillerie with cartredges doe thus Put first a cartredge into the mouth of the Peece and then with a rammer thruste it into the lowest end of the Peece his concauitie and next driue a woodden tampion with a rammer into the same concauitie home to the cartredge then ioyne a good bigge wadde of hay strawe toe or of vntwisted ropes vnto the sayd tampion and put a fitte pellet into the Peece close vnto the sayd wadde and when a Peece so charged shall shoote downewardes at a marke thruste an other like bigge wadde into his concauitie harde vppon the pellet This done put a long pricker into the touchhole of the Peece so charged and with the same pricker pearce diuers holes thorow the cartredge lying within the Peece or which in mine opinion is a better deuise cut cleane away before you doe put the cartredge into the hollow Cylinder a peece of the outside of the cartredge in that parte which shall lie directly vnder and next vnto the touchhole Finally fill the touchhole of this Peece with good and dry corne gunpowder and make about the touch-hole a little trayne of powder and considering that the tampion within the sayd Peece if the powder lying behinde the same tampion should happen to be moyste must be drawen out with a long yron worme An admonition or cutte in peeces with a long yron cheesell which will be a perillous worke to doe I counsel you to discharge the sayd Peece within a conuenient time after it shal be so charged with a tampion The 52 Chapter How without a Ladle you may lade any Fauconet Faucon Minion Saker Culueringe Cannon or other like made Peece with his due charge in loose gunpowder PVt a long straight and smoothe staffe into the bottome of euery Fauconet Faucon Minion Saker Culueringe Cannon and euery other like made Peece that shall be charged and hauing thruste the staffe downe close by the mettall into the concauitie of his Peece so farre as it may goe marke with a knife or with some other conuenient thing that parte of the staffe which is touched with the lippe or outmost edge of the Peece his mouth Then drawing the sayd staffe out of his Peece measure along vppon the same staffe with a compasse beginning at the sayd marke and proceeding downewardes in a straight line towardes that end of the staffe which was at the bottome of the sayd concauitie the iust length of the roome which a due charge in gunpowder will fill vp in the sayd concauitie You may see in the 49 Chapter of this Appendix what roome a due charge in gunpowder will fill vp in any Fauconet Faucon Minion Saker Culuering Cānon or any other like made Peece and make an other visible marke vppon the staffe at the end of the same length and for a distinction call it the lowermost marke After this throe Gunpowder into the Peece with your handes vntill by estimation the Peece hath receaued thereof a due charge and with a rammer as you haue beene taught in the precedent Chapter thruste the same gunpowder downe into the bottome of the Peece and to the ende you may be guyded by the sayd staffe to throwe no more gunpowder into the Peece than is requisite and to take out the excesse when you haue throne too much gunpowder into the Peece put the sayd staffe agayne into the Peece home vnto the gunpowder and looke where the lowermost marke vppon the same staffe is For as the Peece lacketh a parte of his due charge in gunpowder if the sayd lowermost marke shall now be within his mouth and hath more than his due charge in nwe gunpowder if the sayde lowermost marke shall be without his mouth So if you haue throwen into the Peece his due charge in gunpowder the sayd lowermost marke will now neither be within the mouth of the Peece nor without the mouth of the Peece but touch exactly the outmost edge or lippe of the Peece his mouth The 53 Chapter How you may duely charge any Chamber peece of Artillery and how you may charge any Cannon Periero PVt into euery chamber so much powder as his peece requireth for a due charge and with a rammer beate a tampion of softe wood downe vppon the gunpowder Moreouer put a bigge wadde into the peece at that ende where the mouth of the chamber must goe in and after the wadde thruste into the peece at the
peece a round sharpe poynted pricker of yron or steele that may touch and pricke the end of the sayde staffe which if no stone scale or other lette be within the sayde concauitie will lie vnder the touchhole Then taking out all the stones scales and filthe which are within the sayd hollow Cylinder make cleane the same with a scourer or which is all one with a spunge for such thinges lying within a hollow Cylinder charged with gunpowder may cause the same hollow Cylinder in his discharge to breake or cause a moysture in the same hollow Cylinder which will weaken the gunpowder that is there and make it vnable to expell a pellet with so great force as it should doe After this lay the tayle of the peece vppon the grounde against a woodden planke backed with a wall or banke of earth and perceauing by such meanes as before in the 43 Chapter of this Appendix haue beene declared that no hony combes flawes or crackes are in the sayd hollow Cylinder put blocks vnder the mouth of the sayde hollow Cylinder or gunne to mount and eleuate the same mouth as before I haue tolde you vnto 30 degrees This done charge and discharge the sayde peece thrise togeather for his proofe with a fitte pellet and a due charge in gunpowder according as you haue beene taught in the 40 Chapter of this Appendix I say thrise togeather because a faultie gunne that taketh no hurte by the first shoote may receaue a little harme by the seconde shoote and breake in peeces at the thirde shoote Last of all make a trayne of gunpowder from a place behinde an high banke of earth or wall vnto the touchhole of the peece and standing alwayes when you doe prooue any great peece at the ende of the sayde trayne behinde the banke or wall geue fire vnto the sayde trayne An admonition and beware that you doe not remooue from the sayde standing place till by putting fire to the trayne you haue discharged the peece The 57 Chapter How you may by fiue sundry wayes disparte any Fauconet Faucon Minion Saker Culuering Cannon or any other like made peece how you may finde out the middle and vppermost parte of mettal ouer the tayle of any peece how you may finde out the middle and vppermost parte of mettall ouer the mouth of any peece and how you ought to set the disparte of euery peece vppon the middle and vppermost parte of mettall ouer the mouth of the peece 1 MEasure with a calaper coÌ„passe the greatest heigth of mettall in the taile of the peece also the greatest heigth of mettall at the mouth of the peece subtract the lesser heigth out of the greater heigth and take halfe of the remaynder for the