l e m e . l i b r a r y . u t o r o n t o . c a s t c 6 8 5 9 v e r . 1 . 0 ( 2 0 1 9 ) To the fauourable Studious Ingenious Reader touching these Diffinitions and Theoremes, concerning the newe Science of great Artillerie. THe Auncient Philosophers and Mathematicians that were either the first Founders or amplifiers of any Science with newe and rare Inuentions, were euer enforced at the first to vse manye newe and vnaccustomed names to distinguish and breefely to expresse such seuerall subiects as the Methodes of their dis­ courses did occasion them to handell. Let no man therefore marueil, if my selfe being now to Intreate of so newe and rare a Science as this of great Artillerie bee also enforced to vse sundrie strange tearmes, not vnderstande perhaps of the verye Artificers themselues that most Manedge that kinde of Engine. For albeit in all such vsual actions as Can­ noniers commonly practize, they haue wordes good inough to expresse their owne meanings. (And therein I vse also the same, except I finde them verye improper or misaplied) yet in the remote and hidden mysteries of Randonnes and of the seuerall Proportions of the mettaline Bodies and Soules or Cylinders of all seueral Peeces and of the strange varietie of the Circuites of all Bullets in the Ayre, by reason of the repugnance or variance of the violent and natural motions: In these Mysteries I say scarsly thought on, and farre beyond the compasse of ordinary Cannoniers without exquisite knowledge in the Mathematicall Sciences to intermeddle withall. I finde not anye wordes in vse that can serue my purpose, and haue therefore chosen such as in my iudgement are most proper and effectual, and to take awaye all obscuritye, haue set downe euery of their Diffinitions that are not in my Pantometria, alreadye sufficiently explaned: which Booke together with my Stratioticos, amplyfied with new Additions, I haue new published as Pathes to leade y ingenious Countrimen to the vnderstanding also of this newe Science, when I shall publish the same in her best perfection. And in the meane time as many yeares sithence I propounded pub­ likely sundry Questions concerning this facultie, to stirre vp bothe Theorical and Practical spirites of all sortes more profoundly to searche the hidden secrets of this Arte. So haue I nowe thougtht good to Imprint also these halfe hundered Theoremes, resoluing the most part of all those my former Propositions, wherein I must neuer­ thelesse admonish the reader that I haue enterlaced a verie fewe that are not in the seuere examination of Geometrical Demonstration perfectly exact, albeit they ap­ proche so nighe as ordinarie experiments will hardly discouer the difference, which I haue of purpose doone, the rather to animate Mathematical Practisioners by tri­ all to finde them out, and thereby perhaps also to discouer other more rare Secrets then I haue hitherto thought vpon. For by experience my selfe haue founde manye rare Mysteries in that Science, which I should neuer once haue amused on, if suche Scales and Theorikes (as my Father by his long painefull chargeable experiences in great Ordinance ioyned with his Mathematicall Science first inuented) had beene reduced to their accomplished perfection. And yet without those first principles left mee I must truely confesse I might haue spent the greatest part of my life in meere obscuritie, albeit I had by Office or otherwise enioyed the Manedging of all sorts of great Artillerie at my owne pleasure charge free. The burden where no doubte hath beene the cheefest cause that so many rare Mathematicians as Tarta­ lea the Italian and diuers others of these late ages in Europe haue mistaken so much, and performed so little toward the accomplishment of that Science. And although by publishing the same my Treatize of Martiall Pyrotechnie and great Artillery in the Latin toong, I should I knowe greatlye amplifie myne owne Fame, and the admi­ ration of such rare Mathematicians as at this daye liue in seuerall Nations of Chri­ stendome, from whome I haue for farre inferior Inuentions Imprinted in my Trea­ tize, Intituled Ala seu scala Mathematica, already receiued no small applause. Yet if I publish the same at all, I doe constantly resolue to doe it onely in my Natiue Lan­ guage: Aswell to make the benefite thereof the more priuate to my Countreymen, as also to make thereby other Nations to affect as much our Language as my selfe haue desired to learne the Highe Dutche: for the workes onely of two Famous men that wrote their Bookes in that toong, which cannot possiblye by anye other that haue not the same Spirites and perfection that was in the verie Authors be Transla­ ted: as appeareth euidently by diuerse Treatizes vtterlye peruerted by the mista­ kings and misconceauings of the Translators. These Praeludia therefore of a matter more serious and Important, good Rea­ der accept in goode parte, so shall I bee animated the more speedelye to imparte the rest, which some con­ trarye effect hath hitherto detayned from thee. Certaine Diffinitions, taken out of my thirde Booke of Pyrotechnie Militarie and great Artillerie, for explanation of the these Theoremes ensuing. The first Diffinition. FOrasmuch as by the direction of the hollowe Cylinder or Truncke of the Peece, the violence of all shot of great Artillerye is not onely directed but also increased I call that hollowe Cylinder of the Peece her Soule. The 2 Diffinition. The Metalline substance of the Peece of