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 MU?:* 
 
 
 
 
W P/ROTECHNIA 
 f Or aDifecurie ofarfificiall } 
 Fire worker for Pleaflire 
 
 Irupyrounels o^y jfrb' 
 are ■n^airiefy anti -peripicucuflv 
 lata downed loyelher'i v Jundrj 
 
 fief (Fiction) (tol/i* (?dia Cl amt) 
 
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 Circular, ' yeyermed by y deLyc* 
 
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 TO 
 
 THE RIGHT HONOV- 
 
 RABLE, THE EARLE OF 
 
 JMettporf, Mailer of his Majefties Ordnance, 
 my lingular good Lord, 
 
 Honourable ; 
 
 Am not induced to prefent this 
 Treatife to your Lordlhip for any 
 worth that is either in it, or in my 
 felfe,the Author of it; the thing be- 
 ing of fmall moment, and my felfe 
 ©fas little account ; but your Lordfhips Angular 
 clemency to all, and your Honourable favour 
 vouchlafed to me in particular, hath made me thus 
 bold, and hath caufed me thus farre to prefume. I 
 have beene for ceftaineyeeres paft, and fo at pie' 
 fent am, one of the inferiour Gunners of his Map 
 ftie } . and ever fince I held that place, I have endea- 
 voured to gainefoch skill and experience, as I e- 
 
 fteemed moft recjuiiite for that lervice. And to that 
 end I have bellowed fome time and expence, as my 
 occafions and ability would permit, in the pradlifo 
 of 'tA ftiUery and Fire-rnrhes , wherein though I 
 have chiefly aymedat fuch conclufions as might 
 be ufefullagainll an enemy in the field, yet thefe 
 halcyon dayes of peace and tranquility, which 
 
 through 
 
 y 
 
' TheE piftle Dedicatory. 
 
 through thegoodnefie of God we havefoTciwen- 
 joyed, have given mee occafion to invent and & pra- 
 <5tife fuchalfo as thefe following; which howfoever 
 they may feeme to ferve onely for delight and exer 
 cife, yet as by the handling of thefe there may bee 
 gained knowledge in the natures and operations of 
 
 the feverall ingredients and their compofitions- fo 
 
 thedueconfideration of the ordering of them may 
 excite and ftirre up in an ingenious minde, fondry 
 inventions more ferviceable in times of* warre 
 Now becaufe your Lord flop hath of late, by the 
 gratious providence of the Almighty, for your ex- 
 traordinary wifedome and worth, beene advanced 
 to that eminent place, upon which I have fome de- 
 pendance, and to which I ftand obliged by my fpe- 
 ciall fervice (to which alfo all workes o fTyrotech- 
 me may feeme to have relation)I hold it my bouii- 
 den duty to prefent thefe firft fruits of my labours 
 to your Honour, as an unfayned teftimony,and an 
 undoubted evidence of my faithfull obfer vance, and 
 fingular refpedt to your Lordihip : which if ’you 
 lhall beplealed to take into your fpecial Patronage 
 and protection, I lhall be in good hope to be freed 
 both from the venomous tooth of Mamin, and 
 from the malevolent afpedt of Zoilus, and from the 
 poyfoned breath and ftingingof the reft of that vi- 
 perous brood,and lhall alwaies remaine 
 
 Your Honours in all dutijdll objeryance^ 
 
 Iohn Babinot os. 
 
 / 
 
TO 
 
 THE READER 
 
 Courteous Reader, 
 
 i y 
 
 * or name owne private recreati- 
 on^ [pent fome vacant boures in the 
 finely and contemplation of tbofe ar- 
 tificial! Fire-works which are dif- 
 • courfed of in the enfuing Treatife • f 
 held it requijite for my further and better Jath facti- 
 on > as any opportunity did offer it felfe , to make expe- 
 riment of fome of the particularities there fet downe^ 
 and 1 did accordingly now and then bring into A& 
 that whereof before l had but a nicer e Notion, and 
 the bare and naked Theorie ; which becaufe it could 
 not be done fo privately, but that of necefiity fome times 
 it would come to the view of others • by that meanes it 
 is come to paffe , that more notice thanf was ever wil- 
 ling to , hath beene taken, thatff ha’Ste beflowed feme 
 thoughts upon that fubiett, and takpn more than ordi- 
 nary paines in it. And not foonely, but thereupon alfe 
 feme of my intimate friends and acquaintance, who 
 have afpeciall intrejl in me, haye beene very infant 
 and urgent with me that f would make my labours 
 more pub tike , and communicate them to the world, by 
 committing them to the Treffe : whereto though f was 
 
 a 
 
 
T o the Reader. 
 
 a long while utterly unwilling, as being confcious to my 
 felje of mine owne inability and infujjictency to devi/e 
 and contrive any thing worthy to come to fucb publih 
 view, yet their importunity hath at lijljo Jarre pre - 
 Vailed with me, thatthofe rude and unpoljjhed lines 
 are now like to fee the Sunne^and to come abroad to 
 be [canned andeenfured by others, ff thou Jhalt hskp 
 upon them with a fair e and favourable eye, Ifballbee 
 encouraged to beflow mypatnes upon Jome other thing, 
 which may happily give thee more content, and in the 
 meane while jball reft 
 
 Thy true friend and well- wilier,’ 
 
 Iohn B A * I N G T <) N, Gunncf i 
 
In laudem Autboris Ioann is Babinqton 
 c Jmiri & in sArte CMathefios 
 
 celeberrima Socii. 
 
 T He pleafapt objea of clofe ardent Bo wres, 
 Envelloped with Florae’s fragrant flowres, 
 
 The goodly Profpea of Skie-kifsing Hils, 
 
 Or fertile Plaines vein'd ore with purling Rils ; 
 
 More raviih not my fences with delight. 
 
 Then doth thy Pjrotecbnie.Mzny write 
 
 Of Arts inthemlelves worthy, buttheir worth 
 
 Is much impairdeby thofe that fetthem forth , 
 
 Wholly unskill’d in Mcgatbologic> . . 
 
 The very foule of each deepeMyftetie- 
 I wiih fuch (hallow men would meddle lefle. 
 
 And with their fenfele(Teftuffe notcloyihePrefTe. 
 
 All fuch his Schoole to paffe by Plato wude 
 In beautifull Geometric not skild. 
 
 Well haft thou then my Friend enpreft thy At , 
 
 Since this rare Science hath the greater part 
 Shar'd in thy Wotke, giving it winged fare, 
 
 To mount it up-aloft,and deck th e?y re • 
 
 With fplendent ftars, filv er and golden (howers , 
 
 Thefe are th'effeas of Mathematkk powers 
 Which crown their Authors temples, no? w - y > 
 
 But with a wreath of flats and fulgent rayes. 
 
 Fairly goe on,«hy felfefuchTrepfoer reate. 
 
 That neither time not E>rw may outweate; 
 
 Tboi StuteviU. pbilomathesl 
 
Vnto his worthy Friend, and induftrious Artift, 
 
 Matter Iohn Baring ton. 
 
 W Hen as I did thy Books by chance effie. 
 
 With divers figures gr act, moft curioufly 
 Qontriud,aU new ,and of thine own invention > 
 
 With Jmdry Engine s made by iuft proportion ; 
 
 1 did admire thy skilly thy attive braine, \ 
 
 Whereby thofe things thou didft Jo Well dttaine ; 
 
 Juftly 1 mighty for of no Nation yet , 
 
 There s any bath this path fo fully beat * 
 
 Nor laid thofe grounds that thou haft done y whereby 
 We might attaine to things that tend fo high. 
 
 For Jenceleffe things with life thou feemft to filly 
 Making them wondred at by commonskill. 
 
 Thou fundry doubts unfoldft , and with mucheafe , 
 
 Thou teachcfl its to meajure Land and Seas. 
 
 When as 1 thought on theft , and knew how rare 
 Men thus addicted, and thus given were , 
 
 My mind, my band, my hand did force my pen, 
 
 T* offer my mite of thankes ’mongtt other men, 
 
 Accept it then, and let it no lejfe bee 
 Fleafing,then greater gifts are unto thee. 
 
 v 
 
 Thy truly afFeftionate , and wel- 
 wifhing Friend, 
 
 John T&ate-j* 
 
In commendationsof his worthy Friend Matter 
 fohn Babington Gentleman. 
 
 I f I were worthy to extol! the Name 
 
 0 f him that fpcnds the’Elixcrof hisfpirits, 
 
 H ow rate definde, I fhould fee forth the fame, 
 
 N ere Ihould 1 flinch* for why tby great demerits 
 B ravely ttiould armc me boldly to oppofe 
 
 A gainft thy Criticks and back- biting foes , 
 
 B rave man of worth proceed .• the rareft wits, 
 
 1 f thy rare Worke doe come but in their view, 
 
 N ere doubt, but they as foone as God permits, 
 
 G reat love and aid will then exprefle to you, 
 
 T hat fpends your time, fpirits, and great cxpcncc 
 O n Countries good for love, not rccompence. 
 
 N ow tell me thou that haft a Tallent lent. 
 
 Which was receiv’d from God Omnipotent , 
 
 And hor’dft it up, burying it with thy Name, 
 
 It there takes Period, ending with thy frame. 
 
 When this my Authors fame, Iiuftprcfage, 
 
 Shall flourifh Rill, and not wcareout with age. 
 
 t 
 
 Thy Friend Iohn Hicks, alias 
 Bridghampton Gunner, 
 
 i 
 
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C H A P. 
 
 A Tabic of the Contents. 
 
 H 
 
 2 
 
 3 
 ,4 
 
 5 
 
 6 
 
 8 
 
 9 
 
 i° 
 
 11 
 
 12 
 13 
 4 1 
 
 15 
 
 1 6 
 
 17 
 
 18 
 IP 
 
 20 
 
 21 
 
 22 
 
 2 3 
 
 24 
 
 25 
 
 26 
 
 27 
 
 28 
 
 2 P 
 
 3° 
 
 31 
 
 32 
 
 33 
 
 34 
 
 35 
 
 Ow to make all forts of moulds in a true proportion with the Rollers. and 
 
 --drift. . . P3 § ei 
 
 How to make your Cofines of paper. P *4 
 
 How joHjbadchoake a Rocket. , . . , \ em 
 
 The manner of driving a Rocket .with the moments belongwgto thefame^ 
 The manner of beading a Rocket .with the order of capping the fame. p .7 
 
 The manner of finding a Rocket. . , . P* 8 
 
 The manner offering Rockets , »** */ - A# 
 
 P* ^ ^ 
 
 Divers compofitions for flarres. 
 
 The manner of making the heft fort of ftarres. p. 
 
 The manner of making filver and golden rame. p. 1 4 
 
 Howto make ff gigs which feme call Serpents. laem 
 
 How to make the reports or breakers. P" 5 
 
 How to make a Runner on the Line. P* 
 
 Themannerof firing your Runner. n* T a 
 
 Howto compofe a tvheele. P * 1 ' 
 
 How to make a ground wheele. ■ P* 
 
 Another manner of ground JVheeles. p,X 
 
 The manner of making a fixed tvheele which fhaU give divers reports. p.2» 
 How to make a fixed tvheele which /ball caft forth many Rockets 
 
 *Howto make a fixed tvheele which {hall caft forth divers fif gigs .and like wjfe 
 
 ThemmleVof making a tvheele to r untie two w dyes, which u forward and 
 
 ^Themanner of compofing a tvheele . which having fnifted hU' revolution, 
 
 ; How toZprefent a Coat tf eArmes in fire which having burnt af mall while, 
 the [aid Coat fhal appear e in per f eft colours. and fhal continue fo a long 
 
 How to reprefent an ant Usance by the helpe of fire , which J hall moovetn a 
 
 Another way for making an antickjance which is not fo violent at the former, 
 
 ' P*2 P 
 
 How to compofe a Caftle of fireworks, with the manner of placing the Tvorg 
 
 How^o reprefent divers motions in a Caftle of Fire-worke. P- 3 0 
 
 l Another lay to performe the fame Motions, and will not be fo violent as the 
 
 ~Hwto reprefent the forme of an oArmy of an hundred men marching.whoch 
 [hall prefent and fire at on certaine place appointed. . . , ia , eai 
 
 How to reprefent Mufique playing {by the helpe of fire) with anttek* dan- 
 
 • P*3 ^ 
 
 C How to make a Dragon or any other creature run on the Iwe , by the he ¥*f 
 Zno.horv,., fir nuking a, firry Dragon to fajfr on Min. Mon, the hrlp. 
 
 £ £ J * J / 
 
 Howto reprefent Saint George fighting with a T>ragon on the line, p .3 7 
 How to make a trunks of fire , which [hall caft forthdivers fire- h f s 'P'*t I 
 Themamerof making a Club which [halt caft forthdivers fmallworkes or 
 rr ■ P‘4 2 
 
 fifg'V- -ity 
 
3<s Another fort of eltth.rihkh he, ng fired finite man, repZZ 
 
 3 7 Another n>htch I caR Iacke inaboxe. 7 P P- 4 ? 
 
 , 4 *^ „ w> >« 
 
 3S,ft * tt '*"** ^ -** *•» .«* v 4|3 
 
 40 K>w „ Wl fe a halfetnootte of rockets appear e in theatre. J' 4 * 
 
 41 makeacafe of rockets to rife I once. 7 £47 
 
 4 :PoZ U ' , ~’ herein theayre, after the^J™, 
 
 43 £&» to reprefent a figure of the Sun )C aJfin £ fath his b,*™*, « * £ 
 
 " s ? ^-!=i'S£ , ;ias 
 
 -* —— ,k; 
 
 ^M ndf0rt \ thei t fi I ° ^ ° ther '"^greJviouL C **"***b M 
 
 *9 H ow to snake a buckler, which (hall call forth a /,,, j j r v • IcJem 
 
 making his report. 1 7 * ****** **r 
 
 50 Mow tomakethe C nr t lax, fruiter, or Fauchion M J 
 
 the neater reieh £ rea?Jl 
 5 2 eaSrenter h all rthich [halt Jheot forth many retorts Wcn > 
 
 59 H z;;xxS:'- w ^ 23* ^ S ** ^ -;2 
 
 <0 «,w » i7«» .r Mermaid plat ine on the renter £* } 
 
 Z~SZ£2E*ft.Z$£ ttsir'-*- *••5' 
 
 *'2£sg&itr**' L * 4a. «-r;: 
 
 6 5 The manner of making °f *9 
 
 66 Another engine for the fame. * idem 
 
 ^7 *sf third Engine for the false. P- 7 * 
 
 68 Another Engine for trying the firength of powder by water. 
 
' A Treatife of 
 
 ARTIFIGIALL FIREWORKS, 
 
 mod of them being invented and ap- 
 proved by the Author. 
 
 Chapter I. 
 
 How to make all forts of moulds, in a true proportion, 
 with the fowlers and Drifts. 
 
 Hat I may fet downe the true procee- 
 ding in Fircworkes, it is requifitc in the 
 firft place to lay downe the true order and 
 forme of making ail forts of moulds, afwell 
 greater as leffe : and to proceed , youmuft 
 get of the beft drie Box you can finde 5 if 
 not, offome other tough wood, as Crabbc- 
 tree, Holly,or fuch like wood, which when 
 you have provided according to your fize 
 you meancto ufe it behoveth in the next place to be known, of what 
 diameter you will have the heighth of your bore, and from thence all the 
 reft is derived: For example, I defirc to have one bored of an inch high, 
 which I get bored by fomc Turner ; and to know of what length it rauft 
 be, I take for the fay d length fix diameters of the bore, which maketh 
 fix inches, and for the thickneflc it ought to be halfc a diameter on each 
 fide, fo that being turned true round, it contayncs two inches in diame- 
 ter. Then have you to provide a bottome, which is to be fitted in fuch 
 fore as you fee deferibed in this figure : the proportions heerafcerfollow. 
 
 A is the foot of the mon/d, And is in heighth two diameters, which muft bee 
 two inehes ; and one diameter and ~ in breadth , whether it bee fquare or 
 
 round. 
 
 B ferveth only for a ft ay, and muft arife one inch into the mould, which is 
 one diameter, andfo proportional/ in all other forts. 
 
 C is for the mouth of the rocket, and is in diameter j of the bore • fofetting 
 one foot of the compares in the center, deferibe the arch , which is the fuH 
 heighth required. 
 