disparte of the peece 2 Adde the diameter of the greatest circuÌ„ference of mettall at the mouth of the peece to the diameter of the greatest circumference of mettall at the tayle of the peece and diuide the whole length of both those diameters into two equall partes This done opening your compasse to the measure of one of those equall partes set one foote of your compasse fast in the vndermost parte of the concauitie at the mouth of the Peece and extende the other foote of your compasse right ouer the vppermost parte of mettall in the greatest circumference about the mouth of the peece and take that heigth which is betweene the sayd vppermost parte of mettall and the sayd vppermost ende or poynt of your compasse for the true length of the disparte of the sayde peece 3 Measure with a girdle or stringe that will not stretch the greatest circumference of mettall in the tayle of the peece multiplie the measure of the sayde circumference by 7 diuide the product thereof by 22 and note in your memoriall the quotient number for the diameter of that circumference Likewise measure with a girdle or stringe that will not stretch the greatest circumference of mettall about the mouth of the peece multiplie the measure of the circumference last named by 7 diuide the product thereof by 22 and note in your memoriall the quotient number for the diameter of the circumference last named This done subtract the shortest diameter out of the longest diameter and take ½ parte â—… the remaynder for the disparte of the sayde peece 4 Prepare a long ruler marked with ynches halfe ynches quarters of ynches and with other lesse equall partes Lay that ruler ouerthwarte and equidistant to the Horizon vppon the greatest circumference of mettall in the tayle of the peece let a line and plummet hang right downe from the sayde ruler first close without any bending by one side of the same circumference and after close without any bending by the other side of the same circumference note exactly the partes of the ruler which were at both times touched with the line and in like manner note exactly the poynte of mettall in the sayd circumference which lyeth directly in the middest betweene the sayde two noted parts This done take the space betweene the sayde two noted partes for the diameter of the sayde circumference and marke with a file or some other thing the sayde poynte of mettall for the middle and vppermost parte of mettall in the sayde circumference Likewise laye your ruler close to the mouth of the sayde Peece and let a line and plummet hang right downe from the sayde ruler first close without any bending by one side of the greatest circumference in the mettall at the mouth of the peece and after close without any bending by the other side of the circumference last named then noting well as you did before the partes of the ruler touched at both times with the sayde line and also the poynte of mettall lying in the circumference last named directly ouer the middle parte of the space which is betweene those noted partes take the same space for the diameter of the sayde circumference at the mouth of the peece and marke the same poynte with a file or some other thing for the middle and vppermost parte of the last named circumference After all this subtract the shorter diameter from the longer diameter and taking â…“ parte of the remaynder for the disparte of the Peece set a strawe or a peece of a small waxe Candle of equall length to the sayde disparte vpright vppon the sayde marke in the middle and vppermost parte of the circumference last named and call that strawe or peece of a waxe Candle the dispart of the peece 5 Thruste a pryming yron thorowe the touchhole of the Peece downe to the bottom of his concauitie and then marke with a redde stone that parte of the yron which is equall in heigth with the vppermost parte of mettall in the greatest circumference at the tayle of the peece This done pull vp the sayde yron out of the touchhole set that ende of the yron which went thorowe the touchhole vppon the vndermost parte of the concauitie in the mouth of the
peece and holding the marked parte of the sayd yron right ouer the middle parte of mettall in the greatest circumference aboue the mouth of the peece take the space betweene the sayde marke vppon the yron and the sayde middle parte of mettall ouer the mouth of the peece for the desired disparte which if it be set in his due place will alwayes direct you to lay the concauity of his peece leuell and right against any appoynted marke The 58 Chapter How with a Fauconet Faucon Minion Saker Culueringe or Cannon you may alwayes strike any appoynted marke within poynt blanke AFter you haue charged a Fauconet Faucon Minion Saker Culueringe Cannon or any other like made peece with his duetie in powder waddes and pellet according to the precepts expressed in the 49 Chapter of this Appendix disparte the peece and set his disparte vpright with a little waxe vppon the middle and vppermost parte of mettall in the greatest circumference ouer the mouth of the peece and lifte your peece vp or downe vntill by laying your eye vnto the middle and vppermost parte of mettall in the greatest circumference at the tayle of the peece you may perceaue that the marke at which you will shoote the toppe of the disparte and the vppermost parte of mettall at the tayle of the peece doe lie in a perfect right line and in an equall heigth Then doing your duety as you haue beene taught in the first Chapter of this Appendix discharge your peece and you shall see that the pellet shotte out of the same peece will strike the appoynted marke which lyeth within poynte blanke When you shall haue occasion to shoote at a light seene in the night time disparte your peece with a lighted vnflaming waxe candle or with a lighted gunmatch or set a lighted gūmatch vpright by the disparte that you may see by the light of the fire in the same gunmatch to lay the middle and vppermost parte of mettall at the tayle of the peece and the toppe of the disparte in a straight line with the marke and to place the concauity of the peece right against the marke as before in this Chapter I haue taught you to doe The 59 Chapter How you may know what number of feete yardes pases or scores any peece of Artillerie will shoote in an vnsensible crooked line or as the Gunners terme is at poynt blanke CHarge the peece for whose poynte blanke you seeke with his duetie in good corne gunpowder and with a fitte pellet turne the mouth of that peece towardes a wall butte or banke of earth scituated in a conuenient distance from the peece and lay the peece leuell by the helpe of a Gunners semicircle or quadrante as you haue beene taught in the first Colloquie of the first booke of Nicholas