what kinde, shape or proportion soeuer I call the Body of the Peece. The 3 Diffinition. This Soule in all principall Peeces of Batterye, is euer a perfect uniforme Cylinder, com­ prehended with a Circuler columne, and two equall Circles, whereof the one I call the Head, the other the Base. The fourth Diffinition. That direct line which by Mathematicall Imagination dooth conioyne the Centers of the two circles and is the perfect and true direction of all Shot made out of great Ordinance, I terme the Axis of that peeces Soule. The fift Diffinition. Of this soule or hollowe Cylinder one parte is proportionally euer to be limitted for the Poul­ der and Bullet and that parte I call for distinction sake the charged Cylinder. The 6 Diffinition. The other emptie parte which is more properly called the Soule, because it bothe directeth and according to the difference of her proportion encreaseth or deminisheth the violence and force of the shotte I call also the vacant Cylinder. The 7 Diffinition. But in all such peeces as haue the Chamber for their Poulder either a lesse Cylinder or in forme Conicall or Campanall I terme the vacant Cylinder, onely the Soule of the peece, and the other her chamber be it Conicall or Campanall or Cylinder. The 8 Diffinition. Of the peeces body there is one parte of Counterpeyze called of Mathematitians Centrum Grauitatis whereabout there are to all peeces bodyes in their foundings adioyned two stayes which I call the Peeces Eares. "Eares" in this sense not found in OED. The 9 Diffinition. That parte of the Peeces body where the touchehole is or ought to be made to geue fire in the discharging of all Ordenance, I call the Coyle of the peece. "Coyle" appears to antedate earliest OED quotation for this sense ("coil," n.4, 1706). The 10 Diffinition. That parte where the body of the Peece is least neere the Head or Mouth. I call the Necke of the peece, and at these three points the Coyle the Eares and Necke, the Bodyes mettalline of all peeces are to be measured to knowe whether they holde their proportion of perfection for that kinde and purpose they are destinate. The 11 Diffinition. Anye peece is saide to lye Pointe blancke with any marke, when the Axis of her Soule directeth perfectly to the very middell or Center of that marke. The 12 Diffinition. And a marke is sayde to lye within Pointe Blancke when the Peece beeing directed with her conuenient Bullet and charge is able to reache and strike that marke. The 13 Diffinition. A marke is said to lye within the mettall of the Peece, when the Peece beeing directed not by the Axis of the Soule, but by the Cornice or upmost ring of her head and Coyle is able to reache the marke. The 14 Diffinition. The difference of these two ranges, I call the difference of the leuell ranges of the Soule and Body of any peece. The 15 Diffinition. The difference of these two measured in the body of the Peece I meane the excesse wherby the Semidiameter of the Ringe or Cornice of the Head dooth exceed the Cornice of the Coyle I call the Anomalye or Difference of the Soule and Bodye of all Peeces truly founded, and of com­ mon Cannoniers is called the Peeces Disparte. The 16 Diffinition. The Axis of the Bodye of any peece, I terme that straight line which passeth betweene the Centers of the two vtmost Circular Cornices at the coyle and Head of the Peece, the which in all Peeces truely founded is also the verie same Axis of the Soule. The 17 Diffinition. If the two Axes differ the Peece is false founded, and then they are either Parallele or make an Angle, if they be Parallele their difference I terme the Distance of the Axes of that Peeces Bodye and Soule. The 18 Diffinition. If they bee not Parallele, their Angles of variation are considered two wayes, that is to say in Altitude and Latitude, and those Angles accordinglye named the Anomalie Angles of Altitude or Latitude of those Peeces. The 19 Diffinition. There is in the Axis of euery Peece one onely pointe, wherevpon if the Bodye of the Peece should be suspended, she shall hang in a perfect Counterpoyse, and that pointe I call the Center of her Grauity or pointe of Counterpoyse. The 20 Diffinition. If the Peece should be deuided into two partes by a plaine Perpendiculare, cutting the Axis in that pointe of Counterpeyze, the section will be circular, and for Distinction shalbe called the Counterpeyze Section of that Peece. Diffinitions taken out of my fyrst Booke of Martiall Pyrotechnye and great Artillerie. Firste. FOr asmuch as euery Bullet violently throwne out of any peece of Ordinance at any Angle of Randon passeth a good distance directlye without anye great variation from the right line pointed out by the Axis, and then falleth into a Curue Arke, and last of all finisheth either in a right line or in a Curue, a­ proching nighe a right againe. For Distinction sake. The first Diffinition. THe first parte of the violent course of Gunners, commonly termed the peeces pointe blanke reache, I call the Direct Line of the Bullets circuite. The 2 Diffinition. The second parte beeing a Curue Circuite, beginning at the foresaide declination from the Axis, ascending to the highest altitude aboue the Horizon, and ending at a like Altitude to his beginning I terme for Distinction sake his middell Helicall or Conicall Arke. "Helicall" antedates earliest OED quotation (1613). The 3 Diffinition. The rest euen to the Horizontall plaine againe I call his Declining Line The 4 Diffinition. The Altitude