 EE 
 
V ,Vw' t vi vVi.i ^ . > nil. nU .lx 
 
<zA rtificiall Fire^Workcs* 
 
 E E fervethfor the payer being raveled, and u ‘ part bfthe diameter on each 
 fide . 
 
 E F is the thickneffe of the mould, which is halfe the diameter of the bore, 
 that is in this place halfe an inch . 
 
 F G the length of the mould, which is fix diameters, 
 
 *D the length and bigneffe of the needle, which is- the length of the mould, 
 andbigneffe to be\ of the diameter of the bore at the bottom, and fow taper to 
 the top . 
 
 When you have provided your mould according to your defire, then 
 you are to fit your rowler, which muft be two third parts of the diame- 
 ter of the bore of the fayd mould, and the length thereof to bee fix inches 
 longer than your mould, which is for the roling of your paper, and is 
 deferibedby the letter A in this fecond figure, with a hole to be bored in 
 the bottom to receive a wyer, which muft bee faftned in another peece of 
 woodfomewbatlhorter, which is to take out at plcafurc, as you may fee 
 deferibed by the letter D; there is required no proportion of length 
 for this fhort peece • only it fufficcth if it be but folong as a man may 
 well hold it in his hand j theufc hereafter (hall be more plainly deferibed 
 when I come to fpeake of the order of making the coffins ; which (hall 
 be in the next Chapter* When you have fitted your rocket according 
 to this dire&ion, proceed to the making of your rammers, (or more pro- 
 perly tailed drifts,) which muft bcc alwayes two at the leaft to, each 
 mould, and as your mould incrcafcsin largenefle, fo muft you have more 
 rammers, by reafon of the largenefte of the taper needle : the manner and 
 form you may fee deferibed by the letters B C. 1 
 
 B is the hollow rammer, and hath a hole in it anfwerable to the length and 
 hignejfi of the taper needle , as appeareth in that figure. It mufi be a fmall mat- 
 ter le fife than the rowler, becaufe that otherwife in putting it in, you will put 
 down the paper , which is very prejudicial l to your rocket . 
 
 The other rammer is not halfe fo long , and is fad, that when you have beaten 
 to the top of the needle, you make ufe of it .* it is deferibed by the letter C. 
 
 When you have fitted your rammers, you muft provide a peece of 
 Box made after the form as you fee deferibed ; which muft ferve to make 
 your large coffins to put the work which you intend, on the head of 
 your rockets. It is deferibed by the letter F, as in the figure is manikft. 
 
 The letters E E fbew the diameter , which is thejuft bignejfe of your roe - 
 kyt, and muft befo in all fiz.es. 
 
 G G Jhewes the largenff r of the cofin, and muft bee two diameters , which in 
 this figure is two inches. 
 
 HHHH Jhewes the length of the coffin, which ought to bee two diameters 
 cfyour rocket , which in this place is two inches ; but we are not tied to that fo 
 precifeiy‘,for we are to alter that according t* the works which we put therein. 
 
 3 
 
 A * 
 
 C H A P, 
 
4 
 
 *Pyrotechnia, or. 
 
 G HAP. II, 
 
 \ * , ’ r, , . * ' > . 
 
 How to make your coffins of paper* 
 
 having explained the manner and forme of 
 the moulds, with the reft of the dependants, I 
 come now to (hew the ufe of them in their fevc- 
 rall orders : and firft for the ufe of the rowlcr, 
 which is deferibed by the letter A. 
 
 Y ou muft provide fomc good ft rong paper, as 
 old Law books, which are bothftrongjand large j 
 and cut out your fizes of paper for your work.* 
 now to know what length your paper muft bee, let it bee alwayes the 
 length of your mould : fo (ball you have one diameter left above the 
 mould, the ufc whereof (hall be fhewn in his proper place. Now having 
 provided your paper in length ready, take your rowlcr, and one length 
 of paper, and begin to rowle. when you have rowlcd one fticer, vou 
 Figure i\ G. muft have a board ro rowlc it with (the board is marked in the fccond 
 figure * ) which muft be done in this manner : you muft hold the rowlcr 
 in your left hand, and with your right hold the board s then lay down 
 your rowlcr upon fomefraooth chcft, or table, or fuch like - which when 
 you have done, lay on your board, and rowle it very hard, only one 
 way j which having done, rowle another length, and fo proceed in row- 
 ling between every fhect, till you have fowled on fo much as will fill the 
 mould very ftraight ; when you have fo done, draw forth your rowlcr 
 one diameter, which in this place is one inch ; and then take the other 
 part of the rowler, which is fhort, and marked with D, and put it in as 
 you fee deferibed • and there have you a place left for the choaking of 
 your rocket,of which we come now to fpcak: 
 
 Chap* III. 
 
 How you [ball cboak a rocket. 
 
 Hen you come to choak your rocket, you muft have 
 a ring to ferew into forne poll, at which you muft: 
 tie your cord, which muft be bigger or leflcr.aceor- 
 ding to the bignefle of your rocker, by reafon that a 
 fmall cord will not choak a great rocket for want of 
 iftrength 5 and again, a great cord will not ferve f6r 
 a final!, in regard that it will make too great a cboak- 
 ing • fo that you muft have a bigger and leffc ; which when you have fo 
 provided, tying one end to the ring, you muft about a yard off tic a 
 ftick, infaftiion of a handle for afwing, which muft bee ftrong, by rea- 
 fon that it muft beare the whole weight of the body, (the letter G in the 
 ^l^a.K-fccond figure expreffeth the fame •) which when you have provided, 
 
 put 
 
6 ,c Pj>rotechnia , or, 
 
 put the fticke bet wccnc your legges, and windc the cord about the roc- 
 ket cafe in the place appointed, which is betweene the long rowlcr and 
 thefhorc, when you have fo done, girt it by degrees, ever turning your 
 fouler, to the end it may come together more clofc and neat (the man- 
 ner is expreffed in the third figure, by the letter K ) fo when you have 
 Fh rez choaked it fufiScicntly, draw forth your fliorc rowler, and where your 
 * K* 5 * choaking is,tyc it about with firong packthrcd*, and fo drawing forth 
 your rowlcr, you have a coffin ready to be filled when occafion fervetb, 
 the forme whereof folio weth. And becaufc the choaking of a rocket is 
 very laborious and dangerous, in regard of the breaking of the cord, 
 which often hapnethjl haue therefore invented a ccrtainc Engine, wber- 
 by a childe may choake the ftrongeft rocket. The parts ofit arc a ferew 
 roovingawhcclc,on theaxcltrce of which isfaffened your cord tor 
 choaking, with the other end of the cord fattened to a ftaplc on the fame 
 Figure p j, oor( j ; the f ormc whereof you (hall findc deferibed in the third figure, 
 
 B - by the letter B.C. 
 
 Figure $. ^ t y C offin of a Roeket who Hi fnified, with his checking. 
 
 B The forme of an Engine for choaking a Rocket . 
 
 C The mannner of ufing the Engine . 
 
 F Is ameafuremade of home or fatten. 
 
 G Is afunnell with a hAndleto fill fmall Rocket /, And other [mall works', 
 
 H Is a fine Pearce, with a receiver to feArce your ingredients. 
 
 I Isa morter to mealeyour fowder, and your other ingredient s t which muft 
 he of wood , with a peftle. 
 
 5 Having deferibed the order and formes of all things ncceflary to the 
 making of a rocket, it refteth now that wc know the man ner of driving 
 ir, as alfo what ingredients arc molt proper for every fize. 
 
 Chap, IV. 
 
 fhc manner of driving a Rocket, with theinfiruments 
 belonging to the fame, 
 
 ►Hen you have finifbed your coffin of paper, take it, 
 and with your hollow rammer force it downe clofe 
 into your mould, which when you have done,(trike 
 two or three fmatt blowes to fettle the paper into his 
 right forme: which being done, you muff begin to 
 fill your coffin, in doing whereof, you muff have a 
 
 great care, al waics providing a mcafure, which may 
 
 containe part of your whole Rocket- fo by that raeanes you Qaall not 
 fade, but every Rocket (hall have a true proportion alikc^as for Example, 
 I have a coffin, which being filled, will hold an ounce of mixture or ther- 
 abouts. I take the twentieth part, and when I findc what quantity it is, 
 I make a meafure of home, which ffiall containe fo much, and then I 
 beginne to fill my coffin with one meafure at a time, and putting in my 
 ' v ram- 
 
 / 
 
aA rtificiall FireAVor^es. 7 
 
 rammer, ftnkefoure or five fmarcblowcs with a good ftrong mallet, and Figure 3. 
 then ! fill another meafurc, and ftrike againe, fo I continue til! I come to Mi 
 the top of the needle, then l take the fad rammer, and fo continue with it, 
 ti ill come to the top of the mould': now the paper which is above the 
 top ofrhe mould, muft be turned dewne, and beaten hard down,which 
 being done, the Rocker is finifhed from the mould- which force out, with 
 as much cafe you can, for the lefle you force it (being filled, and the 
 needle taken omj the better it is, for knocking loofens the powder, and 
 fo caufcs the Rocket to faile: now it refts to know the rcceits proper for 
 every fort of Rockets. 
 
 And firftfor Rockets of one ounce, you may take only powder duftjscing ve- The ingredi - 
 ryfine fearced • which rifes very fwiftybut carries no taile of fire with it,and eats for ordi- 
 ojten times br cakes, unlejfe they be very thicke of paper : but the befi andfu - nary Rockets, 
 refi way is,to allay your powder with coale dufi being wellfearced, which catt- 
 fes a more glorious (btw\ and you may ufe it at your diferetion. The ordinary 
 allay for f mall Rockets is, I l.of powder, two of coaledufi, which ferves till 
 you come to Rockets of four e ounces, then muflyou take to every 1 1, of powder 
 2'. ^ of coledufi, continuing that quantity till you come to Rockets of tenue 
 ounces , and from tenne to fixtee ne ounces, which is one poHnd'.your Allay muft 
 be to one pound of powder, three ounces of coale. 
 
 No w when you have provided your powder, you muft firft mcale it, 
 and then fcarcc it, fo that it may be free from any cornc though never fo 
 fmall. Like wife take good dry coalc, well burnt, and beat it to duft, 
 fearcingit very fine, which when you have done, mixe them according 
 as youroccafion ferveth, and as your directions arc. 
 
 C h a p. V. 
 
 The manner of heading a pocket , with the order of capping it. 
 
 Ow we come to (hew the manner of heading a Roc- 
 ket, in which we are to ufe our thicke Roler, fpecifi- 
 cd in the fccond figure, and marked with F. Vpon 
 which you muft role fome paper or fine paft-board, 
 and paft itfo thatit may bee very clofe, and then 
 choake it at the length of the thicker part, fo that it 
 may come clofe to your fticke in the [leflfer part, 
 which will fit to be tyed to the top of your Rocket, 
 fo fhall you have a coffinc to put in your workes, which muft bee of di- 
 vers forts. That being done, you muft provide Taper caps, which muft 
 be adjoyned to the top of the large coffin. The ufe of them is to keepe in 
 your workes, and to caufe them to pierce the ayre more fwiftly; The 
 manner of making thefccaps,is,to take a paircofCompafles,and deferibe 
 a circle in paftboard, then cat it forth with a paire of (heeres, and that 
 fhall make two cappes, being cut in the middle, and turned one corner 
 under the other, and fo paftcdj and let them fo pafted, be put in a napkin 
 
 preflc. 
 
Tjrotechnia , or, 
 
 preffe till they be dry, and when they be dry, cot out a fcmicirclc in pa- 
 per, which (hall fit round about the faid cap, and (hall ferve to pafte on 
 the cap to the coffin: the forme whereof is exprefled in the fourth figure, 
 by the figure 14. and 1 5. fo have you all things ready to the finifhing of 
 your Rocket, which muft be done as folio weth. 
 
 Chap. 6 . 
 
 The manner offinijhing a ${ocket* 
 
 HenyoBr Rocket is driuen, as I have (hewed you, 
 with the paper turned downe, you (hall firft prime 
 it, which muft be with cotton wickemadc for the 
 faid purpofe, which you (hall put up into the vent, 
 leaving a peece to hang lower than the mouth of 
 your Rocket, by three or foure inches, which being 
 done, tye a piece of paper over the mouth, to the 
 end it fall not outrnow having primed your Rocket, 
 you may proceedc to the heading of it, and that is done after this man- 
 ner.Takeyour Rocket, and on the head (where I told you, you (hould 
 turne downe the paper, you muft with a bodkin, pierce two or three 
 holes, to the intent that the Rocket having fpent bitnfelfc, yourworkes 
 which are on his head, may take fire* which holes, prime with a little 
 powder duft, and then put on his head, with the choaking fitted to your 
 Rocket, which muft come over the Rocket, in fuch manner, that the 
 bottome of the greater part muft come even with the top of the Rocket; 
 which tye faft toyour rocket with threcd, and then put in your workes: 
 but before you put in your workes, whether they be ftarres,or any other 
 workes, you muft put in a little cotton wooll, being rowlcd in powder 
 duft, to the end your ftars may fire, and likewife may blowout: which 
 having done, put in your ftarres, or other workes, and if you makemore 
 than one tire (as you may doe of your ftarres) then muft you put more 
 cotton rowled in powder duft amongft them, or betweenc every tire, to 
 the end they may all take firej then take your cap (o provided as I have 
 formerly (hewed, and fill the hollow place with cotton, becaufe it is 
 light, and likewife will fire quickly: which being fitted, pafte it clofeto 
 the top of the coffin, in fuch manner, that it may ftand very uprightjthen 
 muft you fir on your fticke, for the pealing of your Rockct,which ought 
 to be about eight lengths of your Rocket without the head. You muft 
 get the fmootheft and Iightcft you can, fuch as basket makers ufc; which 
 when you have got, you muft make veryftrait, and then cutting one 
 fide of it, fiat at the great end, make two notches on the round fide, pro. 
 vided that the one be differing from the other, fo much as is betweene 
 the choaking of your Rocket, and the end of the vent j becaufe if you 
 (hould tye it upon the vent, it would (oofen the powder, and focaufc it 
 to breake in the firing. Now that you tye not the wrong end of your 
 
 Rocket 
 
'Pyrotechnic or, 
 
 Rocket uppermoft, as fome fooliflily have done, for want of better in- 
 ftru£Hons,you muft alwayes tye the end downewards, which ischoaked, 
 and with a piece of ft rong thred tye it faft to the lower notch, juft about 
 the choaking, fo (hall you be fare your ftickes (hall not fail off, neither 
 will it indanger the hurting of your rocket. When yoa have tyed that, 
 then proceed to the tying of it higher, which as I fay, muft be fotnewhat 
 higher than the top of the vent, and let your fiicke come even with the 
 top of your rocketj which having done, peafe your rocket, which rouft 
 be after this manner. Lay it on your finger two or three inches or more 
 fromthc mouth, and if you findc the flick be too heavy , cut it (horter,fill 
 you findc your Rocket to ballance your fticke, for the fticke being too 
 heavy, caufcs your rocket tefiugge, and being too lighr, it makes a rocket 
 fall before he is halfcup: thefc things being provided, you have your 
 rocket ready to be fired, which muft be after this manner. 
 
 Chap. VII. 
 
 T be manner of firing Rockets , with the defection of a 
 fiaffe for the firing ofthem. 
 
 Rovide a long ftaffc with a pike at one end, which 
 maft be thtuft hard into the ground, and a three 
 legged ftaffc with a hollow hoope at the top, to let 
 this long ftaffc Hide up and downe, to the end that 
 having rockets, whofe ftickes arc longer then youe 
 Paid ftaffc, yet by raifing it through the faid iron 
 
 hoope, you may make it foure or five foot longer 
 
 than it would be ftanding on the ground.Now this long ftaffe muft have 
 a Hiding peccc cut with feveraH points, which muft be neere the top; and 
 at the bottome there muft be a ring of wyer,to let the fticke goe through, 
 which muft be madelikewife to Hide up and downe; fo thrufting the 
 fmall end through the faid ring, your rocket will reft upon that part a- 
 bove, which muft be juft oppofite in a ftraight line, fo open the mouth 
 of your rocket, and pull out the end of your cotton wickc, and with a 
 pccceof match, fattened in a Linftockc, give fire to the faid wicke, and 
 by degrcees, you (hall fee it fire your rocket; which being well ordered, 
 will mount very ftraight and high : now having (hewed the whole order 
 ofconapofing a rocket, with the firing of the fame, I will (hew you an 
 order for making of your ftarres, and other workes which are neccffary 
 for the heads of your rockets; and fir ft of all I will (hew you the making 
 of divers forts of ftarres, with their compofitions; and fincc wee cannot 
 make them without the compofitions, I will firft fet downe the compo* 
 fitions, and then proceed to themanner of making them. 
 