Tartaglia his Colloquies Then setting the true disparte of the peece vppon his mouth according to the doctrine written in the tenth Colloquie of the sayde first booke of Colloquies and in the 57 and 58 Chapters of this Appendix discharge the peece at a small visible marke fixed in a poynte of the sayde wall butte or banke of earth that is leuell with the toppe of the sayde disparte and with the highest parte of the mettall at the tayle of the peece This done note diligently where the pellet doth hit and euermore when the pellet so shotte doth strike aboue the marke When the pellet shotte in this maner striketh aboue the marke then the extreame farthest ende of the poynte blanke which you seeke is beyonde the sayde marke When the pellet shotte in this maner striketh vnder the marke then the extreame and farthest end of the poynt blanke which you seeke lyeth betweene your peece the said mark remooue the peece backwardes to an other place more farther from the sayde marke and out of the more remote place shoote at the marke agayne as you did before with one sorte of gunpowder and with a like pellet till the pellet so shotte shal strike in the middest of the marke For when the pellet so shotte doth strike precisely in the middest of the marke then by the reasons alleaged in the nynth Colloquie of the saide first booke of Colloquies the number of scores pases yardes and feete betweene your sayde peece and the sayde marke is so much grounde as your sayde peece can shoote in an vnsensible crooked line or as the Gunners terme is at poynte blanke But if the pellet so shotte shall strike vnder the marke drawe the peece forwardes towardes the marke and from a more nearer place shoote againe as you did before with one sorte of powder and with a like pellet till the pellet so shotte striking in the middest of the marke shall shewe vnto you by the reasons alleaged in the sayde 9 Colloquie that the distance betweene your peece and the marke is so much ground as your sayd Peece can shoote in an vnsensible crooked line or as the Gunners terme is at poynt blanke The 60 Chapter How the poynt blanke and vtmost ranges are proportionall in all peeces of Artillerie How by the rule of proportion you may knowe what number of yardes any peece will reach at his vtmost randon And how by the sayd rule you may know what number of yardes any peece will reach at his poynte blanke THe poynt blanke and vtmost ranges as some authors haue written are proportionall in all peeces of Artillerie wherefore knowing the poynt blanke and vtmost range of any one peece and the poynt blanke of an other peece you may tell the vtmost range of any that other peece In like manner knowing the poynt blanke and vtmost range of any one peece and the vtmost range of an other peece you may tell the poynt blanke of that other peece As for example let vs suppose that this question is asked If a Faucon carrying poynt blanke 320 yardes will at his vtmost randon range 1280 yardes how farre will a Saker reach at his vtmost randon that at poynt blanke or leuel rangeth 360 yardes I say that the rule of proportion serueth precisely to answere the same and all such like questions And that multiplying 360 in 1280 and diuiding 460800 the product thereof by 320 the quotient will yeelde 1440 for the number of yardes which the sayd Saker shall reach at his vtmost randon Againe let vs suppose that I am required to answere this demaunde If a Faucon which rangeth at his vtmost randon 1280 yardes will carrie poynt blanke 320 yardes how farre will a Saker reach at poynte blanke that at his vtmost randon rangeth 1440 yardes To doe that which is required I multiplie 320 in 1440 and hauing diuided 460800 the product by 1280. I finde in the quotient 360 to be the number of yards which the Saker will shoote leuel or as the Gunners terme is poynt blanke And thereuppon I conclude that after this manner by obseruations vsed in any one peece of artillery and by the arte of proportion
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
second shoote against the said marke in euery respect as it did lie at the first shoote and afterwards raise vp the dispart vppon the mouth of your peece till you shall see by the vppermost part of mettall in the taile of the peece and the toppe of that dispart the place where the pellet strooke at the first shoote This done imbase the mouth of that peece till the said vppermost part of mettall and the toppe of the same dispart doe lie in a right line with the marke and then giuing fire to the peece you shall see that by this meanes the peece will shoote into the marke To amend a loe shoote Also when a pellet shot at a marke within point blanke doth strike somewhat vnder his marke you may amend the said loe shoote in this maner Recharge your peece and after you haue for the second shoote laid it against the marke in euery respect as you did lay it for the first shoote set vpright vppon the vppermost part of mettall in the taile of the peece a waxe candle of such a length as that you may see by the toppe of the saide candle and the toppe of the dispart vppon the mouth of the peece the loe place where the pellet before did hit Then hauing mounted the mouth of your peece till the toppe of the saide waxe candle and the toppe of the dispart vppon the mouth of your peece doe lie in a right line with the saide marke giue fire to the peece and so you shall shoote into the marke To amende a shoote wide vppon your right hand But when a pellet shot at a marke within point blanke shall strike wide vppon your right hand then to amend that wide shoote recharge the peece which shot that pellet and laying it for the second shoote against the marke as it did lie at the first shoote remoue the leuell sight vppon the taile of your peece somewhat towards your left hand so as the top of your nwe leuell sight and the toppe of your peece his dispart may be perceaued to lie in a right line with the place where the pellet before did strike This done mooue your peece to and fro till you shall see that the top of your nwe leuell sight and the toppe of your peece his dispart do lie in a right line with the marke for an end of this worke giue fire to your peece which now without faile will shoote his pellet into the marke To amende a shoote wide vppon your left hand You may amend a shoote wide vppon your left hand as you haue been taught to amend a shoote wide vppon your right hand sauing for the amendment of a shoote wide vpon your left hand you must alwaies remoue the leuel sight vppon the taile of your peece somwhat towards your right hand The 73 Chapter To make an engine which will make a great spoile and a merueilous slaughter PLace a great peece of Artillerie within a brode yron hoope and lay a great number of Caliuers or Muskets in the said hoope rounde about the said peece according to the figure next folowing and when need shall require charge and discharge all the same peeces togeather This engine discharged out of a ship at men in a Gallie Foyst or any other like vessell as Girolamo Ruscelli writeth will make a great spoile and a merueilous slaughter The 74 Chapter Instructions for all those that are vnskilfull to handle and vse an Harchibuse Caliuer or Musket 1 EVery person vnskilfull to handle and vse an Harchibuse Caliuer or Musket ought first to learne to handle and carry soldier like the saide peece and the Flaske and touch boxe belonging to it the alowed bore of a caliuer in Ao. DniÌ„ 1588 the alowed bore of a musket in Aº DniÌ„ 1588. 