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ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A06780	A treatise of artificial fire-vvorks both for vvarres and recreation with divers pleasant geometricall obseruations, fortifications, and arithmeticall examples. In fauour of mathematicall students. Newly written in French, and Englished by the authour Tho: [sic] Malthus.; Traité des feux artificiels pour la guerre, et pour la recreation. English	Malthus, Francis.; Cecil, Thomas, fl. 1630, engraver.	1629 (1629)	STC 17217; ESTC S109781	49,979	283

head then foure times 8 is 32 and set them vnderneath and the whole will bee 21 32 parts of a fathom which certainely containeth the required superficies CHAP. XI Multiplication of entiers and Fractions TO multiply ¼ by 2½ you must first of al reduce the whole into fractions and then as here aboue multiply numerator by numerator and denominator by denominator and the product will bee 45 ●8 as plainely appeares by the example following But if it were proposed to multiply greater numbers as 20 by 15 26 29 then multiply the 15. intiers by the deno 29. of the fraction then adde the numerator 26 of the same fraction which done will mount to 461 29 then set the 461 ouer a line and the 29. vnder it and afterward multiply the 20 intiers by the 461. which done diuide the product of the whole by the denominator 29. and the numqer required shall bee 317 27 19 as appeares CHAP. XII The diuision of Fractions TO diuide ¾ by ⅓ each numerator is to bee multiplied by each denominator opposite and set the product ouer a line aboue them and then diuide the greatest product by the least as followeth CHAP. XIII To diuide intiers and fractions by intiers and fractions TO diuide 12⅔ by 3⅙ they must first be reduced all into fractions as before and then you must multiply the numerators by the denominators acrosse as followeth and then diuide the greatest product by the least as this example doth cleerely demonstrate CHAP. XIV Evaluation of fractions which may not be abridged SVppose you were to abridge 7 9 parts of a fathom first you must consider what are the parts of the intier or whole as 6. foot or 72. inches then you must multiply the numerator 7 by the denominator 72 parts and let the product bee diuided by the denominator 9 and then you will finde 56 inches for the eualuation of 7 9 parts of a fathom By this meanes any fraction may be abridged as well in Geometrie as as commerce although they seeme not to be abridged CHAP. XV. For the eualuation of measuring lands YOu must consider that the fathom of 6 foot in length doth containe in superficies 36. and that the 72 inches in length doth contain in superficies 5184 inches and of other measures then to valuate a fraction of 19 4● parts of a fathom square in superficies you must multiply 5184 by 19. and diuide the product by 47 and there will be 2095 inches for the square of 29 47 of a fathom square and so of other like measures CHAP. XVI Of the rule of three without fractions MVltiply the second number 400 by the third 12. and product 4800 by the first number 4 and the quotient shall be the number required and dispose your rule as followeth months pounds months If in 4 400 12 The probation of this Rule IS to multtplie the first number 4 by the fourth number 1200 and to multiplie the second by the third and the two products will bee equall if the rule bee well made CHAP. XVII Of the rule of three with intiers and fractions FIrst all the intiers must bee reduced into fractions as followeth yards pounds yards If 2¼ 12½ 7½ 9 4 25 2 15 2 Which done you must multiply the second number of fractions as by the third number of fractions 15 then againe multiply the product by 4 the denominator of the first number and then say 2 times 2 or 4 and 4 times 9 is 36 which must bee set vnder the line by which you shal diuide the first product 1500 and the quotient shall be the number required as appeares Heere followeth two examples differing the one from the other whereof the manner of multiplying the one is more easier then the other the first is multiplyed as the precedent but the last is multiplied first by all the intirres viz. by 3 by 8 and by three leauing the fraction ● by it selfe and after all take the thir● of the intier viz. of 50000 saying th● third part of 5 is one rest 2 for the 10 which is valuated at 20 then say the third part of 20 is 6 and so rests 2 for the second 0 and so to the end and what shall rest at last shall be set ouer a line and your 3 4th or 5 vnder the line then all being added together you shal diuide the product cutting off the figures to the quantitie of the first number saying by ten by a hundred by a thousand by ten thousand by a hundred thousand the remainder is the number required as appeareth 191⅔ The first example The second number being mul●●plied by the third doth mount to 57500000 and being diuided by the first multiplyed by 3 as before is taught the quotient will be 191 2 ●0 The second example CHAP. XVIII Extraction of the square roote FIrst dispose your numbers as followeth out of which you meane to draw the roote separating your