of any Bullets circuite I call that line Perpendicular, which by Immaginati­ on Mathematicall, falleth from the Bullet at his verie highest of his Mount Perpendicularly downe to the plaine Horizontall: which line of Altitude coupled together, with the right lines from the top and foote, concurring at the center of the peeces circular Base, dooth make a right Angled Triangle. The 5 Diffinition. The Horizontall line of that Triangle I call the Base. The 6 Diffinition. The other sloope line is the line Hypothenusall. The 7 Diffinition. The peeces direct line of that circuite which is alwayes aboue the Hypothenusall for di­ stinction sake, I call the line Diagonall, for that there are seuerall of these Diagonall lines to all Angles of Random, and together with the line Horizontall, doe comprehende the Angle of Mounte. The 8 Diffinition. The peeces leuell Horizontall range, I terme the distance betweene the Peece and the first graze or bounde of the Bullet, when the peece at her discharge lyeth leuell vpon her cariadge not mounted vpon anye loftie Platforme, but such as lyeth euen with the true Horizontall plaine whereon the Bullet must playe. The 9 Diffinition. All other Ranges made by the Bullet on any Horizontall plaine, when the Peece is mounted at any seuerall Randones, I terme the Ranges Horizontall. The 10 Diffinition. And because euery Peece hath some Grade certaine of the Quadrant wherevnto mounted she maketh her vtmost Horizontall Range in such sorte as if yee mounte the Peece higher the Bullet shall flye a shorter Distance, and the Horizontall Ranges returne lesse and lesse againe. That pointe of vtmost randone Horizontall, I terme the Tropike point or grade, The 11 Diffinition. And because in Mounting the Peece Higher and Higher aboue the Tropike grade, the Ranges growe still shorter and shorter, so that at length yee shall come to that grade which shall cause the Bullet to range exactly his first leuell Horizontall Range, that Grade or pointe for Distinction sake I call the Grace Æquorizontall. "Æquorizontall" not found in OED. The 12 Diffinition. A declining plaine I terme any plaine grounde that lyeth not Leuell with the Horizontal plaine but descendeth downeward, making an Acute Angle with the plaine Horizontall and that Angle I call the Angle of Declination. The 13 Diffinition. An Enclining plaine I call that which from the Peece ascendeth vp, making likewise an Acute Angle with the plaine Horizontall, which Angle I call for Distinction sake the Angle of Inclination, The 14 Diffinition. And because the Bullet violently throwne out of the Peece by the furie of the Poulder hath two motions, the one violent, which endeuoreth to carry the Bullet right out in his Line Diagonall, according to the direction of the Peeces Axis from whence the violent motion proceedeth, the other Naturall in the Bullet it selfe, which endeuoureth still to carrye the same directly downeward by a right line Perpendiculare to the Horizon. For Distinction sake I call the first his Diagonall motion Violent, and the second his Perpendicular motion Na­ turall, and the compounded motion of these two his Mixte helicall Circuite. The 15 Diffinition. And as for the discouerye of the strange varietie of the Planets courses in the Heauens, Astronomers are enforced to vse sundrie kindes of supposed Circles Excentricall and Concen­ tricall, with their Epicicles moouing regularly sometimes on their owne Centers, and sometimes on Centers of Æquation, which they terme that Planets Theorike. So likewise in the discoue­ ring of the Reciprocall most strange varietie of these Bullets Helicall Circuites in the Ayre, making continuall alteration according to the Quantitie and Qualitie of the Angles of Ran­ don or Angles of Inclination or Declination of the Plaines whereon the Bullets playe, or An­ gles comprehended betweene the Diagonall violent and Perpendicular naturall motions: Be­ ing I say likewise enforced to vse portions of Circles, some Concentricall, and some Excentrical, some uniformelie deuided on their owne Centers, and some from Centers Equant in more strange manner to discouer and finde out these Helicall motions, I doe likewise terme the same Theorikes or Scales. The 16 Diffinition. And that which serues to discouer the different violence of all Peeces at Pointe blanke, howsoeuer Mounted (by me termed the lines direct of the Bullets Circuites, and lines Diago­ nall) I call for Distinction sake the Theorike of lines Diagonall. The 17 Diffinition. The other that discouered how high Bullets at all Randons can Mounte possiblye aboue the Horizon, I terme the Scale or Theorike of Altitudes. The 18 Diffinition. The thirde which discouereth the varietie of Ranges, of all Peeces at all degrees of Ran­ dome, I call the Theorike or Scale of Randons. The 19 Diffinition. The fourth and fift which discouereth the varietie and alteration of all ranges, by reason of the Inclination or Declination of any markes from the plaine Horizontall of that Platforme where the Peeces playe, I call the Theorike of Inclining Plains. The 20 Diffinition, The sixth composed of all these, and by conference of all their partes together framing a Theorike of perfection, discouering in all plaines Horizontall or varrying for all kinde of Pee­ ces and Bullets, whatsoeuer their Ranges at all Randones, the Altitude of their Circuites, together with their lines Diagonall and Hypothenusall shall bee named the Theorike of Ar­ tillery generall.