4 Also he ought to learne how he shall in a commendable maner charge his peece and how he shall afterwardes when need shall require lay it to his cheeke 5 Hauing learned to charge he ought also to know how hee should shoote in the saide peece at randon and likewise how he should shoote in that peece at a marke within the leuell of the same peece and how vppon a small stay in march or skirmish hee should charge and discharge speedily his peece 6 Also he ought to prooue before hee hath vrgent cause to vse his peece whether it bee good and meete for his purpose or like to breake 7 And in a skirmish made only for practise or sport let him take heed that hee doe not charge his peece with any bullet whereby any person may be maymed or put in hazard of his life or limmes 8 Also for diuers reasons which are not meete to be expressed in this booke let no person at any time vse to shoote out of his peece any pellet of lead after hee hath chawed it in his mouth and bitten it with his teeth The 75 Chapter How to mount a morter peece for to shoote out of the same fireworks or great stones ouer walles or other high places into cities townes or camps to burne and beate downe houses tents and lodgings within the same places IT behooueth him which will shoote out of a morter peece any fireworke or great stone for to haue it fall right downe vppon the appointed place to know these 3 things The waight of the shot how much ground his peece wil shoote at the best of the randon how far the place which he would burne or beate downe is from him The said three things being knowne he may easily by this example following learne to doe as he intended Example The peece will shoote the fireworke or the great stone at the best of the randon 800 paces and the place to be burned or beaten downe is distant from that peece 600 paces therefore that peece must be mounted for to doe this exploit at 48 degrees and ½ degree But if the fireworke or the great stone will flie at the best of the randon 900 paces and the place to bee burned or beaten downe bee distant from the peece sixe hundred paces then the saide peece must bee mounted at fortie one degrees and almost ½ of a degree And when the fireworke or stone will flie at the best of the raudon 1000 paces and the space betweene the peece and the said place doth containe 600 paces the said peece must be mounted at sixe thirtie degrees and ½ part of a degree but for the better vnderstanding hereof marke well this figure following â— for t to be burned or beaten downe The â—…etus or perpendiculer line A morter peece set vpright In the said figure there is a Quadrant and vppon the same with a moueable Hipothenuasa or Index a right angled triangle is fashioned The base of that triangle representing the space betweene the peece the marke ought to bee diuided into so many equal partes as the said distance betweene the peece and the marke doth containe paces Likewise the
you must instruct the Pyoners to vndermine deepe within harde grounde and to make the way of the myne three foote in breadth and sixe foote in heigth and to digge the sayd Ouen and place of greatest effect sixe or seuen foote in breadth and nine or tenne foot in heigth to this ende that the gunpowder laide in that place may make his vent vpwardes and that the ayre which is within the saide holloe place may ayde the gunpowder to open and ouerturne the ground which is right ouer it When the saide Ouen and place of greatest effect shall happen to be made in a stonie grounde where the stones are like to fall then you must vnderproppe them with holloe pypes of timber filled ful of good gunpowder and remember alwaies to obserue a meane in making the Ouen and place of greatest effect because it ought in no manner of grounde to be too bigge or too little The myne being finished according to your saide platte couer the ground or floore in the saide Ouen and place of greatest effect with boordes and hauing stroed vppon those boordes a sufficient quantitie of good gunpowder put so many barrelles without any heads or couers full of good and strong gunpowder vppon the same boordes as will execute the thing appointed to be done and in so doing perswade your selfe that the better and greater the quantitie of gunpowder which shal be laide in the saide Ouen place of greatest effect is the more greater will be the effect of the same Moreouer for to fire the said gunpowder when time shall require lay a gunmatch made of fine bumbase cotten that hath beene well sodde in vineger brimstone and saltpeeter well roled in gunpowder and well dried in the Sunne within a Trunke Pype or case of boordes which gunmatch and trunke must extende and reache in length from the gunpowder stroed vppon the boordes in the saide Ouen and place of greatest effect vnto the mouth and beginning of the myne and also somewhat without the same and hauing couered the saide gunmatch all ouer with a traine of dry gunpowder close vp the said trunke with a couer of boordes so as no soile or moysture may come vnto the gunpowder within the same Trunke Or if you will you may tie a peece of a gunmatch vnto the ende of a small line and when the saide ende of a gunmatch shal be a fire drawe the same by that line running on a pulley thorow a traine of gunpowder made within a Trunke vnto the barrels of gunpowder in the saide ouen and place of greatest effect But before you doe fire the gunpowder in the myne with a gunmatch after the doctrine last taught or in any other manner you must with earth rootes of trees blockes of timber stones and such like things walle fortefie and ramme vp the mouth of the saide Ouen or rather all that parte of the myne which C D and E in the figure next following doth represent so as no fire or aire may breath out of the said ouen and place of greatest effect by any other way than by the saide holloe Trunke For in so much as that parte of the myne which is noted in this figure next following with E lieth not right against the saide ouen and place of greatest