figures by two and two beginning at the latter end but first strike the halfe circle 73 21 01 and then say the root of 73 is 8 and set 8 before the half circle rests 9 then double the quotient 8 and say 2 times 8 are 16 and set the 6 vnder the last figure of the second part of figures and 1 vnder the first figure of the first part a● in this first example Then say how many times is 1 in 9 and it shall be 5. which you shall also set vnder the 1 of the second separation as apppeares in this second example And then say 5 times 1 are 5 which taken out of 9 rests 4 and 5 times 6 are 30 and 30 out of 32 rests 2 and 3 out of 4 rest 1 and then againe say 5 times 5 are 25 which out of 3● rest 6. and 3. out of 12. rest 9. and then double the quotient and say twice 5 are 10 set 0 vnder 0 of the last separation and keepe ● in memorie and say twice 8 are 16 and 1 that I keepe in mind makes 17 then set downe 7 vnder the 5 and the 1 vnder the 6 of the middle separation as appeares in this example following And then say how many times is 1 in 9 and it shall be 5 times which shall be set downe for quo●ient and also vnder the last figure 1 and then say 5 times 1 are 5 out of 9 re●ts 4 and 5. times 7 are 35 which out of 36 rests 1 and 3 out of 4 rests 1 and 5 times 0 is 0 and 5. times 5 are 25. out of 31 rests 6 3 out of 10 rests 7 and 1 out of 1 rests 0 and so the rule is ended as appeares following CHAP. XIX Another example of the square root After you haue separated your figures by two and two and drawne 251 the square roote there doth yet rest 268 which must bee reduced into fractions and to begin set that rest 268 ouer a line at the end of your root and that rest

tackit of the locks fasten an yro● rod and let the other end of the 〈◊〉 rod passe through the ship and ●ee made fast to peeces of strong wood in the manner of a gyrdle on ●he outside of the ship which is re●resented in the figure by the points ●o that touched vpon the outside a●y thing rudely the locks must needs ●trike fire and set going all the rest ●nd to make it give fire being hooked in the inside to draw it ashore 〈◊〉 out of the way let there be made ●ast to each clicket of the locks long wyers and the other ends of the wyres may be fastned to pieces of wood in the inside of the ship round about the edge so that the first thing that shall touch it sets all going as vpon the outside but the pieces of wood vpon the outside ought to be very neere the water as doth demonstrate the figure with the points and so to conduct this ship as neere to t●● place as may bee without dang●● there may be fast ioind to the stern piece of timber noted A B to the en● whereof may bee fastned two lon● ropes and to them two little boats i● which men shall be for the condu●cting therof This here is but a spar● of inuention to which the industri●ous Enginier shall adde of his wha● he please and take this but for an entry of such workes for although haue here set downe gunlockes t● giue fire to the Canons my meaning is that they bee made like gunlocks but ten times stronger and harder i● going off leauing to the iudgemen● of the discreet Enginier the true disposition of his owne designes CHAP. XII How to make a Petard DIego Vsan a Spaniard Francis Tibourele a Loreine and Master Robert Norton an English man hauing al written of fireworks and neither of them all vnderstanding how to charge a simple Petard I thought fit to end these fireworkes for wars by the description of the same that being of great violence to make entries breaches into towns castles or houses the morter prescribed may serue to petard a place as hath beene sayd already but whosoeuer would make exactly a Petard ought to cast a Morter much like vnto an Apothecaries morter as doth represent the figure A observing the rules following if you make it to weigh sixe pound of mettle let the calliber or bore be of such bignesse to containe one pound of powder or one pound and a halfe if you adde or diminish more or lesse mettle augment or diminish the calliber likewise to hold the fourth part of powder which the mettle doth weigh and for the charging of the Petard fill it only with the best gunpowder you can almost to the brim and then couer it with a round bord made fit for the purpose leauing aside all frivolous directions written by others aforenamed and for the ●riming of the Petard make a port-fire of slow composition as for the precedent fireworkes of what length you please and to breake open the place you desire if it bee accessible then with the heele or breach of the Petard vpon the ground or some great stone or piece of wood and the mouth against the part of the dore gate or elsewhere which you shall iudge fittest but if the place bee vnaccessible then make a kinde of a little Cart with two or foure wheeles as doth appeare by the figure B with a long forke very strong to beare the Petard and also support the requile of the Petard shooting off This forke is represented by C but the backer end of this forke must bee stayed either in some hole or against a stake or other meanes Now here in this treatie not intending to imitate these late Authours who writing