 CHAP. 
 
II 
 
 < l A rtificiall FireJVor^es* 
 
 Chap. VIU. 
 
 Divers Qomp options for flarres. 
 
 A Compofition for ftarres of a blew colour, with red. 
 
 Ake of powder mealed , 
 Salt peter , 
 
 Sulphur vive. 
 
 Meale thcfe very fine, and mixe them together 
 with a g. of aqua vitc,and 3 g.of oyle of fpickc, which 
 let be very dry before you ufeit. 
 
 Another Compofition which maketh a white fire and beautiful]. 
 
 Take powder , 
 
 Salt peter , 
 
 Sulphur vive t 
 Camphire , 
 
 Meale your ingredients, and mixe them; now to powder your Cam- 
 phirc, you rauft dip your peftle in oyle of Almonds, or fuch like oyle : 
 you muft not ufe your wooded peftle for this, becaulc that oyle will 
 foake into it, which is an enemy to fomeworkes* therefore take a brafle 
 peftle and mortcr, and dipping the peftle in oyle of Almonds, put it to 
 your Camphitc,and fo ftirring if by degrees, it will powder- which when 
 you have done, keepe it very dofc from ay re, till fuch time as you uic it, 
 othetwife the Camphire willlofe his fpirit, and become of no ufe. 
 
 Another white fire which lafteth long? 
 
 Take powder, 4. g 
 
 Saltpeter, j / 
 
 Sulphur vive^ S § 
 
 f'ampbur, 2 g 
 
 Ojle of peeter, sg 
 
 Meale thofc which are to be mealed, very fine, and mixe them accor- 
 ding to the former dire&ions; 
 
Pyrotechnic or, 
 
 CHAP. IX. 
 
 The manner of making the bef fort offlarres . 
 
 O w having fct downc the coropofitions for ftarres, it rc- 
 fteth to know how thefc ftarres arc made, which is di. 
 vers waics, but I will fee you downc oncly two waics 
 both which arc very good, fo that you may take your 
 choycc. The firft is this, you muft make little fquarc pie- 
 ces of brownc paper, which fill with your compoficion 
 F| . 4 you intend, and fo double it downe, rolling it till you make it fomewhat 
 
 & n. g, round, about the bignefle of a nut or bigger, according to the fize of your 
 rocketiyou may putina dozen on the head ofa fmall rocket; when you 
 have made them up in this.formc,you mud birckthem round with fmall 
 thred, which done, draw through a cotton wickc prepared for priming, 
 as hereafter (hall be fhewne. 
 
 The fecond fort are made after another manner, which is thus; you 
 muft have a rowlcr, as big as an ordinary arrow, which (hall be to rowle 
 a length of paper about it, and with a little mouth glue, or pafte, paftc it 
 round ;fo have you a hollow trunkc of paper, which you (hall order af- 
 ter this manner: Fill it by little and little with your fmall fonnell, ftill 
 tfarufting it very hard, till you have filled it to the top; which done, cut 
 it into fhort pieces, about halfe an inch in length; then having in rcadi- 
 nefle cither hot glue, or fize mingled with red lead, dip one end of your 
 fhort pieces, to the end, that both ends of your ftarre fire not, and alfo 
 that it may not blow out; which being fo finifhed, fet to dry till you ufe 
 them, and then putting the other end into powder duft, you may put 
 them on your rocket, in one or two tier; alwaics provided, as I faid be- 
 fore, that you put in powder duft bctwcenc every tier, to the end they 
 may all fire; thus have you the manner of making your ftarres, the formes 
 whereof you (hall have deferibed hereafter. 
 
 Priming for The priming before fpoken of, is made after this manner; take oyle of 
 
 'Rockets. Camphirc, and foakefome cotton wicke in it, then take it out being 
 rnoy ft, and rowle it in fine powder duft, which having done, you (hall 
 hang it up till it be thorow dry, fo have you prepared a very good pri- 
 ming, which muft be kcptclofc from ayre, till fiich time you have occ> 
 fion, otherwife tbcfpiritof the Camphir will decay. 
 
 The defeription of the ftaffe for firing of Rpckets. 
 
 A The long ftaffe to rife through the ring. 
 t <r BBB T he three legd ftaffe. 
 
 C The ring or ho ope of iron for the long ftaffe to flide thorow . 
 
 D A ferew to ferew faft the long fluff t being raifed. 
 
 E A piece of iron filed with notches to hang the Rockets on. 
 
 F The ring of wyer to pu t thorow the fticke, which may be raifed higher , or 
 put lower , as occafion proffers. 
 
 G G The defeription of two ftarres .with the priming.K.and the binding L.' 
 
 H The defeription of the trunks, or cafe , which is to be filed with your ftar 
 mixture } andfo cut into fhort pieces . as you fee reprefented by the figures i.i. 
 
 where 
 
Tjrotechnia , or. 
 
 where the uper part represents the open end , and is marked with M, and the un - 
 der part which is glue d t is reprefented by the letter N,/o have you the Jlarres 
 wholly deferibed. 
 
 CHAP; X. 
 
 The manner of making flyer and gold raine. 
 
 Ow I will fhew you the order for making of golden 
 raine, which is after this manner; you muff prouidc 
 (lore of Gcofc quils, which hauing, you muft cut off 
 the quill as longas you can Ieaucit, and cut notoff 
 the other end, but leaue it clofe as you fee prefented 
 by the letters OP. Figure 4. where O reprefents 
 one filled, and P one empty. The rcccit which 
 you makeyour golden raine, muft be the fame which 
 you make your rockets of onc ounce, which is to 1 1. of powder, 2 §.of 
 ; coaleduft: now hauing filled many ofthefc quils, as I haue (hewed you, 
 they muft be put on the head of your rocket, with the open ends down- 
 ward, to the end they may take fire fo foonc as your rocket is fpent, and 
 fo (hall you fee appeare a fhower of gold, which by fomc is called golden 
 raine: the like way may you make filucr raine, filling your quils with the 
 mixture preferibed for your white ftarres, and ufing them in the fame 
 manner, you fhall fee them fall downe like a fhower of filucr, which is 
 called filucr raine* and thus much fliall fuffice to be knownc for this fort 
 of worke. 
 
 CHAP. XI. 
 
 Howto make Fifgigs, which JomecaB Serpents • 
 
 O w I will Chew you to make another fort of work, which 
 we call Fifgigs, or as the French namethem, Serpents, 
 which are made as folio weth. You muft provide a fmall 
 mould, of* of an inch diameter, which muft bee made 
 without a needle, which when you have, you muft make 
 your cafes, as you make for your rockets, choaking them 
 3 an inch from the end, which fhall ferue for occafion as it fliall bee prof- 
 fered; when you haue made your cafes, fill them three inches with pow- 
 der duft, and then choake him, and after put in a little corne powder, to 
 the 'end that your Fifgig hauing plaicd a while to and fro, hec may 
 breake and giuc a report; the ufe of the making fo deepe a mouth at your 
 firft choaking is, that you may fill it with your ftarre mixtnre;fo that put- 
 ting diuers of them on the head of a large rocket, they will firft appeare 
 like fo many ftarres, 3 nd when the ftarres arc fpent, taking hold of the 
 powder duft, they will runwrigling roand fro like Serpents, and after a 
 while they will giuc Co many reports, which will giuc great content. 
 
 Thcr c 
 
dA rtificiall Fire-lVorkes. 
 
 There arc many works which are made of thefc fisgigs, which wee will 
 fpeak of in their places. 
 
 CHAP. XII. 
 
 How to make the reports or breakers. 
 
 O W I will proceed to (hew the manner of making re- 
 ports to place on the head of a rocket • you muft make a 
 coffin of the fize of your rocket of one inch, but you 
 muft rowle your paper a great dealc thicker, to the in- 
 tent your report may be the greatcrjalfo in choaking.the 
 mouth muft bee left very large, to the end that on oc- 
 cafionyoumay fill it with ftarre mixture ; now when you have made 
 divers coffins about three inches and better in length, you muft leave a 
 fmall vent at the choaking, the bignefle of an ordinary wy er, which you 
 muft flop with a little paper, while you fill the coffin almoft full, or with- 
 in halfe an inch of the top, with goad corn powder, turning down fourc 
 or five folds of paper, choak it clofe at the top, and binde it round with 
 thred, foyou have your reports ready, againftfuch time you come to 
 ufe them ; which muft be done in this manner : firft beccarcfull to pull 
 out your ftopple, which having done, fill the mouth with your ftarre 
 mixture, and (o fatten him on the top of your rocker, alivayes putringa 
 little paper about the top of your rocker, and in it put a little powder 
 duft, and fo fet on your report, and tie it faft on, with the mouth to. 
 wards the head of the rocket, fo that the rocket having fpent himfelfc, 
 you (hall fee a large ftar appearc.and when it is neere the ground, you (hal 
 heare the report ; the order thereof you (hall findc deferibed in the fourth 
 figure. 
 
 1 Is the report ready finifted. < 
 
 2 The rocket with the report on the head. 
 
 3 The report faftned on the head of the rocket. 
 
 4 The paper to fafte %t the report to the rocket , which muft firft bee tied to 
 the rocket y and likewifhto the report . 
 
 8 Reprefenteth a fisgigfinijhed. 
 
 9 The choakingyas lhave fbewed, which muft bee filled upward with corn 
 powder. 
 
 10 The mouth of your fisgig, which upon occafion you may fill with your 
 ftarre mixture , to put on the head of your rockets. 
 
 I I Reprefenteth a fi/gig, with a bladder, which muft be tyedon to the head 
 of them t in fitch manner, that the fteck , L of the bladder may go into the fisgig , 
 andfo befafttyed, that they ftirre not ; the ufe of them is, only to fire in your 
 handy (for being fired with a little powder duft in the mouth of it) and fo caft 
 away fromyeu, it will fiy to and fro without ceafing , till it hath fpent it felfe ; 
 and by reafon of the bladder which is tied to ity it will not ftick^faft to the 
 groundy as others do which have no bladders. 
 
 I 2 Reprefenteth a cracker faftned to the top of a rackety fo that the rocket 
 having fpent himfelfe, it taketh fire , and maketh many reports ; the, manner 
 
 B 2 of 
 
Tyrotechnia, or. 
 
 i 6 
 
 offaflning him u thm ; you muff: fir ft tie on your rocket , leaving the flick fo 
 ' much higher than the top , as will fuffce to tie on ycur cracker , which muff he 
 
 tied about the faid flick-, infuch manner % that the nofe of it may come into 
 the head of your rocket ,whicb be ing primed with fomc powder dufl; trill take 
 fire. § 
 
 5 Reprefenteth arocket with feveraH works, whether flarres, or ferpents, 
 andmufl be with a large coffin on the top , with his cap. 
 
 6 Is the coffin, which as f have Jhewcd you, mtsft beefomewhat bigger than 
 your rocket. 
 
 7 Is the cap, which muff be taper. 
 
 I 3 Sheweth thefaflningof the flick i, which mufl not bee higher than your 
 rocket, befide the large cofin. 
 
 All which I have formerly deferibed, with the form and manner of 
 making them, and their fcvcrall ufes 5 fo that I have fuily layd down the 
 whole order of finifhing a rocket for the ayre. Now it reficth fo (hew 
 what other works may bee done by the fayd rockets, which arc many * 
 for all forts of Fire works for pleafure, do wholly depend upon them, ex- 
 cept the water bals : and to proceed, 1 will firft deferibe unto yon the 
 order of making the runners on the line, which muft bee done in manner 
 following. 
 
 CHAP* XIII. 
 
 How to mule a runner on the line: 
 
 O V muft provide a (mall rocket mould, which 
 muft be faalfe an inch or more, with rowlers, and 
 rammers, according as I have deferibed, lave only 
 that your mould muft have no needle, nor your 
 rammers hollow * when you have provided 
 them, make up your cafes, after the form which I 
 have (hewed you, fome longer, and fome (horter, 
 which muft be ufed as foiloweth ; your fhort ones 
 muft be beaten up to the top, which muft not bee above fourc inches ; . 
 yotfr longer, which muft bee 5 finches, muft bcc likewife filled foure 
 inches high, and the reft to be filled with corn powder within halfc an 
 Receipt for inch of the top, which muft be choaked clofe, and tied up ; the receipt 
 runntrs, for thefc forts muft be only fine powder duft. 
 
 Now when you have driven them as is (hewed, you may proceed to 
 the finifiiing of them, which muft be in this manner 5 you muft r«wlc 
 a pecceof paper about the head of your (horter rocket, (which muft be 
 left open to give fire to the next) which paper muft befive inches broad, 
 and being ro wled on, you muft firft try if the mouth of your other roc- 
 ket will cafily go in, which when you have done, draw forth your other 
 rocket which you tried, and bindc your paper faft to the top of your 
 (hort one, in fuch manner, that foure inches may remaine hollow above 
 the top of your rocket, which is to be filled with powder duft, about two 
 
 inches 
 
— gp— — — - — 
 
 <tA rtifciall Fire-Worlds. 
 
 inches high ; then put in your longer rocket, (with the mouth inward) 
 fo farre as it may touch your powder duft * and tic the paper faft about 
 tbechoaking, as you (hall finde deferibed in the fift figure \ after you 
 have done this, proceed to the putting on of your cane, which muft bee 
 after this manner 5 you muft firft provide canes of fuch bigneffc as will 
 fit your line, and cut them three inches long, or fomewhat better, and 
 then notch them with three notches, which when you have fo provided, 
 firft tie it to your longer rocket which is to fire Iaft, and then doubling 
 them together, (in fuch fort that the nofe of the firft come farther out than 
 the tay le of the fecond) tie it to them both 5 the reafon of this is, bccaufe 
 other wife, if it were tied to them both together, and not to one fevcrally, 
 fo foon as the firft were fired, the cane will grow flack, and often fall off, 
 and never make his return *, and againe,ifyou fhould not put the mouth 
 of the one farther out than the tayle of other, it would fire your other 
 rockct,andfomakcaconfufion : therefore that you may the better un- 
 <3erftand what I have fhewed you, I have fet down in this fift figure, the 
 whole order offinifhing a runner for the line. 
 
 A I s the ft or t racket. 
 
 B Is the longer, which muft bt beaten f our e inches "with powder duft % And 
 one inch with corn powder. 
 
 C C Tour two rockets joy nedi the mouth of one to the tuyle of the other , 
 in fuch for t, that there may be two inches between tfem, 
 
 D The cofin of paper which joynes thofe two together, and muft bee filled 
 With powder duft, lightly put in. 1 
 
 E E The rockets doubled, with thecane tied on, 
 
 E The cane , which muft be three inches long, or more, 
 
 G The cord that paffeth thorow the cane. 
 
 H <tA peece of cordon the end of the line. * ' 
 
 CHAP. XIV. 
 
 The manner of firing your runner. 
 
 W having thus finifhed your runners, you muft pro- 
 vide a line, which may bee a hundred yards, or more, as 
 your ground will permit, fo faftning your cord at the 
 fartheftof your diftance, provide a peece of board or 
 cork, with a hole of the bigneffc of your line, which 
 muft bee put on the end of your line, to the end that 
 your rocket may not reft againft any thing that may hinder it in the rc- 
 trogade motion j alwayes provided, you fopeyour line very well, for 
 fearc of firing : then puton your runner at the other end (with the mouth 
 of the rocket towards you, which muft bee primed with powder duft) 
 and pull your line very ftraight, which is a great help to the running of a 
 rocket, fo faftning your cord, you may fire your runner, which being 
 well ordered, will run to the fartheft of your line, making his return, 
 with a report at laft ; fo have you finifhed the runner, 
 
 B 3 ’ G HAP. 
 
< lArtlficiall Fire-JVorkj, 
 
 1 9 
 
 CHAP. XV. 
 
 How to compofi a wheels. 
 
 O W I will (hew you the order of compofing a wheele, 
 which is a prime work, being well ordered $ of which 
 fomc are movable, and fome immovable : of the mo- 
 vable, Tome move horizontal), and Tome vertical!, which 
 is toward the zenith: and firft of the movable wheelc. 
 