effect and likewise for that the place of the myne which D in this figure following doth represent lieth not right against C and also for that the mouth of the myne which B representeth in the figure next following is not right against E and D it is certaine when the gunpowder in the saide ouen and place of greatest effect shall be set in a fire after the way of the myne from C to D is so stopped vp with earth rootes of trees blockes of timber stones and such like thinges that the saide gunpowder will with a great and horrible violence bloe and ouerturne all the ground and buildings ouer the same The 102 Chapter How a caue ought to be made rounde about a Castle or Forte that is besieged to the intent that they which are in the saide caue may heare and perceaue at all times whether or no the enemie doth woorke to vndermyne the same Castle or Forte WHen a Castle or Forte is besieged and the Captaine of that Castle or Forte doth feare that the enemie will vndermine the same place then the Captaine to auoid the hurte which may come by the saide myne ought to commaunde his Souldiers to make a deepe pitte within their Castle or Forte and from the bottome of the same to dyg a caue vnder the foundation of the walles of their saide Castle or Forte and also vnder the ditch which enuironeth the saide place vntill they shall come vnto the outside of the saide ditch and from thence to vndermine on the outside of the saide ditch as the ground will suffer them to woorke rounde about the saide Castle or Forte When the Souldiers haue brought out of the saide caue all the earth which was in the same they may fortefie the walles of their Castle or Forte with the same earth and laying sackes of wooll straightly bounde about with cordes in diuers places of the saide caue they ought to put vppon euery of the saide sackes a latten bason and cast into euery of the saide basons sixe or eight harde peason to this ende that they which are in the saide caue may heare and perceaue at all times by those peason whether or no the enemie doth worke to vndermine the same Castle or Forte for at euery stroke that the Pioners shall strike the peason in the saide basons will vndoubtedly make an audible iarre whereof the Captaine ought presently to haue warning that he may in conuenient time with countermines or by some other pollicie make the myne of his enemies to be of no effect Moreouer to knowe whether or no the enemies doe make any myne against you this may be done Sinke diuers deepe welles in diuers places towardes the suspected myne and hauing made diuers holes with a long auger in the sides of those welles cause vigilant and skilfull men to watch and harken continually at the saide holes or in the bottome of the saide welles whether or no the enemies doe vndermine towards you But if this way shall not like you take a drumme and set one ende of it flatte vppon a very plaine peece of ground neare vnto the head of one of the saide welles and then vppon the vpper ende or head of the drumme lay fiue or sixe haukes belles or such belles as are commonly set in collars for little dogges or for wante of such belles a conuenient number of drie beanes which will make a sounde at euery stroke geuen in the myne with any mattocke or pickaxe if the enemies doe vndermine within fourty or fifty paces of the saide drumme and that sound will be by so much more audible by how much more nearer to the drūme the enemies Pioners doe come Also you may
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
summe of 950 feete the heigth of A F and thereof will come 1140 feet which sheweth what number of feete are in the Horizontall distance that is to say betweene E and F and betweene C and B. And in like sort you must proceede to finde out at the second standing the Hipothenusall distance betweene X and A An admonition and the Horizontall distance betweene X F but it behooueth you to note in this kinde of mensurations by two standinges that sometimes your eye in one standing will not be so high from the grounde as it will be in the other standing especially when your Instrument hangs vpon a thing that standes fast in the ground And although that difference is but little yet many times the same will breede great errors and therefore to auoyd the occasion of such errors I exhort you to prouide a line and plummet which may reache from the center of the quadrant to the grounde and direct you at your first standing and also at your second standing Moreouer to auoyde errors I counsell you to hang your Quadrant so as it may turne vppon no other part thereof then vppon his center but nowe to returne vnto our purpose if by chaunce you shall stande so neare vnto the altitude as that the line and plummet of the quadrant falleth vppon the right shadow you must work otherwise than you did before I meane you must diuide those parts cut with the said line by 12 in this case the quotient must alwaies bee set downe like a fraction the which fraction you must reserue and after you haue marked the place where you stoode goe from thence so farre as you list in a right line forwardes or backewardes and then placing your saide Instrument againe as you did at your first standing lift the said Instrument vppe or put it down till you may through his sights see A the top of the altitude This done note aduisedly vppon what part of right shadowe the saide line and plummet falleth and that part diuide by twelue the whole number of partes of one side of the scale and the quotient thereof must of necessitie bee set downe like a fraction This fraction subtract from the other fraction first reserued or in plainer words subtract the lesser of those two fractions from the greater and reserue the remainder thereof Then measure the space between your first and second standing by feete paces or any other kind of measure that you will and diuide the number of that measure by the remainder which was before reserued and adde vnto the quotient of the saide diuision the heigth betweene the center of the said Instrument and the ground and by so doing you may conclude that the totall summe thereof is the altitude of the thing seene For an example hereof if at the first standing the sayd line and plummet shall fall vppon the thirde parte of right shadowe diuide that number of three by twelue the whole number of partes in one side of the scale and the quotient thereof will bee in a fraction ¼ Reserue this fraction of ¼ and then marke your first standing with a staffe set vpright vnder the center of your Instrument and then goe from thence backwardes in a right line so farre as you list and placing there your Instrument as you did at your first standing mooue it vp or down till you shall againe espie through the said sightes A the