of artifi●iall Fire-workes have prescrbed natures and compositions of almost all manner of drugges the meanes whereof may bee found in anie Apothecaryes shopppe doubtlesse eyther to perswade the curious Readers that they had profound knowledge many rare secrets or else the better to hide their ignorance by that great confusion and expence whereunto few or none would extend and vse their purses to make proofe and experience of I will finish this treatie of artificiall Fire-workes for Warres and goe forward to the second treatie of Fire-workes for pleasure and recreation and explaine in the Preface apologitike for what vse all these vnknowne dregges are fit for which seemes to those that are ignorant of such rare and wonderfull effects As Salarmoniake Antemonie Arseneeke Vitrioll Stonelime Thutie Adamant stone not forgetting quick siluer THE SECOND TREATISE OF ARtificiall Fire-workes for pleasure CHAP. I. PErspicuous plain shall be the method to make all manner of Fire-workes for pleasure which heare I will set downe for the contentment of all curious and ingenious Artists without such a number of vnknowne dregges for mixtures as many heretofore haue prescribed more fittest for some prodigious actions then to mingle for artificiall fireworkes and principally for those which are invented for pleasure for these haue no need of venemous smoaks to poison the spectatours making mirth turne to mischiefe which notwithstanding cannot be done in an open ayre neither haue they need of such a continuing ardent and violent flame as to consume Cities or habitations but onely of a gentle and pleasing flame to the eyes of the spectactors and thus they are divided into three sorts The first are those which ascend and mount into the ayre The second are such as consume vpon the earth The third and last sort are those which swim and burne in the water Those which worke their effects in the ayre are ●●kewise divided into three sorts the ●hiefest and most noble of all are the ●allouns The second the rockets ●nd the third are flying saucissouns ●hose which stand fixt vpon the ●round are also distinguished into ●hree sorts The first are the rockets ●or the ground the second the fierie ●nces and the third saucissouns The ●res for the water may haue their ●iple diuision globes or balls make ●he first double rocket the second ●nd single ones the last and to treate ●f euery one in particular I wil begin ●ith the rockets for the ayre and ●●rst of all describe their moulds and ●he measures which must be obser●ed in making of them CHAP. II. A method to make moulds for rocket for the Ayre ALthough that ballou● are absolutely th● most noble sort of fir● workes yet for so muc● as all great fireworkes are compose● rather of rockets then of balloun● I thinke it conuenient to begin th●● second treatise with these first of a●● making the description of the moulds which may bee made eith●● of brasse or wood the one being 〈◊〉 good as the other for vse if the mea●sures following be obserued whic● ●●all be conuenient for all sorts of ●●gnesses because they depend one●● vpon the calliber or bore and that ●eing enlarged the other parts will ●e all enlarged also that being dimi●●shed all the rest will be

shal be required to hold those rockets which you meane to place in each one bu●1 these boxes must haue a false bottom full of holes for to passe euery rod of euery rocket apart and hauing filled let the boxe which by proper name is called a partment be couered with a leafe or two of paper pasted close but to giue fire to the rockets let there be made a hole thorow the partment through it shall passe a little peece of stoupel or cottē wieke and giuing fire to that all the rockets within the partment fly out and in the same manner shall you giue fire to all your fierie lances with a stoupel going from the one to the other and as for your girondells you shall giue fire to them with a match as you desire that they should play and by this meanes all your fire-workes shall begin to play at once except those parts which shall bee reserued without priming to be fiered by the hand as best shall seeme to the artist or enginier and so the industrious shall not faile to accomplish his designes obseruing all the rules prescribed which being at large laid down I will goe forward to the next chapter and there shew how to make a most pretious vnguent for all maner of burnings as well of common fire as of artificiall fire if by hazard anie mischance arise CHAP. XXII A most pretious vnguent for any burning LEt no man wonder if hauing ended this Treatise of fireworkes I take in hand to describe a little part of Chirurgerie whch I confesse to haue taken out of a Treatise written by Thybourel a Chirurgion of Loraine and hauing made experience of this vnguent diuerse times as well for burnings as that for other accidents I may say with boldnes truth that there was neuer the like secret of this kind left to posteritie specially against hurts come by fire and which leaues lesse scarres after the healing of the places wounded and therefore I haue set downe the very words which Thybourel hath written in the last