 You muft provide a whccle of fuch diameter as you 
 plcafe, which muft be made into fquares, according to the circumference 
 of your wheele, and to proportion your wheele into a juft number, you 
 may allow five inches or better for every fide, fo that your wheelc being 
 finches diameter, the circumference will be as 7 to 22, which is 44 
 inches circumference ; Co being divided by j, there will bee 8 fquares, or 
 more properly, 8 fidcs, which will every one containe 5 inches and^^J'S* 
 which is the cord of 4 5 degrees • thefe fides muft bee hollowed with a 
 groofe fitting your rockets, and at the ends of every fide it muft bee filed 
 with notches, tofaften yourbinding that it Hide nor, when you bindc faft 
 your rockets 5 the form whereof you fhall findc in the fift figure N 1. 
 
 A Sheweth the SJidet. c 1 
 
 B The places of fafinwg. 
 
 C The ferew which fitji net h the wheele to fome 
 
 { -i ; - ' ’ n • 
 
 Note al wayes, that as your wheele doth increafe in diameter, fo you 
 muft increafe in the proportion, for that rocket which forces about a 
 wheelc of 14 inches, will not, force a wheelc of 18 inches s nor that roc- 
 ket whichforceth one of 18 inches, will not force one of 24 inches 5 but 
 that you may come to a necre proportion, I will fatisfieyou fo neere as 
 I can s firft feek the diameter of your wheele, which imagine to bee 
 1 8 inches, I take the third thereof, which is 6 , fo that your rocket for 
 1 8 inches diameter, muft be finches long, and your wheele of24inches 
 diameter, will require rockets of 8 inches 5 yet as your wheelc encreafeth, 
 you may alter this proportion by dividing it into more fides. 
 
 Now having provided your wheele, with your rockets of a juft fizc, 
 you (hall proceed to the finilhingof ir, which muft bee after this man- 
 ner 5 you muft joine your rockets one to another, in fuch fort as I (hew- 
 ed you for your runners, that is, with the mouth of the one tothetopof 
 the other, and fo proceed till you havefaftned fo many as will (erve your 
 wheelc, al wayes leaving fo much fpace between each rocket, as may fuf* 
 fer them to come round about your wheele, without breaking any ; 
 which when you have done, proceed to the tying of them on to your 
 wheele, which muft be fo ordered, that you tie them where the notches 
 are, to the end they faile not in firing, by Hiding off. In tying them on 
 you muft provide that you leave a little diftance between the firft and 
 the laft, which muft be parted with a bolder of paper well foaped, to the 
 
20 
 
 Tyrotechnia , or, 
 
 end that the fir ft fire not thclaft, andfo caufcagreatconfufi^nTNow 
 for the manner of placing them, it is according to the workmans plea- 
 furc, which muft be either horizontal!, or vertical! 5 for the horizontal! 
 whcclc you muft provide a poft faftned in the ground, and ferew your 
 whcelc to the top of ir • for the vertical], you muft fere w it on the fide of 
 the poft, fo having fired them, you (hall fee one run parallel! to the ho- 
 rizon, and the other to the zenith, as you (hall fee deferibed in the fife 
 figure, 
 
 N 2 Reprefenteth the horizontal! rvhtele. 
 
 N 3 Reprefenteth the vertical wheelc. 
 
 There arc many other works which do wholly depend upon the 
 whcclc, of which I will fet down fome few. r 
 
 CHAP. XVI. 
 
 How to make aground wheele . 
 
 ‘ / 
 
 Ere I will declare unto you the manner of making 
 a paire of wheels to run upon a plain horizon ;pr <5 
 vide two wheels, (fuch as arefpinning wheels) of 
 one bignefle, which muft bee faftned to a fmall 
 axel tree, in fuch manner, that they may not move 
 about the axeltrec, and on the middle oftheax- 
 cltree faften a fire wheelc, which let bee fo much 
 r . th an the other, that it touch not the ground, 
 
 lo that being faft upon the fame axeltree, it cannot run unlefle it carry 
 the other with it, which being fet on a plain horizoo, will run a great 
 way without ceafing : now that you may make it return, you may pro- 
 vide your wheelc in fuch manner, thatit may have rockets on both fidcs, 
 io that one fide being fpent, it may give fire to the other, which being 
 fauned with their mouthes the contrary way, will make a return with a 
 fwift motion. 
 
 The form of thefe ground whcelcs you may fee reprefented in the/ift 
 figure, N 4. 
 
 A A the tree wheeles faftned to the axeltree. 
 
 C C the axeltree on which the three whteles are aH faftned. 
 
 B the fire wheelc, which it reprefented of a lejfer dt ante ter than the other 
 two. , 
 
 CHAP. 
 
a Artificial Ftre~)f r or!{S. 
 
 21 
 
 -if 
 
 CHAP. XVII. 
 
 Another manner of ground ypheeles. 
 
 Here is another kinde of ground wheelcs, and that 
 ‘ is made fo, that the whccles may move about the 
 axeltree * but this fort is not moved about by a 
 whceie, in regard the axeltree muft ftand ftiil, but 
 it is made after this manner ; you muft make your 
 axeltrce fomewhat broad about the midft of it, 
 and in that place you Ihall boare two holes, int» 
 which you (ball put two rockets, which muft bee 
 fo clofe one to the othcr 9 that they may almeft touch, [and muft bee fo 
 joined together, that one having fpent himfePc, the other may take hre, 
 after the manner of your line work, to the end that being fired, it may 
 run firft one way, and then the other taking fire, may make his return by 
 a fccond motion : now the rockets which you put into this place, mult 
 alwayes bee proportioned according to the bigneue of your whceie, 
 which if you perform according to the direction, you (ball have your 
 
 The form of this wheclc is expreffed in the fife figure N 4. 
 
 A A the two yoheeles being loofe upon their axeltree. 
 
 B B the axeltree in which the rockets Are put. 
 
 C the place for the two rockets to befafin'J, 7vhich ” dtred > th4t 
 
 the mouth of one may joy ne to the tayle of the other. 
 
 It isefpeciallytobe noted, that thefe wheelcs muft run upon a very 
 plain horizon, fuch as the place for the game of Pall Maile at St. Iamfa, 
 or fome other very finooth place 5 by rcafon that after the fitfl finngoi 
 a rocket, his violence is over, and foa fmall thing will Bay him. 
 
 There ate alfo fundry forts of whccles, which do perform divers 
 offices s fome fot delaying of a Coat of Atmes, and others for fitting 
 of divers circular works, fome of them I will fpeak of } and firfl I will 
 (hew the manner of making a horizontal wheele, which with one firing 
 fhatl give divers reports, and fhall (land fixed. 
 
 Ch ap» 
 
2 z . Tyrotechnia , or. 
 
 Chap. XVIII. 
 
 The manner of making a fixed wbeele, which Jball give divers 
 reports • 
 
 O V muftfirft get a whede turned by fomc work- 
 man, which muft be two foot in diameter, (or as 
 you pleafe to augment or diminlfh your work) 
 which muft have a groofe turned out of the upper 
 fide, of halfc an inch wide, and likewife as deep • 
 to which groofe you muft have a pecce of wood 
 fo fitted, that it may juft Aide in, which pecce of 
 wood muft havefo many fmall holes bored in it 
 asyou will have reports about it, alwayes provided, you fetthem not 
 too neere together, becaufcthc firing of one may not beat down the 
 other 5 when you have thus provided your whcele, make a conveyance 
 or hollow trunck of paper which will iuft fill it, which muft bee filled 
 with fome of your flow mixtures for ftarres, and then putting on the 
 cap of wood fo fitted with holes, and made very faft with glew, pierce 
 every hole into your hollow conveyance, fo that putting a quill into eve- 
 ry one, they may take fire, and to the faid quill fatten a report, fofhall 
 you have a pcale of Chamber* placed in a fmall roome, which being 
 Figure 6, once fired, will follow in order till the whole train be fpent, The form 
 A- you fhall fee exprefled in the fixe figure marked A, 
 
 Chap. XIX, 
 
 Howto make a fixed wbeele which fballcafi forth many rockets 
 into the ayre . 
 
 Here is likewife another fort of wheelc not much 
 unlike to the former, which fhall give fire to divers 
 rockets (landing circular, the order differs nothing 
 from the former, only you muft make a hole for 
 every flick to paffethorow, 3nd therefore it muft 
 be made fbmewhat broader, which will effcift the 
 fame as the other doth, by conveying fire from one 
 rocket to another, till they bee all (pent ; the mix- 
 ture for this conveyance ought to bee very flow, wherefore I advife you 
 to take this enfuing, which is both flow and fare; 
 
 'Take Roch peter, g-r 
 
 Sulphur vive, , « 
 
 Camp hire, \ £ 
 
 Fine powder duft t * 9 
 
 Mealc 
 
<zA rtlficiall Fire 'Worlds. 2 $ 
 
 Meale thcfe ingredients very fine, and incorporate them, adding of 
 Linfeed oyle, and \ § of oyle of peter; thcfe oylcs muft be dropped in by 
 degrees, and fo wrought up, till you findc your mixture bound like , 
 dough, which ifyou performc well, will bee both flow and (urc. The 
 forme of this wheelc isexpreffed in the fixth Figure, by the letter B. 
 
 . ; Chap. XX. 
 
 How to make a fixed wbeele, which (ball ca(l forth divers 
 Fifgigs, and likewife as many reforts or breakers . 
 
 ftufea whecle to bee turned, with a groofeon the 
 top to putin your conveiance of paper; then fit on 
 a pccceofwood, as I have formerly (hewed you, 
 with fmall boles to put in quils, which are for the 
 firing of your reports, and muft bee placed round 
 about the u per part of your wheelc; and on the fide 
 thereof, (hall be made diuers holes of the bignefle 
 of y oar Fifgigs, (which (hall be fo pierced thorow to the paper convei- 
 anccjthofe fifgigs that arc placed round on the fidc,& the reports on the 
 top, one trainc (hall fire them all, and in firing, you (hall fee all the Fif- 
 gigs fly inground about, one after another, as the fire pafleth to them; 
 and for every Fifgig which pafleth out, (hall bee fired a report, fo that 
 there (hall be a contiuuall motion until! the whole trainc bee confumcd ; 
 the forme of this wheelc is reprefented in the fixth Figure, by the let- 
 ter G. 
 
 G Reprefents the whcele finifhed, with Reports an d Fifgigs. 
 
 R R Reprefertts the reports, placed on the uper part ofthewheele . 
 
 F F Reprefents the Fifgigs placed round on the fde of the wheelc* 
 
 Chap. XXI. 
 
 X he manner of making a wheele which (hall rume two waies, 
 which is-, forward and backward* 
 
 ufe a wheelc to he made, fo that the rockets may 
 be placed on each fide, with a hole thorow one 
 fide, which (hall ferve for a vent, pafliag from one 
 fide to the other, then place your rockets firft up. 
 on one fide, provided that the laft rocket be placed 
 over the faid hole, and boring a fmall hole in one 
 fide of that rocket, put in a cotton wickc for pri- 
 ming, and let it come through your whecle, to the 
 mouth ofanother rocket, which (hall bee turned the contrary way; fo 
 thatthc whecle having finifhed his revolution one way, may take fire 
 
 on 
 
 { 
 
V 
 
 
<iArtificidl Pire-Worfa. 
 
 ontheother fide, and fomake a retrograde motion : and as you doe this, 
 fo may you after the fame manner, make a wheclc which (hall runne di- 
 re^:, and continue t wife fo long as another of the fame bigneffe, which 
 is by placing; therockets the fame way on both (ides. The forme of this 
 is exprefted in the 6 Figure, by the letters D and £ . 
 
 D Reprefents thewheele with Rockets placed oh the one fide^ the laft roc- 
 kets having a vent , to paffe through to the other fide. 
 
 E Reprefents the f aid wheele finifhed with Rockets on both fide s. ' 
 
 *5 
 
 CHAP. XXII; 
 
 The manner of compofing a wheele > which haying finifhed his 
 reyolution } fhall nprefenta (bat of Arnes. 
 
 Ake a whcele of fome light board, fo that it may be 
 without any fpoakes, and upon one fide of it, let 
 be drawne,that Coat of Armes you intend to re- 
 prefent, then boarc fo many holes in the wood, as 
 may conveniently Hand on the traced lines, then 
 on the other fide, neere the top, fhall a place bee 
 made, which may containc your rockets, with a 
 hole pierced thorow where the laft rocket muft 
 reft. This being done, place your rockets round about, fo that the laft 
 rocket may be placed on the vent which muft bee primed carefully, to 
 paffe thorow to the other fidcj having placed on the rockets, fill thefe 
 holes on the other fide with forae flow mixture, fuch as is for your ftars, 
 or the like, then cover it over with paper, and put in fome powder duft 
 to fire it, and to break the paper, which being done,fopc it well over for 
 fcare of fome fparkes lighting on the paper before the appointed time of 
 firing, fo haveyou a wheclc ready which you muft put on an axeltrce, fo 
 that it may ftand vertical!, and then firing ir, you fhall have your de- 
 firc,for fo foone as the whcele hath fpent his moving work^, it will giue 
 fire to the other fide 5 and then (landing ftill,you fhall fee a perfeft Coat 
 of Armes in fire. Figure 7 . A. B- 
 
 A Reprefents that fide of the whcele which hath the Rockets placed on it. 
 
 B Reprefents the Coat of Armes 3 in which the round (pots fignifie the places 
 to be filled with a flow mixture , which mufi bee moift, to the end it keepc 
 clofcin. 
 
 c 
 
 Chap. 
 
<iJ rtificiall FireAVorhfs. VJ 
 
 CHAP. XXIII. 
 
 Howto reprefenta Coat ofArmes in fire y which baying burnt a 
 /mail while , the f aid Coat /ball appear e in his perfect colours > 
 and j hall continue Jo a long while . 
 
 jrft caufc a board to be made foure fquare, of what 
 dimenfion you pleafe, which let be jan inch thicke, 
 and caufe a Painter or fome drafts man totrafeout 
 what Armesor other figure you pleafe, upon the 
 faid board* alfo let there be another which (hall bee 
 an inch and 3 thicke, and of the fame breadth, which 
 fatten to the t other| with fome fraall tackes, till you 
 have boared fo many|holcsasyo« have occafion for, 
 which (hall behalfe an inch afunder, and likewife halfc an inch boare- 
 then boare your holes thorow your inch board, and let them enter an 
 inch into the thicker plankc,then make foure fquare holes (one at each 
 corner) in the thicker planke, to receive foure fquare pieces of wood, 
 which mutt be an inch fquare, which glue faft into foure holes oppofite 
 to the other in the thinner planke, to the end it may Hide to and fro* then 
 Men an iron rod in the midft of the thinner, fo that it may come thorow 
 the thicker planke, and be fattened to a piece of wood, which may turnc 
 upon a joy nt; to the end you may draw the thinner fquare neerer as your 
 fire confumcs, and mutt draw it too foot at leaft* then provide a fmall ar- 
 row of two foot long, and upon it rowle fo much paper, till it fill your 
 fmall holes cxaftly, then fill fo many as you have holes already provided 
 
 in your fquare, and put them thorow the thinner piece, and the ends 
 thereof into the thicker, which let be glued faft into the bottome of that, 
 fo that they may ftand very faft, and likewife let them paffcfoeafily tho- 
 row the other holes.that theboard may Hide nearer or furthcr,to or from 
 thefirc,atp!eafurcsthcnfitapiece of paft-board, fo that it may come 
 clofe about thefe rouled lances, and may fit asexaftly as the board doth 
 at the other end. and let this come within halfc an inch of the firing end, 
 then prime them all with quickc powder duft, and cover it over with 
 paper, which having performed, you arc ready againft fuch time as you 
 have occafion to fire it, which mutt be after this manner, obferving which 
 fide the windc is; ftand on that fide, and fire it at the lower corner, fo that 
 by the helpe of the winde, you fhali have it all fire at once; which ha- 
 ving burnt a while, will come to the paft beard and fire it, fo that falling 
 away, there will be rcprefentedaCoatof Armes in colours, clofe to your 
 fire, which may be drawne in by one ftanding behindc, fo that it fhali 
 feemealwaicsto be ftanding in one place, and the light not to grow 
 fhorter till the laft. The forme of this frame is prefented in the feventh 
 figure C D. 
 
 A The frame without the fcutcheen or letters. 
 
