The third part of the principles of the art military practised in the warres of the United Provinces vnder the Lords the States Generall and His Highnesse the Prince of Orange : treating of severall peeces of ordnance ... : together with a list of all necessary preparations appertaining to an armie ... / written and composed by Henry Hexham.

TREATING OF A PETTARD, WHICH IS A KIND OF A short peece of Ordnance, devised of late yeares, for the blowing open of Gates, Ports and breaking down of draw-bridges, Their making, use, and manner of charging are here discribed. The eleventh Chapter.

THE Modell or forme of a pettard, represented unto you in the next plate and figure, is not much unlike to a Grocers, or an Apothecaries Spice-morter, and some are ta∣pred much like a Coopers payle, little deeper then the Dyamiter of their mouthes but being not aboue ¾ in dyamitre at their bottome, or breech of their mouthes calibre, and in thicknesse of mettell •• of the Dyamitre at their breech, and lessening by degrees in thick nes towards their mouthes, Their magnitudes are some to hold but one pound of I ow∣der, or lesse, and others to hold 50 pound or more, and they vsually allow foure pound of brasse, or fiue pound of yron, to cast a pettard for one pound of powder, and two hundred 50 pound of brasse, or 3 hundred pound for a pettard that shall hold fifty pound of powder, using those proportions diminished for lesser, and augmented for greater, as Mr Norton in his practize of Artillery describeth.

The demonstration thereof out of Diego Vffano.

Being massie and heavie (whereof the figure A is the mouth, B the breech neere the touch-hole) it must be carried upon a thick-board or planck, marked E E, and then layd upon a Karr noted C D, which serues not only for the use of it, but also to raise it, when you are to hang and fasten it upon a Port. This planchier in the midst, hath a round hole in it marked H, Through which the nose, or mouth of your pettard is enchased. Aboue it there are two yron rings to hang it on to two Crochets marked G screwed fast into the port marked A with a match to giue fire unto it. A A are the Bungs, or tampkins wherewith the mouth of the Pettard is bunged up or stopped.

The outside on which the planchier is enchased being three inches thicke is even and plaine, armed with strong plates of yron to defend it from splitting: it is also to be under∣propped with the forked rest, and stayed in the ground at the hirder end to keepe it from recoyling.

When you charge your pettard, you put a round stick into the very midst of the mouth of it down to the bottome, about the length of halfe a cube and some two fingers in cir∣cumference, & put no more into it at a time, then the better part of a pound of fine come powder, and so fill it litle and litle, stamping it well in, round about the said stick, with yron drifts or wodden stampers within the concaue of the Pettard, vntill it be filled within one fingers breadth of the top and haue its due charge, then tume your stick in the midst about draw it out gently and fill up the hole out of which you draw the sticke with fine pow∣der that when you are to giue fire at the touch-hole, the whole charge within may be fired in the twinckling of an eye, And having thus giuen it the full charge, then stop the mouth of it closse with the bung or tampkin noted A, which must be of the thicknesse of your litle finger, and lastly couer the mouth thereof with a thick waxed cloath, and power melted waxe vpon it some two fingers thick aboue the tampkin, & thus much for the charg ing of a pettard.

Now we come to the fastning and hanging it on a gate, to do this well, you must first scrue in fast into the Gate the Crochets marked G. and make choice as neere as you can of the weakest place of the Gate or Port, where it may easiliest be broken open, upon this hang your Planchier and put the mouth of your Pettard through the hole of the Planchier aboue mentioned, then fasten it firmly to the Port. There is also a third ring or a crochet, and the eare of your Pettard through which you put a roap to bind your pettard fast to the Port.