chapter of his 4th booke intituled Recueil de plusieurs machines militaires Take fresh hogges grease or lard as much as you please and boyle it taking off the skim vntill there arise no more skim then set the lard three or foure nights in the ayre abroad after which it must be washed in running water to take away the saltish nature and also to clense it white then melt it and keepe it for your vse Bacon may serue in stead of lard Otherwise The white of an egge or fresh butter being mingled together and well beaten to an oyle are excellent Another sort most excellent Take a stone of vnslacked lime or otherwise called quicke lime and let it dissolue in cleere water and when the water is setled powre it gently out from the lime through a linnen cloth then put as much sallet oyle as you take water together and beating it all to an oyle you shal haue a most excellent vnguent for all kind of burnings neither of these vnguents haue any scarre but are precious remedies for the afflicted We haue seene Impostures couer sores with this water alone but obseruing superstitious ceremonies saying vaine prayers but we assure the posteritie that the water onely is sufficient to heale wounds and s●res onely washing them with it and couering them with a linnen cloath wet in the same water without any superstition it doth modifie and percute by which it doth supply nature and doth heale sores better then our ordinary vnguents Thus may you see how this braue Chirurgion that set forth to the face of the world the perfection of this vnguent which cannot be sufficient-praised confirming by his own confession that the Chirurgions do not vse such good remedies in their shops and ordinarie operations wherfore I haue set downe his owne words that no man may esteeme mee inuenter of Calumnies against the practitioners of Chirurgery nor any others as many now adayes seemes to write with serpents tongues stinging vertue on euery side against whō viperous venoms patience is the only antedote leauing them to sweat vexe and torment themselues in their insatiable rage and to end my discourse touching the perfection of this vnguent I will assure all these who shall haue neede and make vse thereof that they shall find in operation what I haue here set downe in description A Treatise of practicall Geometrie TO satisfie diuers of my friends and yeeld to their desires whose treaties haue bin such powerfull commands to me that I haue beene constrained to lay aside and forsake my own proper will and follow theirs I haue set forth this little Treatise of practicall Geometrie to the view and censure of the world which I acknowledge to be vnworthy of so many singular and industrious wits as yearly spring vp in this Iland and the adiacents thereunto notwithstanding I haue giuen way to their requests for their priuat contentment and to assure the world that I haue nothing no not my owne will proper to my selfe but that I will follow as neere as possible I may the precepts and documents of that ancient wise and diuine Philosopher Plato who saith Non nobis nati sumus sed patriae amicis we are not borne for our selues but for the seruice of our countrey and friends then for the satisfaction of my friends and seruice of those who will accept these my labours I haue cleerely and in few words set downe the manner how anie man who hath neuer so little studied Geometrie may take any distance or heighth depth or breadth with two little stickes yea e●en strawes being laied a crosse also I haue set downe a method how to take any kind of heighth distance or depth with the Sector without anie arithmetike or rule thereof and also by the sines tangents and secants the whole beeing very portable to refresh the memorie to strengthen and augment the knowledge of those who for want of practise haue not the perfect vse of those instruments then first of all I will set downe the manner how to accomodate and dispose the sticks twiggs or strawes for the measuring of any distance The method how to make the Crosse. HAuing two stickes the one long and the other somewhat short as are represented in the figure following by CF and DE then marke vpon the sticke CF points the one distant from the other precisely halfe the length of DE and let there be a hole made through the sticke DE so that it may slide vpon CF from end to end and you shall know the two parts of the crosse by these names the longest part CF shall be called the index and the shortest DE the crosse Now if you haue any heighth to take then fasten to one end of the crosse as to D a perpendicular or plummet and for the more easie and iust operation you should haue a foot to support the crosse the instrument being thus prepared you may measure