 B The btoke fide of the frame, with 4ft iron rod pajjing thorow it,(tndfafilentd 
 
 c a ti 
 
‘Pyrotechnic or. 
 
 to the other part, And the moving part which flideth to and fro At occaftttt 
 
 proffers. 
 
 D The frame finifbed ready to put in your lances. 
 
 F Reprefents the face of the frame , or thinner board. 
 
 G The inner part of the fixed piece , with holes beared in each alike , to put in 
 jour lances of row led paper , filled with flow compofit'ion . 
 
 •. CHAP. XXIV. 
 
 Hoyc to reprefent an antike dance , by the helpe of fire , 
 wbicbfhall modern a circular forme. 
 
 Aufc a board to bee made of two foot fquarc, fo that one 
 fide of it may bee hollowed, (or grooved,) to lay your 
 rockets in j then caufe another board to bee made of the 
 fame largcncffe, fothat it may fit clofe on the other, the 
 rockets lying bctweenc, and in the center of the fame 
 board, place a brafle focket, which muft paffe thorowthe 
 other for the center pinne to enter into it; then place your antikefigures 
 on the top of the faid board, with wiers paffing thorow both; to the cad 
 they may be turned about in their motion, by certaine pinnes placed in 
 another board, which muftftand fixed; fo that moving about the faid 
 board, the pinnes take hold of the wiers which come thorow, and turnc 
 them backward and forward; but in regard of the extraordinary vio- 
 lence of this motion, it will tcare all in pieces, unlefle you have a great 
 care in making all things to runne very exa&Iy, which muft bee tried be- 
 fore you come to ufeir. The order of this is reprefented in the feventh 
 Figure by the letter E. 
 
 ABCD The bottome board, which (lands fixed with a focket to put on 4 
 low pole , and hath a [mail pinne flan ding at each corner. 
 
 E EE The under boardwhich movethjn which is placed the rockets. 
 
 FF The uper board which is faftened to the other , wherein the rockets arc 
 placed, 
 
 G G The wiers paffing thorow both beards which are fafiened to the foot of 
 each anticke. 
 
 H H The other wiers which ftandfafl in the fixed beard, and are to turne a- 
 botst the antick£s paffing by them. 
 
 v 
 
 CHAP. 
 
T 
 
 <>Artificiall FireAVorb^s. 
 
 chap. xxv. 
 
 way for making an anticke dance, which is not fo 
 (violent as the former* 
 
 Akc one of your large fort of whceles, and fallen it 
 on an iron axdtrec, fo that the whcele move the 
 axeltree with his motion* then let there bee a ferew 
 filed on the faid axeltree, which may bee fitted to a 
 fmall whecle of tenne teeth or thereabouts as you 
 pieafe, for the more teeth there is in the wheclc,the 
 flower itgocth,andcaficr, ct centra : which wheelc 
 let it be fo fattened to an axeltree, (on which the 
 board bearing theantickes rauft ftand) that the fire whcele turning about 
 verticall, may move your worke hirozontallj which will move follow, 
 thatthefire whcele will betenne times about, before your Motion will 
 move once about, which being done neatly, will prove a worke of great 
 contentment. The forme whereof is expreffed in the feventh Figure by 
 the letter F. 
 
 A The fire wheels placed on an iron axA***** '* noi made f aft to it. 
 
 B The ferew mad * tUfaui axeltree, or filed out of the fame ft up. 
 
 C The wbeele which the a] ore faid ferew mufi he fitted to runne with, which 
 mufi have fo men] teeth, as you intend tee fire wheelc fall move about for 
 
 once of jour motion. t . , 
 
 D The (cjuare hoard on which the anticke s fiand, and ts faftened to the axe 
 
 tree which hath the wheele. 
 
 E A place for a light to hurne fo long as the worke tndureth. 
 
 F E F T he detent es or pieces which come thorow the hoard from the foot <y. 
 
 GGG Certaine pinnes {landing upright in the fixed hoard, to the end that 
 the others pafing hy may he turned about . 
 
 \ 1 * r . 
 
 • — ■ \ .vwir- v -vi ^ -r 
 
 Chap. XX V I. 
 
 How to comp of e a C a fl e °ffi r * wkenoitb the manner of 
 placing the workes in a true order. 
 
 Repare a Caftle of wood, or plate, of what large- 
 neffe you pieafe, the which (hall bee made fourc 
 fquare, with round towers and battlements, and on 
 the top or inner part of that worke, Is there bee 
 a Idler tower ofthe fame fafluon, with a Vane on 
 the top, or fuch a like Figure, which having prc4 
 vided, let there be a place made dole to the battle- 
 ments, or within one inch ofthem, to lay your con- 
 veyances, (which let be ofbraffe) which is for your reports, which mnlf 
 be placed betwecnecach battlement, and (hall have little pipes of brafle 
 to give fire to each report, which rnuft be fere wed into the great convci- 
 
 C 3 ance 5 
 
 *9 
 
JO 
 
 Pyrotechnia, or. 
 
 ance; which convciance let be filled with your compofition for rockets 
 
 of 1 1. which is one pound ofpowder to ofcoalc duftjand by this 
 meanesyou (hall have then* all fire in order, without any confufion- 
 which having (pent itfelfe, (hall give fire to another convciance, which 
 (hall be placed further in, with a ftrong wall betwecnc, fo that the fire of 
 one doc not offend the other: the ufe of this convciance is to place divers 
 rockets on, fo that they may fire one after another, and (hall take fire as 
 foonc as the reports arc ended. Now for the foure large towers, you (hal 
 ' provide foure pieces of wood, turned and fitted to Aide in exaflly, and 
 (hall have divers Imooth holes boared round thorow the out (id c of your 
 tower, and the wood, till they meet with the hollow which paffeth 
 from the top to the bottome,or within an inch, which hollow (hall bee 
 one inch and a halfe diameter, and muft be filled with a very flow mix-* 
 turc, (to the end it may continue as long as the workc is a burning) then 
 place fome Fifgigs round in thofe little holes, fo that the mouths may be 
 inwardand primed, which will take fire one after another, and flycouton 
 every fide of your Caflle, which will give great content : for the manner 
 of firing this, I could wi(h, that it were firft fired at the foure uper towers 
 and that through one of the corners, may bee a hole, which may goc to* 
 the uper conveyance, that fo thofe reports may fire next, and at the end 
 of that conveyance (hall he another to pafle downc to the lower tier of 
 reports, and at each corner of that convene* (hall be a hole to pafle in- 
 to thofe lower towers, fo that by that time all the reports arc fired, the 
 towers (ball be all on fire 5 then at the end of that conveyance, f as I (aid 
 before) let your conveyance for your rockets bee placed, which taking 
 fire orderly, will conclude the worke.Thcfeand thelike arefor thcplca- 
 fureof princes and great perfonages, rather then for the vulgar. The 
 forme of this Caftlc is laid downc in the eight Figure by the letter A. 
 
 £ B B Expreffeth the angles of the lower tower', 
 
 C C C T he angles of the higher tower, 
 
 DDT he convciance that fires the reports ; 
 
 E The conveyance pajfing to the rockets. 
 
 F F F The Fifgigs placed romd each angle. 
 
 GG R eports placed on the battlements. 
 
 H H Rockets placed farther in -with a. wall be tweene'. 
 
 Chap; XXVII. 
 
 Ho'B* to reprefent divers motions in a Cafile o/Jire-mrke. 
 
 Aufea frame to be made, placing thereon two Ca- 
 dies, that they may fland about twelve foot diftant 
 one from another j this frame muft bee fo ordered, 
 that it may bee hollow underneath, which being 
 done, let the dores of thofe Caftlcs bee placed the 
 oneoppofite to the other, at each end ofthe faid 
 frame, and juft within each doore, let there bee a 
 
 rowlcr 
 
1 1 ( Tyrotechnidy or, 
 
 rowler of wood, fourc inches diameter, which (hall have iron pcvikts or 
 points to runne upon, that they may runne the more cafie; and letthofe 
 roulers be put full offtnall pinnes,and a girt put roundabout them.to the 
 end that the rowlcrs moving circular, may draw the girt in a ftraight 
 line, then placing fome anti kc Figures on the girt(fo that they may move 
 about with it) place your fire wheeles upon the axcltrcc of each rowler, 
 providing another rowlcr at each end to make it Aide more eafily; fo 
 firing the laid wheeles, you (ball fee the antikes come one out of one 
 doore, and the other at the other doore, meeting in the midft 5 and when 
 they come at the contrary end, they make a rcturne with their heads 
 downeward,andcomeupagaineatthc famedoores they went firft out 
 of, which will continue running, fo long as the fire wheeles continue. 
 And when the wheeles ftandftill, the reports lhall gee off on each tower 
 one againft another, which (ball be done after this manner: let one ofthe 
 fpoakcsofboth your wheeles be hollow, and alfopart of theaxcltrec, 
 which let be filled with powder daft, and the rocket which fires laft,(ball 
 be placed over that fpoake which hath the vent, with a piece of cotton 
 wicke to fire it, fo will it runne do wncthorow the axcltrcc, which fas I 
 faid ) muft be hollow, and mnft have paper patted over ir, fo that as foone 
 as the fire comes there, it breakesthorow the paper, and fires a traine 
 . which is laid round about it, which traine paffeth to a ftanding convey, 
 ance, which goeth up to the battlements, and fo giveth fire to thofe re-’ 
 ports; which having paft each corner, the lower tower (hall fire as it paf- 
 feth, and from thence paffeto an inner conuciance, which (ball fire fo 
 many rockets, as may be well placed about it^ this being well and order-' 
 ly performed, will give great content. The forme whereof is expreffed 
 in the eight Figure, N BB, 
 
 B B Reprefents the two Cables ready fitted with the frame. 
 
 A A The twq doores oppofite. 
 
 B The two figures moving forward. 
 
 CCThetwo fire wheeles which caufeth this motion!, 
 
 C Reprefents the frame for this motion. 
 
 D D The two fire wheeles fixed on their axeltree. 
 
 Roler each wheele is fixed to. 
 
 F F The other Roler s which guide the girt s\ 
 
 G G The girts gaffing from one roller to the other. 
 
 HHThe figures placed on the girts. 
 
 
 GHAP. 
 
Pyrotechnic or. 
 
 ?4 
 
 CHAP. XXVIII. 
 
 Mother way to per forme the fame motions and will not be Jo 
 r-jiolent as the former. 
 
 Rcparc your Cadle with the frame fitted as the former, 
 onely upon the axeltrcc of each rowler, let there bee a 
 fmall wheele with teeth, and like wife mud there bee a 
 ferew upon theaxcltrec of each fire whcclc } which muft 
 befo fitted, that they may draw thefe whceles about, 
 which if they be well fitted, will move them with great 
 facilities, and whereas the other fire wheclcs were placed on each fide, thefe 
 mud be placed behindc, or underneath, which you pleafe, or findemod 
 commodious. Now you mud note that your fire wheelc moving once 
 about, moveth buuonc tooth of your other wheele by reafonof the 
 lerew which drawes him, fo that if you make tenne teeth in the faid 
 wheele, your fire wheele (hall make tenne revolutions for one of your 
 rowler: by this meancs it will move after a farre more eafic manner then 
 the former. The manner of this is rcprcfcntcd in the ninth Figure, 
 AAR. 
 
 A A Reprefents the two C aft Its ready placed. 
 
 R T he frame jor the motion. 
 
 BB Two fire wheeleswhich forceth the reft of the work* . 
 
 C C The ferewsfaftened on the axeltree of each wheele^ which forceth the 
 rowlers. 
 
 D D T he two wheele s which are placed on the rowlers , and fitted to the fcreW 
 which force them. 
 
 p P T he two girts on which the figures are placed. 
 
 Chap. XXIX. 
 
 Bow to reprefent theformeofanarmy of an hundred men mar- 
 ching-, which [hall prejent and fire atone certaine place 
 appointed. 
 
 He ground of all thefe motions, are wheele workes; 
 wherefore to proceed, you mud provide a rowler 
 of two foot long or more, which mud be made and 
 placed as the forementioned, to be drawne by two 
 ferewes fadened to the fire whceles, in regard of 
 the great weight they are to draw 5 alfo they mud 
 be fomc what large wheeles, with rockets of the fe- 
 cond fize, which is five ounces in each rocket, pla- 
 cing about 6 ach wheele, 20. or more, which having provided, you muft 
 
 like- 
 
( iA rtificiall Fireworks. 
 
 3 * 
 
 1 kewifeget youfo many figures of fouldiers, wh.ch muft bee cut by a 
 Carver Ind ought to have the joyntsloofe of the right arm ofeacb.with 
 r 1„ 0 r detent to come down from the arm to the thigh of each, and 
 likewifc another, which may move that, and come to the foot s then 
 place tbefe on feverall girts, fo that they may Hand ten in ranck and file, 
 and may be an inch between each, to the end they touch not at the feet, 
 but every file may tun in a feverall groofc ; then placing fmall peeces in 
 
 their hands, which muft bee ready loaded and primed, fet them going, 
 and within two footofthe end of their march, let there bee a crooked 
 
 peece of iron fluck up, between each file, fo that they may ftand luft in a 
 ftrai»ht line, to the end that when the fouldiers move to that place, the 
 detems or wyers are forced againft tbofe pins which draw back the 
 arm, and fo puls the trickers of each Peece in that ranck, fo that the 
 whole ranck will fire altogether, if they bee 
 
 ha ve fired and paft, another ranck moveth forward to the fame place, per- 
 forming the fame ; thus continuing till they have all performed the ike, 
 which being finilhed, and all paft, they Jail make a fecund march, 
 • orderly without firing. This being well and carefully ordered, (ball not 
 fade, and will be a very rare work to behold, but will prove ewraordma- 
 
 ^ The fomo'fXryoSffinde in the ninth figure, by the letter R! 
 
 E reprefents the whole fame, with aU the farts thereof. 
 
 F F are the two fire wheeles, being} laced, one at each end of the rowler. 
 
 GG the fer ewes, being faftned to each fire wheele, which move the two 
 
 wheeles placed on the rowler. 
 
 H H the two wheeles beingplacedat each end of the rowler. 
 
 I I two rowler s, about which the girts do pa fie, which carry the whole body 
 
 kK the girts on which the figures are placed, each girt having upon it ten] 
 
 fo that in the whole t here wiH be an hundred , , 
 
 L reprefentsthefigureofa man fiandtngm that pofiure as hee ought to bee 
 j s the detent which isfaftened to the right arme,and ts tofiide on ajoynt, 
 
 being faftened to the thigh ;/o that it may moveThe arme 
 
 N another detent which moveth the former, as it pafieth by the pm. 
 
 O the fin which putteth by thefaid detent Of it commeth to it. 
 q q the fuid pins in their right placet. 
 
 ChaPs 
 
 f 
 
Pyrotechnic or. 
 
 chap. xxx. 
 
 Bow toprefentmufck playing, (by the help of fire) with anticks 
 dancing . 
 
 Aufeaninftrumenttobee made, rcprefcnting the Virgi- 
 nals, and to it fit a Barrel! fct with fcvcrall tunes, (as I 
 (hall (hew you in another Trcatifc hereafter) then let 
 there be a wheele with teeth faftned on this barrel!, and 
 a fire wheele, with a ferew on the axeltrec, as I have 
 (hewed before, which ferew may be fo fitted, r hat as it 
 moves round the barrell one way, fo it may move another wheele, being 
 placed on the fide, which wheele (hall move certain anticks, as the mu. 
 fick playcth. This and many more may bee performed by the motion 
 of wheele work. 
 
 The form of this isexprefied in the tenth figure, by the letter A: 
 
 B the fire wheele jfixed on the axletree, which moveth a ferew . 
 
 C the ferew , moving a wheele placed on the top of it, and another on the 
 fide.. 
 
 D the wheele fafined to a barrell fet with tunes i 
 
 E the wheele placed on the ftde t which hath a pinion at the end of the axel- 
 tree, marked F ; which carrieth about the wheele G ; on which there are pla- 
 ced foure anticks : this wheele moveth foure pinions marked H, on which is 
 placed four e other anticks. 
 
 I is the barrell fet with tunes. 
 
 K the paUats which caufeth thejackj to move '. 
 
 L thejackj which pa ffe up to the firings. 
 
 M a board or frame covering the firings , on which is placed the anticks. 
 
 Having (poken fufficieutly of the order of motions performed by 
 wheele work, T come now to (hew fome things that may bee done on the 
 Line. 
 