toppe of the said altitude Then looke vppon what part of right shadowe the said line and plummet falleth as if by chaunce it fell vppon the fourth part diuide that fourth by twelue and the quotient wil be in a fraction â…“ Nowe out of ¼ the fraction which was before reserued subtract the last quotient which was â…“ and so â— 12 will remaine then hauing likewise marked your seconde standing with a staffe set vpright vnder the center of your Instrument measure the space betweene the staffe at your first standing and the staffe at your second standing which space in this example I suppose to be eight paces Now diuide this eight by 1 1â— the remainder last mentioned and the quotient thereof will be ninetie sixe and adde vnto the saide number of ninetie sixe the heigth betweene the center of the Instrument and the grounde which in this example I will suppose to bee one pase and so the totall summe amounting to ninetie seuen paces sheweth the heigth of A B. The demonstration of this worke is to be made by the similitude of triangles and their proportionall sides as before the other demonstration hath been made In this kinde of mensurations by two standings you must be very circumspect that the staffe vppon which your quadrant shall hang doe stande plumbe vpright both at your first standing and also at your seconde standing For otherwise it will make you not a little to erre which thing may be easily done by the helpe of your said quadrant or by letting fall a line and plummet close by the side of that staffe The 117 Chapter To know by the helpe of a Gunners Semicircle how many miles paces yardes or feete any shippe lying at Rode in the Sea or Tower or any other marke vppon the land in sight is from you To measure lengthes some say we should auoid hilles and desire plaines for that otherwise great errors will insue But in this kinde of mensuration no such matter is required for here it shall bee onely needefull at the time of your measuring to haue ground enough to go directly backwardes sidewise from your first standing This commodititie of ground enough had whether that grounde be leuell or otherwise worke thus Lay your Semicircle flat and leuell vppon a stoole or some other such thing and mooue the same about till you shal espie through D E the channell in the ruler A B the ship or other thing to which you will meâ—sure your Semicircle so remaining vnmooueable looke through the saide channel E D at some other thing lying directly in a right line 200 yardes or feete more or lesse at your pleasure behinde your standing which thing so espied shall here for an example be marked with the figure of 3. Then the Semicircle remaining still vnmooueable look through the channel F G in the ruler B C at some other thing lying sidewise in a right angle 100 yards or feete more or lesse froÌ„ your first standing noted for an exaÌ„ple with the figure of 1 that thing so espied shall in this place be noted with the figure of 2. After this coÌ„uey your selfe and your Semicircle from your first standing vnto the said thing which hath here been marked with the figure of 3 and lay your Semicircle there flat and leuell as you did before but so as the end of that channell which is marked with E do lie right ouer the point here marked as aforesaid with the figure of 3 and that by moouing the Semicircle about you may at the last perceiue
through the said channell D E that 1 the mark at your first standing doth lie right between you and the thing to which you measure Now without moouing of your Semicircle looke agayne through the said channel F G at some other thing lying sidewise in a right angle from 3 the mark of your 2 standing and goe in a right line towards the same thing last espied till the saide marke which hath here bin noted with the figure of 2 shall stand right betweene you and the thing to which you measure and there make a marke which in this example shal be the figure of 4. This done measure exactly the distāce betweene the marke 1 and the mark 2 cal it the first distance also measure exactly the distance betweene the marke 1 and the marke 3 call it the 2 distance Finally measure the distance between the mark 3 the mark 4 call it the 3 distance Now subtract the first distance from the third and reserue the remainder for your diuisor then multiplie the 3 distance by the second distance diuide the product by your reserued diuisor and so the quotient wil shew the true lēgth from the marke 3 vnto the ship tower or other thing to which you did measure At the figure of fiue there is a shippe lying at Rode in the Sea and from 6 7 8 and 9 a platfourme with ordinance vppon the lande I am required to measure vnto the said ship wherefore making my first standing at the place 1 I measure from thence vnto the place 2 which lyeth sidewise 200 yardes in a right angle from 1. Againe I measure from the saide place 1 vnto 3 the place of my seconde standing which lyeth 300 yardes in aright line with the said shippe behind my first standing Also I measure from the saide place marked with the figure of 3 vnto the place 4 lying 240 yardes sidewise in a right angle from 3 and scituated so as the said place 2 doth lie in a right line betweene it and the said ship then subducing 200 from 240 I keepe the remainder which is 40 for my diuisor and after this I multiplie 300 by 240 whereof commeth 72000 which diuided by 40 my said reserued diuisor yeeldeth in the quotient 1800 yardes for the longitude betweene 3 the place of my second standing and the said shippe The 118 Chapter How you may measure a short distance as the breadth of a towne ditch or narrow riuer without any Geometricall Instrument or arithmeticall knowledge STanding right vp with your bodie and necke vppon the side of a towne ditch or narrow riuer put your feete close together and behold with one eie a grasse leafe stone or other marke in the opposite side of the same ditch or riuer and in so doing pull down your hat or cap ouer your eie till you may see no other thing beyond the marke so espied After this keeping still your body and necke vpright your feete ioyned together and your one eie fast shut turne your selfe towards the plainest peece of ground that is about you and marke well that part of ground which you shall espie vnder your hat or cap most farthest from your station for the distance betweene the middest of your feete and the said farthest part of ground is equall to the breadth of the said riuer The 119 Chapter How you may at one station measure vppon an heigth with a Geometricall square a longitude vppon plaine SEt your Geometricall square very vpright vppon his side or ende X Y ouer the plaine where you will measure an vnknowne longitude This done mooue the Index of your said square vp or downe