shall be numerator of the fraction and to finde the denominator only double the root 251 if it be bigger then the rest but if less as here adde one to the doubling of the first figure saying twice 1 is 2 and 1 that I adde makes 3 adde only double the rest and set it vnder the line and that shall be the denominator of the fraction and to haue the root of this fraction here aboue first take the root of the numerator and set that root ouer a line and it shall be numerator as appeares following Then draw roote of the denominator and set it vnder the line and that shall be a denominator and so you shall finde 16 22 and what rests is vnsensible But because that this fraction 16 22 is not precisely perfect and that there is a rest in each extraction you may operate as followeth to haue it mooue exactly adde as well to the numerator as to the denominator two 00 or foure or sixe c. and from each product or quotiēt out of one figure for euery two 00 which you shall haue added and the more that you adde 00 the more precisely you shall haue the roote as appeares following But if it were proposed to extract the square roote of 16 25 there would nothing rest nor would it bee needfull to adde any 00 for the root of 16 is 4 and the root of 25 is 5 and so wee should haue 4 5 and the like in all such other accidents and thus much for Arithmetike Vale. FINIS THE CONTENTS A Treatise of Fire-works for Warre page 1. The manner how to make the Morter-peece pag. 5. The manner how to make Granades or mettle for the morter or hand pag. 10. The manner how to make Granades of Canuas for the Morter page 16 How to make fierie arrowes pag. 20 How the Granads are to be charged into the Morter page 24 Thn manner how to shoote the Granads page 28 A most violent method to set a towne on fire page 33 How to make Granads to cast with mens hands pag. 39 How to make fierie wheeles to bee cast vvith mens hands pag 45 How to make a ship of wild fire pag. 48 How to make a Petard pag 55 A Treatise of artificiall fireworkes for pleasure page 61 A method to make moulds for rockets for the ayre page 64 How to make flying rockets for the ayre page 69 How to make moulds for rockets for the ground pa. 74 How to make the composition for rockets vpon the ground page 76 The manner how to make Serpents pa 78 How to make golden rayne pag. 81 How to make starres pag. 83 How to make Starres giuing great reports page 86 The manner how to make Saucissons page 88 How to make Stoupell or preparing of your cotton-wieke pag. 91 Thu manner hovv to assemble and set together the parts of a rocket pag 94 Hovv to represent diuers sorts of figures in the ayre with rockets page 97 Hovv to make fierie boxes pa. 101 How to make fierie lances pag. 103 The manner hovv to make rockets for the vvater page 105 Hovv to make Girondels or fiery wheeles pag. 110 The manner hovv to make Ballons pag. 113 Hovv to make flying Saucissons pa. 120 Hovv to make short Guns for the Saucissons page 123 The manner hovv to dispose and build a great or little fireworke pag. 125 A most pretious vnguent for any burning pag. 131 A Treatise of practicall Geometrie page 136 The method hovv to make the Crosse. pag. 139 Hovv to take a height accessible pag. 141 How to take a height inaccessible or one height vpon another height pag. 145 Hovv to take any distance vpon a place accessible or inaccessible page 149 Another manner how to take a distance inaccessible pa. 151 How to take a distance onely vpon a line paralell to it pag. 165 Hovv to take the depth of a Vally p. 157 The manner how to take either distance or altitude vvith the Sector pag. 161 How to take any distance or altitude inaccessible with the Sector pag. 165 Definitions of Sines Tangents and Secants pag. 168 Hovv to take any altitude or distance by the Sines Tangents Secants pag. 171 Hovv to take any altitude or distance inaccessible by the Sines pag. 176 The manner hovv to take the Plane of a towne or any place out of musket-shot page 180 A Treatise of Fortification as vvell regularly as irregularly pag. 184 Denominations of the parties of Fortification pag. 186 Hovv to build a trianguler Fort. p. 189 Hovv to build a square Fort. pa 192 Hovv to build the Pan●agone Fort p. 195 Hovv to build the Fort Hexagone p. 198 Hovv to build the Heptagone pa. 201 Hovv to build the Octogone p. 204 The description of the height de●th and thicknes of euery part of a compleat Fortication p. 206 The manner how to fortifie places irregularly p. 209 A Fortification irregular p. 210 Another manner of fortifying irregularly p. 213 A Treatise of Arithmetike Addition p. 216 Of Substraction pag. 219 Of multiplication p. 222 Of diuision p. 224 Hovv to reduce intiers and Fractions into Fractions p. 229 To reduce all fractions into one denomination pag. 230 Ad●itions of intiers and fractions p. 234 Substraction of Fractions p. 235 Addition of Fractions p. 231 Substractions of intiers and fractions p. 237 Multiplication of Fractions p. 239 Multiplication of entiers and Fractions p 241 The diuision of Fractions p. 243 To diuide intiers and fractions by in●iers and fractions p. 44 Eualuation of fractions which may not be ●bridged p 245 For the eualuation of measuring lands p 246 Of the Rule of three without fractions p ●48 The probation of this Rule p. 249 Of the Rule of three with intiers and fractions p. 250 The first Example p. 253 The second example p. 25● Extraction of the square roote p. 255 Another example of the square roote p. 258 MILITARY BOOKS PRINTED FOR T. and I. 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