 CHAP. XXXI. 
 
 How to make a Dragon, or any other creature to run on the Line , 
 by the help of fire: 
 
 ET your Dragon be made either of pafteboard, or 
 el(e of fine rods, fuch as your Baskctmakers ufc; 
 which mufi bee made hollow, with a place in the 
 belly to pot in two rockets, and (ball bee fo or. 
 dered, that there may come a fmall pipe from the 
 tayle of one, to the head of the other $ then make a 
 place in the eyes, and mouth, to putinto each hole 
 fire, which (hall be made up in rowled paper, and 
 thruft in j then on the top of the back let there bee faftned two final! pul- 
 leys for the line to run in, which being done, your Dragon isfinilhcd, to 
 
 firing, 
 
37 
 
 iA rtificiall Fire-Works. 
 
 filing, which muft be thus ; firfl fire it at the eyes, and mouth, (alwayes 
 noting, that this receipt muft be fome flow mixture, fuch as your ftarres) 
 then fire that rocket which is placed with his mouth toward the tayle of 
 the Dragon, which will make itfecra to caft fire from thence, till hee 
 come to the end of his motion • and then on a Hidden, as a creature 
 wounded with fome accident, {hall return with fire coming forth of his 
 belly, which being well ordered, will give great content. 
 
 T he form of this you (ball finde in the tenth figure, by the letter B. 
 
 B reprefents a dragon to bee forced with rockets, which are placed in the 
 belly . 
 
 C a place made to pat in a rocket , which muft be put in at the tayle 9 with 
 the mouth of the rocket outward. 
 
 D is a conveyance from the tayle of that rocket, to the mouth of the next , 
 which commeth out at the beHy. 
 
 E E two fmall brajfe puUees,fafined in a frame on the back > f or t ^ ie ^ ne t0 
 run in. 
 
 Q HAP. XXXII. 
 
 Another way for making a fiery Dragon to pajfe on the line with - 
 out the help of fire. 
 
 N the former Chapter, I fpakc of a Dragon of a 
 fmall fifcc, of a foot in length, or thereabout * now 
 I come to fpeak of thofc of a greater magnitude, 
 which cannot fo cafily bee forced with fire, in a 
 ftraightline, without fome artificial! help - for 
 Art muft bee alwayes as a handmaid attending 
 on Nature, to help her in her work j therefore 
 having prepared a large dragon, you muft make 
 divers hollow truncks of wood, within the body, which (hall bee to caft 
 out fire, and on a fudden divers fmall bals of fire, other times a greae 
 number of final! fisgigs. Now to make this run on the line, you muff 
 have a hollow trunck faftned on the back, between the wings of your 
 dragon, which muft bee fomewhat bigger than your cord, with a fmall 
 hole ihorow each end s the ufc of thofe fmall holes is, tofaftena fmall 
 cord, which muft be fo faftned, that one end thereof muft bee faftned at 
 the bead of the Dragon, and fo pafle over a pulley ; (which pulley (hall 
 bee faftned at the end of the line) and returning thorow that hollow 
 trnnek in the back,, it (hall be put over another pulley at the other end of 
 the line, and fo making a return, (hall be faftned to the hole in the hinder 
 part of the trunck. Now one of thefe pulleys (hall have a handle or 
 winch to turn it about, which (hall caufe the dragon to move, and (hall 
 be a help to the drawing of it backward and forward at your pleafure • 
 after this manner you may form many works on the line, which other- 
 wife cannot be done, The form of this is fee down in the eleventh figure, 
 by the letter A. 
 
 D 
 
 A 
 
: 
 
vJ rtifictall Bire-Wor\s. 
 
 VT 
 
 A reprefenteth the dragon ready finijhed, with alibis work / . 
 
 B C the manner of the hollow trunckwhich the cord muft pa fie throw. 
 
 B the place for faftning of a fmall cord, which mufi pa fie over the pulley , 
 
 marked D. - 
 
 D the manner of faftning that pulley which mufi bee at the further end of 
 
 the line. ...» 
 
 o o o o the manner of the paffing of the fay d line which is thorow the hollow 
 trunckj, andfo over the pulley marked E, and then faftned to the other end of 
 the trunck^marked G. t 
 
 F a handle or winch belonging to one of the pulley s which maketh the dra- 
 gon move forward and backward, as occafion profereth. 
 
 H H the great line on which the dragon pafieth a and is only for keeping it 
 fteaddy in the motion. 
 
 CHAP. XXXIII. 
 
 How to reprefent S. George fighting with a Dragon in fire on the 
 Line. 
 
 I Aving prepared your figures artificially made, you 
 1 muft make a hollow trunck thorow the body of 
 each figure, for a great line to paffc thorow, and 
 likewife for a fmallcr line to draw them to and 
 from each other 5 which muft bee faftned in this 
 manner : at the breaft of the dragon let one end 
 of one cord be tied, which (hall paffe thorow the 
 body of the George, and returning it about a pul- 
 ley at the other end, faften it to the back of the George, and at the breaft 
 of the George let another cord be tied, which (hall paffc thorow the bo- 
 dy of the dragon, or a trunck on the back, and fo returning about a pul- 
 ley at that end (hall be pulled ftraight, and faftned to the tayle of the dra- 
 gon, foth3tas you turn that wheelc, the George and dragon will runne 
 furioufly at each other ; and when youpleafeyou may caulc them to 
 make a retreat, and come on againc divers times 5 but in all thefc works 
 forget not tofopc your line extraordinary well, and likewife have a care 
 that your work be not too heavy above the line, but that they may hang 
 equilibria , otherwife they will turn their hceles up ward, which would 
 bee a great difgracctothc work and workman : there might bee much 
 written upon this fame fubieft, butto the ingcniousrl think it is (uffici- 
 ent,thcy may order their works according to their own fancies \ only 
 herds the ground of the matter. The manner of this is reprefented in the 
 eleventh figure, by the letter B. 
 
 C reprefening the George. 
 
 E the [mail tine faftned to the head of the dragon , andpaffetb thorow the ho- 
 dy of the George . 
 

 dArtificiall FirefiV irkes, 
 
 y the pulley which gnideth the [aid line 
 
 41 o thcr e [itefaftned t • 'the br^fl of the horfe, which pajfeth throw the 
 
 ^UhfpZt fboufwSit paffeth, and ufaftned to the tayle of the dragon . 
 K theplace of facing thefaid line to the dragon. . 
 
 T T the treat tine which gtitdeth thefe two figures. 
 
 M the winch or handle faftned to one of the pulleys, and ts for the moving 
 them forward or backward. 
 
 CHAP. XXXIV. 
 
 How to make a trunck of fire y which fball cafl forth diners fire 
 bals. 
 
 Rovide a trunck of fours inch boare, and two foot 
 ' long, with a hollow place in the bottom, of two 
 inch boare, & as much deep,to the end it may be 
 put on a ftrong poll \ let there be a bottom left be- 
 tween the two boarcs, which (hall be two inches 
 thick, fo that there wili be twenty inches left for 
 your work, which fball bee filled as followcth- 
 " - - firft fill it with cornc powder one inch, then put 
 
 in vout ball, which lhall bee five inches and a halfe, and round about it 
 pm powder dull, till you come to the top, then fill it two inches and a 
 halfe with flow mixture, and on thm i wo inches of corn powder : then 
 put in another ball, and after it flow mixture, which (hall be filled lo the 
 iol and foreferve it for your ufe 5 note that you muft turn three iplacts 
 for arming of it, which muft be done either with iron hoops or eife with 
 cords, to theend the violence of your corn powder burft it not ; your 
 upper ball (hall be made after this manner : Having made ready a cafe of 
 caavas,fillitwiththis mixture following. 
 
 Take iLoffaltpeter. 
 
 1 1. of powder daft. 
 
 ‘ l.offulphurvive . 
 a % ofcamphire. 
 
 I % ofeyle of peter. 
 
 Mix thefe very well, till itbecomc fomewhat tough, and then fill your 
 ball, and arm it, leaving foure vents, into which you (ball put foure fmall 
 fKcks, till fuch time you have coated ; the manner of coating is, to dip the 
 ball in a mixture of pich, rofin, tallow, and fulphur, but this is for bals of 
 longer continuance ; the coating for this ball lhall be as followeth , 
 
 D 3 
 
 Take 
 
z Tjirotechnia , or. 
 
 The receipt for coating, 
 
 1 1. of pitch. 
 
 * l. of vernijb . 
 
 1 ^ offulphur vive. 
 
 2 ^ of powder duft. 
 
 Melt your pitch and fulphur,and then poureinyour v«rni(h andpow. 
 derduft, and while it is hot dip in your ball, and then caft a little fine 
 powder duft over it, and fo let it coole a little, and then dip it lightly a. 
 gaine, and fo you have it ready 5 whenyouufcit, pull out your foure 
 flicks out of the vents, and fill them with powder duft, and fo put theta 
 in. The lower ball which is laft fired, (hall be full of ftarres, with pow* 
 der duft intermixed, to break the ball, thefe (hall be primed with cotton 
 wick made of purpofe,to the end it may not fire the bal til it be up a good 
 heighth, and then to break into a fho wre of ftarres. 
 
 The receipt of the composition for the trwick. 
 
 1 1. ofroch peter. 
 
 ? *f fine powder duft. 
 
 \ of fulphur vivc. 
 
 2 % of camphir. 
 
 I ^ of l infeed oyle; 
 
 The forme of this erunck is reprefentedinthe twelfth figure by the 
 
 letter A: 
 
 A reprefents a trunckready fimjhtd , with two halt. 
 
 B the hall which lieth uppermeft , and it filled with flow compofitioni 
 
 C the lower hall , which is filled with ftarres t 
 
 D the flow mixture at the top of the trunck 
 
 E the corn powder to fend forth the upper ball. 
 
 F the fecond lay ofeempofition. 
 
 G the powder for fending forth the lower hall. 
 
 0 o o three places left for arming the faid trunek? 
 
 H the bottom of the trunc h, which muft he two inches thicks 
 
 1 a place loft to put inapoft of weed fer it te ft and en. 
 
 CHAf. XXXV. 
 
 The manner of making a Club^ysbieb being fired, (ball caft forth 
 divers /mail works, orfisgigs . 
 
 Aufe apeece of wood to be turned of foure inches diame- 
 ter, boarcit oneinch and ahalfcfrom the cop toward 
 the bottom, only leaving a bottom of an inch thick, and 
 like wife a place underneath to put in your club ftaffc, 
 the length of this trunck may be eighteen inches ; then 
 draw a circular or fpiral line, from the top to. the bot- 
 tom, which let bee in the manner of a ferew, every thred being an inch 
 and a halfeafunder, and in that line boarc (mail holes, (of the bigneffc of 
 oncofyour fisgigsj till you come within a quarter of an inch of the hot- 
 
< tArtificiall Fire-Wor\s. 
 
 tom of each hole \ and then pierce it with a fmall piercer, till you come 
 to the foulc of the trunck. Having done this, make fmall wyers fuj to 
 each hole, which let be faftned, lo that they may ftand oppolite to the 
 faid holes, within two inches off from each hole 5 the ufe of them is, to 
 keep your fisgigs more upright and fteaddy, which other wife would bee 
 apt to fall out, by rcafon they muff bee put in very flack, or elfc they 
 would not fo cafily come forth, when they fhould, then load your trunck 
 with the flow mixture appointed in the former chapter (for a trunck^ 
 and put in your fisgigs, priming each, and like wife each hole, and fo fi- 
 ring it at the top, you (hall findc them come forth one after another, as 
 your trunck burneth downwards, which (hall fcatter abroad after a con. 
 fiifed manner. The form of this you fhall fee in the twelfth figure, by the 
 letters £ I. 
 
 E reprefents the form of the club without the wyers on, or Any other work* 
 
 I is the /did club ready fini/hed with all his worh_. 
 
 K the wyers placed for to ft ay each fisgig in his place . 
 
 L the fisgigs placed. 
 
 M the place of firing. 
 
 N the clubfaft put into the bottom. 
 
 I 
 
 Chap; XXX VI. 
 
 Another fort of club , which being firedy /bah give many reports. 
 
 Rovide a club like unto the former, but let not the holes 
 be boared fo big, but only that a fmall quill or pipe may 
 go in for a vent to every breaker, then having boared 
 your holes at proportionable dift ance , cut fo many 
 hollow groofes with a googe or halfc round chifell, and 
 fit them to your breakers of papec, and place fo many 
 reports round about it • your reports or breakers for this work fhall bee 
 madeas followetb 5 upon aro wlcr of halfean inch,row!efo much paper 
 till you make it an inch thick, and better, choaking it clofe at one end, 
 then fill it an inch and a halfc with good piftoll powder, choaking 
 it at the other end, fo that it be very clofe at each end 5 then pierce a 
 fmall holc.in the middle for a pipe to enter in, which muft bee filled with 
 powder duff, and put into the fmall holesof your trunck, very clofe,then 
 pitch them well round about, and poure pitch all over, that the work 
 may not befeen ; and likcwife that it may hold your reports clofe toge- 
 ther j this pitch hkewife when the fire commcth to it, will cafily fire, and 
 make a very furious light, which will give great content. The form of 
 this is reprefented in the twelfth figure by the letters O and V. 
 
 O representing the club without the reports placed. 
 
 A the groofes to put in the reports, with a hole in the middle of each groofe 
 , to pnt in the quill. 
 
 R a report with a quid ready to be placed in the club . 
 
 ' ' q the 
 
< lArtificiall FireJVorJy. 
 
 q the manner of the quill -which muft bee pu t into thofe [mail holes to fire the 
 reports, 
 
 V the club finifijedy -with the reports placed in it. 
 
 B B the manner of the reports as they are placed in thefaid club . 
 
 CH AP. XXXVII. ' 
 
 Another > which I call lack in a box, 
 
 HE order of making this is after this manner * 
 provide a box of plate, of what largenefTe you 
 plcafe, which let be fix inches deep, wkh a fockct 
 at the bottom tp put in your ftaffc, then putting 
 in a quantity of corn powder or powder duff, (in 
 the bottom of the box) you (hall fill it with fis- 
 gigs,or ferpents, leaving a place in the middle for 
 a cane to go thorow to the bottom, which cane 
 mu ft be filled with (low receipt, in which you lhall put a quantity of 
 camphir, butnooylcs, in regard ofthc narro w paffage it hath to burn, 
 without any other vent $ then put your cane down, leaving it an inch 
 above the box, and take a peccc of thick paftebord, cutting a hole for 
 the cane to pafle thorow, and gtew it clofe tpthe cane, to the end the 
 fire pafle not thorow before the appointed time • this paftebord muft bee 
 offufficientbreadthto cover your box quite over, then pat it on a ftaffe, 
 and light your cane, which will apfJearc only -Wee a candle, and after a 
 pretty diftancc of time you {hall h'earc a fuddcnjpy fc, and fee all thofe 
 fwgigs flying feme one way , feme another. This toy hath given great 
 content to the (pc&ators. The form bfthis'ls ftt down in the twelfth 
 figure by the letters BCD; 
 
 ' *r» " ■ '' * • ' ' i ; ' '■ 'll j.0 JffilSl ... ■» 
 
 B the box without any thine in it. 
 
 C the fis gigs placed in the box. 
 
 D the box finijhed 3 with a cane puffing thorow sdtbediKteni2\ -iu T ' 
 
 '.MsmH vJTY! A / 
 
 — — 
 
 criAP. xxxvm. 
 
 Hoyp to reprefent the Sphere , moving in the ayre without any other 
 Jupportation • 
 
 life a Sphere to bee made fbmewhat light, and on the 
 horizon place your rockets, and in the zenith or upper 
 part, pet there bee a pinne pafle thorow the meridian, 
 with aringfaftnedcoir, to hang it by $ this muft bee 
 faftned to a large Kite, fo as the Sphere may hang fix 
 foot under it, then fatten a match of cotton to the nofe 
 ofthefirft rocket, and light it, which having done, raifeyonr Kite, and 
 
 by 
 
Tjrotechnia , or, 
 
 . - mf ' ' 
 
 byfuchtimeas it is at the bigheft, the rockets (hall take fire, and (hall 
 caufe it to make divers revolutions in theayrcjyou may place the midft 
 ofthis fphere full of lights, which will feeme very ftrangc. The manner 
 of this is reprerented in the twelfth Figure, by the letters K and S. 
 