And being thus fastened, and hung vpon a port, nothing remaines then, but to give fire to it, but your Pettardier must haue a singular care, that he orders his match so, within the Touch-hole, that is giues not fire too soon, but that he and the men which help him may haue leasure and time to come of with safety, before the pettard burst open the gate, least any be mischeived with the violence of the breaking of this diabolicall Engine, which hauing taken its operation, and the gate flying open, your men must presently enter, but one caviat I must giue you by the way, that while they are a fastning and hanging on your pettard, to the gate, you must haue a speciall care, to look to the Percullies, that it be well vnderpropped to keep it from falling, for I my selfe was onee vpon a peece of service at Venlo, that yeere as the Marquis Spinola took in Rhyn-berg, and having burst open one gate of the Town, the petar∣dier hanging his pettard vpon a second gate, a woman throwing a great stone down from the top of the wall fel'd the pettardier while he was a doing his businesse, which gaue the ene∣my so much time that they knocked down their percullis, and so catched some 30 of Moun∣seur Chastilons Company between the last gate and the percullies, who first should haue en∣tred the Town, and being massacred and taken pirsoners, the surprising of that Town by this accident failed. The figures following doth demonstrate all things vnto you that it may be the better vnderstood.

[illustration]

A QUESTION PROPOUNDED TO THE BATAVIAN INGINIERS, by Master John Baptista Mathematician of ANTWERP, for the Battering of a HORNE-WORKE.

ACCORDING TO THE PROVERB. Let skill appeare by good demonstration. And Dissolved and Resolved by that famous Mathematitian, Master JOHN STAMPION of the HAGH in HOLLAND.

[illustration]

The report (Ingenious Batavians) of some of your unskilfullnesse, hath spread it selfe farre abroad, and flown I know not into what country, and yet no speciall thing is come to the view of the world, whether out of your own selfe conceit, or from some blast of Superbitie: It is so that I my selfe have thought good to propose this question unto your ingenuity, as a Touchstone, that it may be dissolved, according to the true Touchstone of that noble Science of the Mathematicks by which it may be known.

THE PROPOSITION IS THIS.

SUppose a Generall having approached to a certain Hornwork which is here decyfered by the Letter H. and hath come with his line or fapp near unto the moat of this Horne∣work, and there desires to cast up a royall battery in the place noted A. for to flanck upon E. D. and D. C. in such sort, that the force of the Canon may beat aswell upon the Face as upon the I lanck, to wit, Proportio Equalis, by an equall proportion. Together that the two wings C. D. and G. I. and the distance G. D. which are all alike to each other, may be flancked with the lines and blowes, yet so, as the distance of the battery A. to the point C. be no more then sixty Rodd or six hundred foot, and the breadth of the Hom-work to be as M. N. or O. P. and being measured, is found to be 34. Rodd, 7. foot, and 4. Inches. The question is how this must be wrought.

Moreover of the same Hom-work the face is as much as the two greatest valuation of 1. a. there a. 1. aaaaaaaa. 875. aaaaa. 3470. aaaa. 20640. aa. 104040. a. are alike to 5. aa aaaaa. 1147. aaaaaa. 28182. aaa. 118800. and the distance A. C. no surther then 900. foot. O. A. and the rest of the conditions as abovesaid. The question is to find out the breadth of the Horne-work, and also the other parts as is abovesaid.

THE MATHEMATICALL DESSOLVTION VPON THIS Antwerpian Question: Dedicated to all the Lovers of that noble Science, by Master John Stampion de John, Mathematician.

[illustration]

Sirs. The wing of fame hath of late fluttered out that now our ingenuity is brought to the tryall of the Touchstone, by proposing of a certain Question under the name of Senior John Bap∣tista of Antwerp, whose pate is swoln with selfe conceitednesse and pride, which being not worth the answering, I will come to the solution of it, ra ••her to give satisfact on to our Batavians, then to fulfill the desire of the Propounder: And this may serve as an introduction unto it, to the end, that the honour which he doth assume unto himself, may not wholy be appropriated to him.

THE DESSOLVTION.