till you may espie through his sights the farthest ende of the desired longitude Then note diligently the partes of the square cut with the fiduciall line of the Index And if the partes so cut be in the contrary shadow multiplie the whole number of partes in one side of the square by the number of feet or yards which are in the heigth betweene the center of your Instrument and that part of the plaine which lieth directly vnder the same center and diuide the product thereof by the partes cut in the side of your square and note the quotient for the true measure of the desired longitude When the partes so cut shall be in the right shadow multiplie the partes so cut in the heigth between the center of your Instrument that part of the plaine which lieth directly vnder the same center and hauing diuided the product thereof by the whole number of partes in one side of the square note the quotient for the true measure of the desired longitude But if the fiducial line of the said Index shall lie directly betweene the right shadow and the contrary shadowe when you espie through the said sights the farthest end of the desired longltude then the heigth betweene the center of your Instrument and the part of the plaine which lyeth vnder the same center is equall to the desired longitude Example Admit that B C is an vnkowne longitude between a ship a gallie tying at Rode in the Sea that to measure the same longitude I haue set my Geometricall square plumbe vpright vppon his side or end X Y in A the maine top of the ship directlie ouer B one ende of the said longitude and that when I saw through the sights vppon the Index the gallie at C the farthest end of the desired longitude the fiduciall line of the saide Index did cut fortie partes of contrary shadowe and that the center of my square is tenne yardes aboue the said B therefore I multiplie 1200 the whole number of partes in one side of the square by tenne the measure of the heigth betweene the center of my square and B and the product thereof being 12000 I diuide by fortie the partes cut in contrary shadowe and so the quotient yeeldeth three hundred for the number of yardes in the measure of the saide longitude This one example geueth light to the ingenious Reader to worke in mensurations of longitudes when the fiduciall line of the index shall cut partes in the right shadowe of the square and also when the same fiduciall line shall lie vppon the square directly betweene the right shadowe and the contrary shadowe wherefore I doe omit to set downe here more examples in so plaine a matter The 120 Chapter How you may measure with a Geometricall square at two stations any longitude in sight TO measure at two stations an vnknowne longitude which here shal be supposed to be A B lay your Geometricall square flat and leuell vppon a stoole or vppon a foote made of purpose to holde it vp Then setting the fiduciall edge of his Index vppon the line H I which passeth directly from H to the beginning of the equal parts marked vpon X Y a side of the square turne the square vpō the stoole or foote his Index remaining stedfast vpō the said line H I
till you may espie through the sights vppon the saide Index B the farthest ende of the said vnknowne longitude This done the square remaining vnmooueable turne the fiduciall edge of his Index to the line V Z which passeth directly from V to the beginning of the equall partes marked vppon Y Z an other side of the said square then looking againe through the said sights note some mark a good space from you the farther this mark is froÌ„ you the better it is for your purpose then pitchinge vp a staffe right vnder the center of your square in A conueye your square vnto the saide marke which heere I will call C and recon to be 40 yardes from A now the square being layde againe flat and leuell vppon a stoole or vppon a foote right ouer C as it was before at A put the fiduciall edge of the Index vppon the saide line H I and turne the square vppon the stoole the Index remayning vnmouable vppon the saide line H I till you may see through the sights vppon the same Index the staffe in A. After this the square remayning vnmouable turne the saide Index to and fro till you may see through his sights B the extreame parte of the desired longitude and note diligently what parte of contrary shadowe is then touched with the fiduciall edge of the Index for if you will multiplie the whole number of partes in one side of the square by the number of yards betweene A and C your two stations and diuide the product thereof by the parte of contrarie shadowe touched with the fiduciall edge of the saide Index the quotient will shewe you the true measure of the saide longitude Example Admitte that at C your seconde station the fiduciall edge of the Index did touche the 100 parte of contrary shadowe and that you did then see through the sightes vppon the same Index B the extreame parte of the desired longitude Then multiplie 1200 the whole number of partes in one side of the square by 40 the number of yardes betweene A and C your two stations and diuide the product thereof which is 48000 by 100 the parte of contrary shadowe touched with the fiduciall edge of the Index at C your seconde station and so the quotient will yeelde 480 yardes for the desired measure of the sayde longitude A B. The 121 Chapter How you may measure with a Geometricall Square any distance or breadth lying in a plaine leuel grounde with your eye or station how so euer the same breadth or distance is scituated BEing required to tell the distance or breadth betweene two Towers which for example may here be named Q and R measure first how farre either Tower is from you which you may doe by sundrie wayes before taught and then laying your Geometricall Square flatte and leuell vppon a stoole or vppon a foote made of purpose to beare it vp turne the Square about till you haue set H I a line vppon one side of the saide Square right against Q the Tower next vnto you For if R the other Tower were nearer to you than the Tower Q you shoulde first lay the line H K right against the same Tower R. This done the Square not being remooued turne the Index to and fro till you may see through his sightes the saide Tower R which in this example as before I haue tolde you is the fardest Tower from you Then opening your compasse to so many equall partes in the side of the Square as there are yards betweene the center of the Square the tower Q. which I will here suppose to be an hundred yardes set one foote of your compasse in the center of your Square and with the other foote of your compasse make a fine visible mark at M vppon the line H I and when you haue so done open your compasse againe to so many partes in the side of the Square as there