 K Represents the Kite which is fupported by the ayre, and to which the 
 fphere it fafiened. 
 
 S The fphere with aU his circle t, the rockets being placed about the horizon. 
 H H T he horizontal! circle about which the rockets are placed. 
 
 Chap. XXXIX. 
 
 How to represent the fphere , with divers circles y Jome 
 moveable , others fixed. 
 
 Aufc a fphcarc to be made, either of wood or mettall, 
 the out ward circles reprefenting the meridian circle 
 with the horizon, the next within (hall reprefentthe 
 Collurs with the cquino&iall, fikewife the tropicks 
 and zodiac kc, whofc poles (hall be i j degrees | from 
 the poles of the, world; by which meanes the cclip- 
 ticke (hall bee , cxcentricke to the cquino&iall, 
 (which (hall be exprefled) fo that fattening rockets about the equinocti- 
 als, and placing two fmall lighten the zodiackc.the one reprefenting the 
 Sunnc,the other the Moone: you (hall fee them move about the earth, 
 (which is placed in the midft of the fpheres) according to the rules of 
 Ticho Brahe, and (ball be according to their naturall manner of motion, 
 which is continually riling and fetling in an oblique motion to the hori. 
 zon and meridian, which alwaies ftand fixed, ana the reft moving on the 
 poles of theequino&iall, although the ccliptickc bee framed from its 
 ownepoalcs. The forme of this is reprefented in the twelfth Figure, by 
 the letter T. 
 
 M The fixed Meridian. 
 
 A A The Horizon. 
 
 £ E T be EcjuinoEliaH . 
 
 £ E The E clipt icke with the S untie and Moone placed round. 
 
 P P The poles or axeltree about which all the inner circles move, 
 
aJ rtificiall Fire^JVor^es, 47 
 
 C H A pi X L» ' 
 
 HoW to make a halfe moone of pockets to appears in the ayre • 
 
 Rovide a piece of plankc of two inch thickc, and 
 turneittoa halfe round, then cutfo many groves 
 (from the center to the circumference) as you in- 
 tend to place rockets about it, and on the other 
 fidejet there be rings for every rod ro paffe thorow, 
 of which let one of each beeclofc to the top, and 
 another ncerc the end of each rod; and note that the 
 plankc muff be fo large, that the ends of all the rods 
 muftmeet in the center; then prime each rocket with a quill filled with 
 powder duft, and put on the top of each groofe, till you have placed 
 your femicircle full; then having primed thefe groofes, (which comes 
 from one center to the circumference ) pafte paper over them, and fo let it 
 ftand till you fire it, which is done after this manner: fet this fame at the 
 top of a poaft, about foure or five foot from the ground, and prime it (at 
 the center) with a little cotton wicke prepared for that purpofe, and fi- 
 ring it, you (hall fee them take fire all at one inftanr, and fo will flye cir- 
 cular, in the forme of a halfe Moone. The forme whereof is reprefented 
 in the thirteenth Figure, by the letters A B. <■ . * 
 
 ■ 0 t*’ * ^ 
 
 A Reprefents the forepart of the frame, in which one prefents the groofe s 
 which paffe to each rocket. 
 
 BD The quits filled with powder dufl, entring into the gr oof es with one end, 
 and into the rocket with the other. * 
 
 B Reprefents the backs fart of the frame. 
 
 E £ The rings below. 
 
 F F 'l he rings above. 
 
 G G The rockets placed on the frame. 
 
 CHAP. X LI. 
 
 How to make a cafe of Rockets to rife at once. 
 
 Aufeaframe to bee made about two foot fquare, with fmall 
 groufes, two inches afundcr, and betweene each groofe s 
 boarc holes for your rocket rods to pafle thorow* you may 
 make tenne groofes, and in each groofe you may place ten 
 rockets, fo you (ball hauc a hundred rockets in one ofthefe cafes, which 
 {hall fire all at once; there mud bee a erode groofe made in the tniddeft, 
 and in the center of that groofe, {ball you fire it, which (ball fuddenly fire 
 all ovcr 9 being primed with a quickc trainc of powder : the charge is 
 great, and quickly fpent, but it makes a very glorious (hew; 
 
 The forme of this is reprefented in the 1 j Figure, by the letters G D. 
 
 A A A A 
 
<tA rtificiall Fire-Wor\s m 
 
 A A A A Reprefents the fqtsire of your cafe which is grooved. 
 
 The white ftroakgs fignifie the qroofes which are to be filled with powder dufi, 
 whereon the month of your rockets rnafi be placed. 
 
 The other fpaces exprejfe the holes where your rods pajfe thorow with a hole 
 in the midfi to fire it at. 
 
 B Reprefents the cafe filled with rockets, their rods Raffing thorow., and is 
 made long, to the end there may be another board at the bottome for each rod to 
 pajfe thorow , that they may be kept more fieady. 
 
 CHAP. XLII. 
 
 HoH> to make letters y or any other figure appear e in the ayre 7 
 after the {pending of a Rocket . 
 
 Aving confidcredofwhatlargcnette yoy will have 
 your letters or figures, make them of paftboard, 
 leaving a hollow to put in fma!l quiis, ( which 
 fiiall bee filled with adcare and ftrong mixture) 
 then put in your quiis, and glue them faft in 5 and 
 jndfo have you finifhed it, till you come to ufeit. 
 There is another manner, which is thusiprovide a 
 mould of plate, and cut out what letter you pleafe 
 in waxc, which having done, fticke it full of quiis in an orderly forme, 
 and put this on the head of your rocket: note this, that thefe arc onely to 
 be ufed on Very large rockets. The forme of thefe are reprefemed in the 
 thirteenth Figure E F. 
 
 n m*i j sWnvoibbriid L. ; ;r;bisid: \'i ‘ ' 
 
 The forme of the letters, the white fpots fignifying the place for fo many quits . 
 \ filled full of flow mixture, to be placedin* . ~4r- " ; 
 
 j CHAP. XL I II. 
 
 How to reprefent a figure of the Sunne cafiing fort ft his 
 beames , in fire* 
 
 Aufea boxe to be made of plate, too inches long, and 
 one inch diameter, which muftbefilled with your 
 flow ompofition, and let the head be made with 
 (mail groofes, croflSsg the center, to the end you 
 may lay in certaine fprings of ftcele, fuch as they 
 ufc to fmall Watches. Thefe fprings (hall bee a- 
 bout fixe inches in length, and mull be fourc, lo 
 that both ends of each appearing, will make cighr, 
 which will make a circular forme, the boxc being the center- now to the 
 end of every one of thefe fprings, muft be fattened oncofyour fraallFif- 
 gigSj&then bent up clofe to the boxe, and fo pur into your coffinc at the 
 
 F , fop 
 
5© ^Pyrotechnic or, 
 
 top of yonr rocket, with powder duft and cotton to fire and breake t he 
 coffine, which as foonc as it breakes, the fprings will caft forth your Fif- 
 gigs, and make them feeme like the fparkling beames of the funne, and 
 the mixture in the center will fecrac as the body of the fame; this will 
 continue a while, and then you (hall fecit breake with divers reports. 
 This I had from a noble Captaineofthis City, namely Gaptainc Fore- 
 flat , who invented the feme, the forme whereof is reprefented in the 
 thirteenth Figure, by the letters L M. 
 
 L 'Being the boxe with the fprings fafiened to the top , with a F if gig at the 
 end of each. 
 
 Mlhefaid boxe fnijbed with the fprings bent ready toputenthe head of a 
 Rocket \the month of each F if gigmttfi come downe to the mouth of the boxe, 
 and fi be put with their mouthes aH downewards . 
 
 Having fpoken fufficiently of workes operating in theayrc,I will fhew 
 you fomething which (hall ferve for ground workes. * 
 
 CHAP. X L IV. 
 
 How to make a pocket which firing it out of your bandy /hall con- 
 tinually be in agitation on the ground fometimes >aml 
 other whiles about in the ayre. 
 
 Aving prepared a Rocket, with a report in the head, tycit 
 to a bladder, fo that the end of the Rocket may come to 
 the mouth of the bladder, and binde it over very ftrong- 
 ly, then firing it out of your hand, caft it away from 
 you, it matters not which way, for it will come to the 
 ground, and by rcafon ofthe bladder, it cannot ftay,but 
 prcfcntly rebounds upward, moviug to and fro, till it be all fpent. There 
 is another fort, and that is a fmall Rocket put into a bladder, and fo 
 blowne up round about it, and tycd about the necke of the Rocket. The 
 forme of thefe are reprefented in the 1 3 Figure, by the letters G H. 
 
 Gibe Rocket with the biadder at the taile of it, 
 
 H The Rocket in the bladder, ' 
 
 ’J 
 
 Chap* 
 
dArtificiall Fire-ff^orfys. 
 
 CHAP; XLV. 
 
 How to make a ball "which J ball be in continuall agitation on the 
 ground , till the fire isconjumsd. 
 
 I 
 
 Au Ce a ball to be made of fome light wood, which 
 muft be made fo, as you may take it afufider juft 
 in the midft, then make on each fide a hollow 
 groofe to lay in two rockets (joyned together af- 
 ter the manner of your runners) fo dole up your 
 ball faft with glue; onely in the place where the 
 two Rockets joy ne, (hall be a groofe, which (hall 
 bepafted over with paper, thar the fccond rocket 
 firing, may have a: vent, otherwife your ball will ferve but once. Then 
 fire it, and you (hall have your defire. This is reprefented in the 13 Fi- 
 gure by the letters I K. 
 
 I Reprefents a pan of the ball, eu it is ready to place in the Rockets • 
 
 K Reprefents the ball, with the Rockets placed in, fo that the other fide be. 
 
 ingfiyned, makes a perfeSl round, 
 
 C C C The vents to each Rocket, which beingclofed, muft have paper glued 
 
 over them , that they be not feene, 
 
 — *— - « *. •. 'T i . V.'VT ^ . . rtr* . 1 -n . nl , ■■ . 
 
 CHAP. XLV I. 
 
 How to make another jort of BaOes for the ground^ which 
 will be a long time in their motion • 
 
 Aufc a ball to be made of fome light wood, and let it bee 
 hollowed, to make it the lighter; then fit in two pieces of 
 wood, fo that you may make both fidcs equal], which 
 pieces of Wood (ball be fo groofed, that you ttiay lay in 
 fo many Rockets as may well be contained about it, pro- 
 viding that at the end of each groofe or rocker, you may 
 have a vent thorow your ball, then place in your rockets as I have (hew- 
 ed you for the whcele: which having done, glue them faft in, to the end, 
 that by the motion of the ball, they may not be difordered, then ioyne 
 your ball together, and glue it faft with paper round about it, to the end 
 the vents may be covered, onely leaving one open to fire if, fo have you 
 this ball finilhed, which firing, will continue along while in motion, 
 Figure 3 6 . 
 
 AThe ball turned hollow with gr oof es to lay in your rockets, 
 
 Ik The other part of the ball, with th'e rockets faftened in. 
 
 C C C C The vents at the end of each rocket. 
 
 e*: 
 
 chap; 
 
Tjrotechnia , or. 
 
 CHAP. XLVIL 
 
 HoW to make a Dragon iffuing forth of a QaVe^ which frail 
 cafi out much fire, 
 
 IRovidca Dragon of fome light matter, as wicker 
 rods or the like, which let bee made fo, that you 
 may put into themidft of the body, one of your 
 greateft rockets, and clofc under the belly let there 
 be a couple of wheeles, which (hall bee fo placed 
 
 in the belly of the Dragon, that no part may bee 
 
 fcenc, but onely the bottoms which ccmcs to the 
 ground; and let the rocket bee fo placed, that it 
 may with trainesfireall parts of the body, as the eyes, mouth, and all o 
 thcr parts; in which you (ball place divers final! workes, which firing 
 fhall flycout,andmakca very great (he w, which (hall burne till all bee 
 confumcd: this Dragon muft be fo placed, that he may come forth of a 
 Teeming cave; which firing on a fudden, will make a great noy fc by rea- 
 lonofthelargencffe of the rocker, and the hollowncfle of the cave hce 
 comes forth of. The forme whereof is reprefen ted in the fourteenth Fi- 
 gure by the letter G. 
 
 G The 'Dragon ready fini/hed. 
 
 A The wheeles on which it mufi rttnne, which mttft bee hid within thebodv 
 3 The rocket placed in the body of the Dragon, which canfcth the motion' 
 G The vent whtch pafeth to this rocket for the fi ring. 
 
 CHAP. XLVIII. 
 
 Hew to make two Dragons to meete each other ^ from fey er all 
 Caves , whic h frail (end forth their fire to each other 
 with great njiolence, 
 
 > Aving prepared two Dragons (both of one fize and 
 weight) after the manner as I have fhe wed you in the for- 
 « Chapter; it is requifite that you know how farre they 
 f. wul runne, then place the Caves at fuch a diftanee one 
 - ™e other, that they may meete each other in the 
 
 , , m ro,d wa ^ l 8n J d th «y° u ra «y doc this the more neater, you 
 fhall h<vc your ground laid with fmooth boards that they may runne 
 more free, and from themidft of the walkc, <° the «nd of each Dragon; 
 lettherebcagroofcmadcin one of the boards, which fhall fervetocon- 
 
 (,' ial . n ^ t0 | C1Ch ’ J ^ r ?** ® r,n 8 ** *** n you fl>*U be fiire, rhat if 
 you hie it in the mtdfl, they will both take fire together; alwaics provi- 
 ded you make a convey aoce ofpaper from theboard to the taile o! each 
 Dragon, or to the mouth of each rocket, which being fired once, they 
 
 (ball 
 
a Artificiall Fire-Works. 
 
 (hall mccte, and caft forth their fite at each other with great violence* 
 The forme of this is reprefented in the fourteenth Figure, by the letters 
 A A. 
 
 A A The two Dragons ready to runne. 
 
 B B The two great rockets which forceth them. 
 
 C C The wheeles which each Dragon runneth on. 
 
 D The midft of their walke, with the groofe to each rocket. 
 
 There are divers other workes which may bee performed after this 
 manner, which for brevity fake I will omit. 
 
 Likewife there arc divers motions to bee performed by the a&ion of 
 man, as (ingle duels, to which appertainc the Buckler of fire, and likewife 
 the Curtlax or Fauchion, the manner of which hath bcenc formerly de- 
 feribed by divers Authors, almoftinall languages, and therefore will 
 fceme more then requifite to relate thofc things fo large as they might be- 
 for whata&ioncannQfcmanperformcby hisinduftry ? and therefore I 
 leave every man to his owne order, oncly I will (hew you the making of 
 one fort of Bucklar, which as yet hath not beene performed, and likewife 
 the Fauchion or Curtlax, and firft for the Bucklar. 
 
 Chap; XL IX. 
 
 How to make a Bucklar 'tohich\ha\l caft forth a hundred Fifgigs > 
 every one making his report. i 
 
 ^ufc a Bucklar to bee made of fome light wood, 
 which let be about two foot in diameter or more, 
 asyoupleafe, then caufc a groofe to bee cut in it, 
 from the center to the circumference in a fpirall or ' 
 Terpentine forme, then fill that groofe with one of 
 your flow competitions, fuch as hath neither oyle 
 nor gummes, by rcafon the fume thereof may not 
 offend the Bearers^ when you have filled it, fit in 
 pieces of wood, which may have holes to receive a quantity of Fifgigs, 
 let every one bee two inches afundcr, and let there be wycr rings to every 
 one of your Fifgigs to hold them fteady, that they fall not our, till fuch 
 time they fire, then put in your Fifgigs, into every hole one, till you come 
 to the center, and then (hall you have a very great breaker, fo that firing it 
 at the circumference, every Fifgig will flyc out as the fire comes to it, and 
 will flye againft his adversary combatant, till they come both to the cen- 
 ter, and then will they give a great report, and fo end. The forme of this 
 is reprefented in the 14 Figure by the letters F G v 
 
 F Reprefents the Buckler as it mu ft be grooved. 
 
 G Reprefents the fame finifhed, with the Fifgigs placed about it. 
 
 H H Reprefents the manner of ufing the faid Buckler , with the Fauchion. 
 
 E? CHAP, 
 
a Artifictall Fire-lVor^s^ 
 
 CHAP* L. 
 
 How to make the Curtlax , Cimiter, or Faucbion . 
 