LET this figure above of a Horn-work (as hee saith) be decyfered by H. whose breadth M. N. is known to be 34. Rodds, 7. foot, and 7. inches, and the required battered noted A. whose place is likewise found out by the known conditions. The first co ••dition is, that the violence of the Canon planted upon the battery A. beates with as much force upon the flanck E. D. as it doth upon the Face C. D. whence it is manifest, that the Angle of the espaule or shoulder EDC. being devided into two equall parts with the right line T. V. D. A. that then this battery of necessity must come to be in the right line T. D A. Secondly, that the face D. C. and I. G. and the distance D. G. may with the like Canon shot be flancked and beaten upon by the battery A. that is, when as the Angles I. A. G. G. A D. D. A. C. are alike one to the other, whence will follow, that through the five points, C. D. G. I and A. a circular circumference will passe. Now for that which concernes the third known part, namely, as that the batterie A. must be no further from C. then sixty rodd, or six hundred foot, A. being the greatest distance in the circumference as is in the third booke and fifteenth proposition which is taken from of the middle-line of Euclids propositions, we have found out accor∣ding

to this preparation, the middle line as C. Y. to be sixty rodds, the right line C. I. to be nine 34. rodds, 7. foot, and 7. inches, or 34. 77/00 and the lines I. G. G. D. and D. C. to be answerable one to another. Let G. now be the Center, Then substract I. G. and Q. D. cutting through C. I. in A. and F. then will I. A. or I. C. be alike to one of the lines, I. G. &c. because now Q. I. stands alike to I. G. as I. G. is alike to G. A. and by the fourth proposi∣tion of the sixt book, as Q. A. is alike to A. F. so also Q. G. is to G. D. or as I. G. is to G. A. the cube upon I. G. with the corps which is made upon the quadrate I. Q. as superfi∣cies, and the depth I. C. are together alike to the corps upon the Quadrate I. Q. as super∣ficies, and the depth to be three times the length of I. G. whence will follow, aswell by the corporall cutting of a dye, as we have shown in our New Algebra which shall shortly God willing come out in English, as by Sectione Com. by which I. G. is found to make 28. ½—V 263. ¼ so doth E. F. or D. C. likewise, and lastly the Angle E. D. C. being devided into two equall parts by the precedent T. D. then you have the cutting of A. in the circum∣ference out of Q. where your battery is to be cast up.

Now whereas Mr Stampion hath not expressed the finding out of the face G. I. by rea∣son of the little space contained therein, the more because he hath fully shown the Dissolu∣tion thereof in his new Algebra, we will here demonstrate the whole working thereof, how the face G. J. by his new Algebra annexed hereunto is to be found out.

The operation.

Setting down for G. I. x. so comes xxx + 31293 alike to 2700. x. or xxx—2700. x like to—31293. which is an equality in the third case of the Algebra of Mr. John Stampion, which being changed by the second case comes to be xxx—2700 x. as 3129. is alike, out of this vacant number 31293. is extracted a Cubice-root, 2700. times, the side as Mr. Stam∣pion teacheth in his new Algebra, pag. 112. and 113. comes the valuation of x 57. whereof the whole working shall here be set down as followeth.

The finding out of the first Letter.

〈 math 〉〈 math 〉

The finding out of the second letter.

〈 math 〉〈 math 〉

This 57. is now the valuation of x as xxx 2700. x is like to 31293. for the same value the signe—set down commeth 57, for the least valuation of the equality then in xxx—2700 x is alike to 31293. Now to find out by this 57. the length of the face, G. I. as followeth in the Rule fol. 138. of his new Algebra, that is, taking the half of 57. which is 28. ½ and multiply the same quadrate, and the product will be 812¼. whose tripple is 2436 ¾. and being substracted out of 2700. the number x. remaines 26; ¼ whose square root is V. 263. and being deducted from the half of 57. as being 28½ there remaines 28½.—V263. for the length of the face G. I. and E. F. and D. C. doth as much also.

Observe the manner of the Operation.

〈 math 〉〈 math 〉