are yardes betweene the center of your Instrument and the saide Tower R which I will likewise suppose to be an hundred and fiftie yardes and putting one foote of your compasse in the saide center make an other fine visible marke vppon the face of the Square with the other foote of your compasse at N close by the fiduciall edge of the saide Index which ought now to lie in that place where it stoode when you did last see through his sightes the sayde Tower R. Moreouer open your compasse to the space betweene those two markes M and N and lay your compasse so opened vppon the partes in the side of your Square and so you shall perceaue how many yardes are betweene the Tower Q and the Tower R. For looke how many equall partes are beetweene the two feete of your compasse so many yardes are beetweene the Tower Q and the Tower R and therefore if sixty one partes shall bee betweene the two feete of your compasse you may boldly affyrme that the distance or breadth betweene the Tower Q and the Towre R doth containe sixty and one yardes â—…derstande â—…teous reaâ—… that M â—…ght to stand 〈◊〉 this picture 〈◊〉 the ende of 〈◊〉 line which â—…tendeth 〈◊〉 the side 〈◊〉 the square 〈◊〉 the fiducial â—…ge of the â—…ex and N â—…ght to stand 〈◊〉 that end of 〈◊〉 sayde line â—…ch adioyâ—…th to the fiduciall edge of the index H ought to stand at the center of the square and I ought to stand at the lowest â—…de of the square where the equall partes begin and that betweene H M are 100 equall partes betweene M N 61 â—…uall partes and betweene H N 150 equall partes The 122 Chapter How you standing vppon the toppe of a hill or drie ditch may measure with a Geometricall Square the deepenesse of the same hill or ditch and the breadth of any drie ditch or valley TO measure the deepenesse and breadth of M N O a ditch or valley measure first his breadth MN as you may doe by sundrie wayes before taught which breadth shall here be supposed to be eighteene yardes Likewise measure by the precepts before geuen the length or depth of M O which here shall be supposed to be fifteene yardes this done square 15 the measure of the depth M O and the product thereof will bee 225. Likewise square 9 which is ½ of the measure of the breadth M N and the product thereof will be 81. Then subduce the square 81 from the saide square 225 and out of the remainder which is 144 extract the Square root which being 12 sheweth the number of yardes that are in P O the depth of the ditch or valley Also in this manner if you stande vppon the toppe of a hill you may measure the heigth of the same hill The 123 Chapter How you may drawe a platte of any peece of grounde which shall containe the true proportion and Symetrie thereof in such sorte that you may tel how farre any place in the platte is distante from other TO drawe a platte of
hole in the center of the protractor I doe turne the protractor to and fro keeping his center ouer the prick last made till I haue set it in euery respect as it did lie before vpon the prick of my first station and hauing made a pointe with a cole in the edge of the protractor at euery degree and parte of a degree noted in the table of my second station I put the protractor aside and drawe straight lines from the prick made for the place of my second station vnto euery of those pointes noting well the crossing of like lines That is to say where the line of the Beacon drawne from the pricke of my first station meeteth with the line of the Beacon drawne from the prick of my second station and where the line of the Tower drawen from the prick of my first station meeteth with the line of the Tower drawen from the prick of my second station and so of the rest for other intersections or crossinges in this woorke are not to be regarded Also to know how farre euery place in this plat is from other I diuide the space before the prick of my first station and the prick of my seconde station into so many equall parts as there are yardes which for example I here suppose to be 200 then drawing straight lines from euery one of these noted places vnto other and opening my compasse to one of the said equall partes I measure how many times it is contayned in euery of the sayde lines and say that the number of yardes in the length of them is as this Table following doth shewe A Table shewing the distance of euery place from the two stations and also the distance of euery place from other and therein this is to be noted that 1 signifieth the first station 2 the seconde station 3 the Beacon 4 the Towre 5 the house 6 the Church and 7 the Windemill FRom 1 to 2 200 yardes From 1 to 3 193 yardes and ¼ of a yarde From 1 to 4 350 yardes From 1 to 5 375 yardes From 1 to 6 425 yardes From 1 to 7 395 yardes and ◠of a yarde From 2 to 3 300 yardes From 2 to 4 391 yardes and ⅔ of a yarde From 2 to 5 362 yardes and ½ of a yarde From 2 to 6 358 yardes and ⅓ of a yarde From 2 to 7 283 yardes and ◠of a yarde From 3 to 4 166 yardes and ⅔ of a yarde From 3 to 5 218 yardes and 2 11 of a yarde From 3 to 6 316 yardes and ◠of a yarde From 3 to 7 340 yardes From 4 to 5 88 yardes and ◠of a yarde From 4 to 6 208 yardes and ◠of a yarde From 4 to 7 275 yardes From 5 to 6 120 yardes From 5 to 7 195 yardes and ⅚ of a yarde From 6 to 7 107 yardes and ¾ of a yarde In this manner by changing my stations I may make diuers plattes expressing the true proportion and distances of Cities Townes Hauens Castles Fortes Campes Mynes Hilles and all other notable places within a whole Region Laus Deo Gutta cauat lapidem non vi sed sape cadendo Sic homo fit sapiens non vi sed saepe legendo The ende of Lucar Appendix AT LONDON Printed by Thomas Dawson for Iohn Harrison the elder at the Signe of the Greyhounde in Paules Churchyarde And are there to be solde 1588. IN SPE Amendements of faults made in printing the three bookes of Colloquies Faultes Page Line Amendmentes BOdie mouing 12 43. and 44. bodie violently mouing 6160 28 50 6146 be loer 53 22 be more loer which conteine 33 64 50 which conteins 33 here and ende 70 44 here an ende is in our 74 9 is now in our Amendments of faults made in printing Lucar Appendix Faultes Page Line Amendments IN some other 10 18 into some other and doe it vnto 10 26 and doe vnto it that time 10 52 the time into the flowre 11 11 into flowre in a Cauldron 11 12 in the cauldron and vineger 14 10 or vineger or after 14 11 and after full of round 15 3 full of litle round their tinder 21 1 the tinder being well wette 21 21 being wett a whole foote 41 23 whole of a foote The 65 Chapter 57 14 the 68. Chapter said pellets 59 45 said pellet next mixture 66 37 mixture next and put 70 23 put peece and close 70 24 peece next and close by it 73 17 by them bloe the forts 93 4 bloe vp the forts before 119 21 betweene