 Rcparc a Curtlax either of wood, or plate, which let bee hol- 
 lowed from back to edge, three inches, and let it bee fo thick, 
 as it may ferve for your fmallcft fisgigs, then you (hall have 
 a pcece of paftebord fo fitted on the back s that your work 
 may be dole covered, only holes left for the ends of your fisgigs to come 
 forth ; then you (hall lay in your lances of fire (which is nothing clfe 
 but your flow compoficion for ftarresput into hollow truncks of .paper 
 made on an arrow) and between every lance you (hall put two or three 
 fifgigs, which (hall fly out fofoon as the fire commcth to them ; having 
 done this, you have finilhed your Fauchion, which muft bee fired at the 
 point, and fo burn downward towards the hilt. This hath been former* 
 ly fet forth by Monfieur T hybavieh French Author, and fince by divers 
 others. The forme whereof is reprefented in the fourteenth figure, by 
 the letters I KL. 
 
 I represents the Fauchion prepared, with agroofe in the bach. 
 
 K reprefents the Fauchion, with holes to put in the works. 
 
 L reprefents a Fauchion wholly finijhed, with the fifgigs placed ac they ought 
 to flank . 
 
 Having fpoken fufficiently of land works, I will come in the next 
 place to (hew the making of fbtne works to bee a&ed on the water 5 and 
 firft of all I will (hew you the making of the water bal$. 
 
 Chap. LI. 
 
 How to make a water hall , which /hall burn on the water , 
 with great r violence . 
 
 Ijlrftjhaving confidercdof what bignefleyou will 
 ' have your ball, take the circumference and 
 halfe it, and of that halfc make a circle, which 
 cutting out in flrong canvas, (hall bee halfea 
 cafe, (o that fewing two of them together, they 
 (hall make a cafe according to your defirc • 
 For Example 5 I have a pall to ma kc whofe di- 
 ameter is fix inches, then the circumference 
 (being as feveo to twenty two) muft be 18 «, fo 
 the halfc will beep which muft bee the diameter of your cloth, and 
 muft bee made true round, fo that fewing two together, and making a 
 cafe thereof, it (hall bee alpsoft fix inches, which the arming will make 
 good ; having made your cafe, you (hall proceed to the filling ofit, which 
 (hall be done after this manner ; you (hall firft put in three or fouregood 
 
 fpoonfuls 
 
5<S \ c Pyrotechnid , or, 
 
 fpoonfulsof your mixture, and then with a flick (made round at one 
 end) force it clofc together, and fo continue filling it, and between every 
 filling put in your flick, and force it together, rounding it continually in 
 your hand, till fuch time you have finilhed it 5 which having done, lew 
 it up dofe, and then arm it with fmall cord, which is called marling j af- 
 ter you have done that, you fhall coat it with a quantity of rofin, pitch, 
 and tallow di(Tolved,and fo your ball dipped over in the fame, providing 
 al wayes thatyou leave two vents to fire it, which flhall be pierced a third 
 part into your ball, and muft bee flopped with fmall flicks, till fuch time 
 you come to ufc them, then pulling forth the flicks, fill the two vents 
 with fine powder duft, and firing it, caft it into the water, and you (hall 
 have your defire ; you muft alwayes let your ball be thoro w fired before 
 you caft it from you. 
 
 A receipt for this ball. 
 
 Take I (. of powder. 
 
 8 ^ of rochpeter . 
 
 4 h offulphar. 
 
 \ 2 ]$(>} camphir. t -• - , .. 
 
 1 % ofoyle of peter, 
 
 l%of pyl of linne, 
 
 3 hof ojle of frike. 
 
 2 h ofcolophoma. 
 
 The forme of this ball is reprefented in the fifteenth figure by the let* 
 ters A B. 
 
 A A the canvai ready cut, to be fewed together. 
 
 B the ball fini/bed . 
 
 CC the two vents, 
 
 D a peece of cord left to hold it by whilfiyon coat it, and likewife tohan% it 
 ttp being fini/hed. 
 
 CHAP. LI I. 
 
 A water ball which ft all ftoot forth many reports. 
 
 Aufe a ball to be made of wood, which fhall bee in 
 two pccccs, fo that you may joy nc it dole together 
 at pleafure ; this ball muft have fmall holes boared 
 round about it, to put in your quils, which muft 
 fire your reports * the reports or breakers (ball bee 
 made of paper choakcdat both ends, and primed 
 thorow the midft 5 they fhall bee faftned round 
 with pitch, and fo covered round about, that no 
 water may pafle in 5 you fhal fil this bal in two halfcs, to. the end you 
 may force it very clofe together, and when it is filled, giew it faft, and 
 arm it well with nealed wyer, then put io your breakers, with a quill 
 
 which 
 
dA rtifciall FireAVt )rkes, 5 7 
 
 which dial enter into the bal, and likewife into the breaker ; the forme 
 whereofyou (hall fee in the fifteenth figure, by the letter C. The receipt 
 for this bal muftbe fomewhat flower than the laft, by reafon of the ma- 
 ny vents it wil have, as the reports paffc away. 
 
 The receipt for this ball. 
 
 T akf I /• ofrochpeter, 
 
 4 h of powder daft. 
 
 3 ^ offulphar vive. 
 
 2% of cantphir, . 
 
 I %of linfeed oyle. 
 
 2% of rofen. 
 
 I ^ of oyle benedick^ 
 
 Powder that which is to bee powdered, and incorporate them well 
 to°ethcr, and by little and little fprinckleiyour oy les,til you have wrought 
 itUkcapafte,and then make ufe of it 5 yourquils which you prime with 
 flial be filled only with powder duft, to the end it fire fuddenly before 
 the quil come to (brink up, which wil be with a flow mixture. 
 
 A the month of the ball where it is to be fired. 
 
 B B B the reports or breaker s, beingmadeof paper, and filled with come 
 powder. 
 
 CCC the quits, which are printed with powder daft, and ferve for firing 
 the reports . 
 
 V the hollow of the ball , being filled with the flow compofition 
 
 CHAP. L 1 1 1. 
 
 I foyto mdeaWater ball , which, after a certaine time of firings 
 (ball ca(l forth divers rockets into the ayre . 
 
 Reparc a ball of wood, of eight inches diameter, and 
 boare a hole in the midft (of an inch and a halfe) and let 
 it come within one inch of the bottom, and round about 
 that great hole you (hall boare eight fmallcr holes of an 
 inch, fothattbey may bee fit for eight rockets • thefe 
 holes (hall be an inch from the greater, and (ball all meet 
 in one at the bortom 5 whercfofe you (hall cut off the bottom of the ball, 
 and fit another to it, which may be fo hollowed, thacyour mixture may 
 be conveyed to all the rockets, then fatten on the bottom (having filled 
 it with your mixture ) and put in your rockets, with the mouth of each 
 rocket down ward, : pafting paper round about it, which (hall bee coated 
 with rofin and tallow, and over each hole where the rockets are placed, 
 let it be foaped over the tallow, to the end that being fired, the fparks 
 may noteafiiy take fire of the paper, which other wife would make fome 
 confufion ; having done this, fit in a pecce of wood to the greater boare 
 of your ball, leaving only a fmallcr vent, of halfcan inch, and by this 
 
 meanes 
 

 j Pyrotechnist, or, 
 
 mcancs the fire will come out with more violence, and having fpcnt ft 
 felfe, within one inch of the bottom, it (hall fire the eight rockets placed 
 about, which by their force Chall break the paper of each, and afeend in- 
 to the ayre, a (mail heighth, and after lie tumbling on the water. *This 
 ball is reprefented in the twelfth figure by the letter D. 
 
 A the place of firing the ball, 
 
 B B thepeece of wood put in to leffen the vent, 
 
 C the greater hollow to be filled with the flow composition as the former. 
 
 D D the bottom, which is loofe , and to bee hollowed to receive part of the 
 flow mixture, 
 
 E E the holes boared to put in the rockets, which mufi bee covered with 
 paper. 1 
 
 F F the rockets placed in , with their mouthes downward. 
 
 G G the place of fitting the rockets. 
 
 CHAP. LI V. 
 
 Another fort of water baU> which fballcafl forth rockets at two 
 Jundry times , and if ter it isfini[bed , (ball give a great report* 
 
 |His bail (ball be made alter the manner of the other,' 
 but (hall bee a foot in diameter, and {hall have 
 iwb circles ol rockets placed roundabout, fothat 
 the lower circle fhall be one inch from the higher, 
 and likewife {hall go down into the ball an inch 
 lower, and under that row of rockets there {hall 
 be placed abreaker of iron, which {hall bee one 
 inch from the lower tyer, fo that the ball being 
 fired, {hall after a certain time, call forth a dozen of fmall rockets, and 
 then continue a while longer, and then in regard of the larger circum- 
 ference of that circle, it fhall caff forth twenty, and after that is ended, 
 their fire comming to the chamber of iron, {hall caufe a very great re- 
 port, and fo conclude. The form of this is layd down in the fifteenth fi- 
 gure by the letter H. 
 
 H the vent for firing the ball. 
 
 1 1 thepeece of wood fitted to the greater boare. 
 
 K the hollow of the greater boare filledwith a flow compofition. 
 
 L L the upper tyer of rockets. 
 
 M M the lower tyer of rockets. 
 
 N the breaker of iron. 
 
 oooo the places to put in the rockets, which mufi bee covered with pttper 
 wellfoaped^upon tallows 
 
 Chap* 
 
6 o 
 
 'Pyrotechnist, or. 
 
 Chap. L V. 
 
 Another fort of ball, with iron chambers } every one ca fling 
 forth a fmall ball. 
 
 Aufc a ball to be made, of twelve inches diameter, and in 
 the midft boarc a large hole of two inches high, hollow, 
 ing it within, and let it come within an inch of the bot- 
 tom ; then boarc fmall holes of an inch from the top to 
 the bottom, in a fpiral line, to put in your fmal cham- 
 bers, which (hall be made of iron, each chamber having 
 a broad plate at the mouth to faften it to the ball 5 thofc chambers fhal 
 be loaden with a quantity of corn powder, and after that a final ball made 
 up in canvas, and primed, as I have (hewed you for ftarres, then having 
 filled the large concave with flow compofition, place in your chambers, 
 whofc touch holes or vents muft bee juft at the breech, and fhal come al 
 in toward the center of the ball, then coat it round with rofin and tallow, 
 and fo baveyou thisbal finifhed • the form whcrcofis reprefenred in the 
 fifteenth figure, by the letter A. 
 
 The fir ft figure marked F, reprefents the infidc of the bal. 
 
 F the mouth of it. 
 
 B B the iron chambers, as they lie with the touch hole or vent of each cham- 
 ber, at the breech of the fame. 
 
 C the concave fitted with flow compofition. 
 
 D a large chamber placed at the bottom : note , that this ball mu fl bee made 
 in two peeces , to place in this chamber , and after glewed well, and bound about 
 with wyer. 
 
 The fccond figure marked G, is the bal finifhed, except theceating. 
 
 G the vent At the mouth. 
 
 B B the reports, with a plate of iron round the mouth of each , to nay le it 
 
 Ufi. 
 
 This bal being thus provided, muft be after covered with canvas, and 
 then dipped in a mixture of three parts rofin, two parrs pitch, and one 
 part tallow, which muft bee firft incorporated on the fire, and fo ufed : 
 this bal may ferve as wcl for fcrvicc in warre, as for pleafure or triumph, 
 by putting into each chamber a bullet of lead 3 and fo fhot out ofa Mor- 
 tcrpeecc. 
 
 a 
 
 CHAP. 
 
<t /Irtificiall FireAVorfy. 
 
 Chap. L V I. 
 
 ’there are divers other forts of bals , as weUfor water as for land> 
 and are to be /hot out of the Mor ter peece. 
 
 N D becaufe the Mortcr pccce is often ufed in Fire- 
 works, I will deferibe the manner of it, with the 
 ufe thereof, as much as is requifitc to this place : 
 and firft for the manner ; the manner of the Mor- 
 tcr pcecc confiftctb only in his proportions, which 
 arc "divers, according to the pleafurc of the work- 
 man 5 butthofeof moft ufe for fire bals, are one 
 andahalfe, and two diameters, in the length of 
 the chafe, and one diameter in the length of the chamber, with halfe a 
 diameter at the mouth of the chamber ; the reafon of this fliortncfle is, 
 that one may come the more comtnodioufly to the firing of the ball j the 
 proportion of this pcecc foiloweth in the fixteenth Figure. 
 
 B is the farm of a%lorter pee$e lying on hu carriage, the quoyn being made 
 to draw with a ferew, as I have wade ufe of. 
 
 A A the diameter or h eighth of the boare, which i* \\ inches , or 1 00 farts 
 of this fc ale. 
 
 A B the length of the chafe , and is two diameters, or 8 * inches. 
 
 B B the h eighth of the chamber , which is halfe a diameter of the Jhot, which 
 is here two inches. 
 
 BC the length of the chamber, which is one diameter of the Jhot , that is 
 foure inches. 
 
 C C the bottom of the chamber, which is one inch, or \ diameter. 
 
 D D the diameter of the tr unions, which is halfe the diameter of the /hot, 
 and it two inches. 
 
 D E the length of the tr unions, and is two inches. 
 
 The proportion of powder for this peece is 2 § for a ftone fhor, and 
 1 § for a Fire ball. 
 
 CHAP. L V 1 1 . 
 
 How to make a ball for tbe Morter peece, which /ball cafl forth 
 a great jhowre of ftars at the breaking. 
 
 His ball cruft bee made of canvas, and muft bee fo propor- 
 tioned, that«bcing armed (as I have formerly (hewed) 
 it may iuft fit the chafe of your peece, which being rea- 
 dy, you fhal! proceed to the filling of it, which muft 
 be after this manner j at the bottom of this ball putin 
 an ounce of fine corn powder, and then putin fomeof 
 your round ftarres well primed, and fo fill them up clofe about with 
 powder duft, ftill putting in more of thofe ftarres, end in the midft put 
 
 F one 
 
/ 
 
qA rtificiall Fire^Workes. 
 
 one ftarre which may be fome wbat great, fo filling it till you come within 
 one inch of the top, then fill it up with a flow receipt, as I have formerly 
 preferibed for balsj and few it clofe up , arming it with fine cord, or mar- 
 linc,and pierce a vent in that place where your flow mixture lyeth, al* 
 waics provided you pierce it not too deepe,that your ball breake hot be- 
 fore his appointed time: then when you would ufe it, bade your niorter 
 piece with one ounce ofcorne po wder, putting afrer a wad d and tampi- 
 on, and put on your ball with the vent towards the mouth of your piece: 
 fo elevating your piece toward the Zenith, you may proceed to the fi- 
 ring of it, which muft be after this manner : provide two matches ready 
 lighted, havingonc in each hand, and firft fire your ball with one hand, 
 andprcfently give fire to your Piece with the other, alwaies holding 
 your head under the horizontal! line of your Piece, for feare theblaft 
 annoy you: this having done, you fhall fee your ball, mount very high, 
 withafairetaileoffire,and whenitisathigheft s fhall breake forth into 
 a goodly fbowreofftarres.* oneofthefc bals will oontaine almoft one 
 hundred fmallftarrcs. The forme of it is reprefented in the \6 Fiigure, 
 by the letter G. 
 
 C Reprefenting the hall cut in funder , that you may fee the order of the fiars 
 
 ^ ~EThe great fiarre in the midfi, with all the refi placed about it. Note every 
 one of thefe fiars mnfi be primed thorow with cotton wicl^e, as I have formerly 
 
 /hewed. . . . 
 
 D The J low mixture, which commeth within one inch of the top . 
 
 * 
 
 CHAP. LVIII, 
 
 jfnother fort of ball for the morter piece, which (ball cafl forth 
 divers Rochets in the ayre. 
 
 His ball muft be made of wood, according as I have 
 formerly (hewed you,onely it mufibe made pro- 
 portionable to the piece, and moreover the vent 
 which in the other is required to be a flow mix- 
 ture, in this muft bee more fwife, in regard it 
 would otherwife continue till it came to the 
 ground, wherefore the mixtute that this ball fhall 
 be filled with, fhall be the fame that your rockets 
 of one pound arc, which is 4 & of coleduft to a pound of powder, and 
 one ounce of faltpetcr. Thefe muft be well mealed, and like wife muft be 
 clofe driven, otherwife it will confumc too faft. This ball may bee made 
 fomewhat cillindricall, in regard of the length of the rockets to be pla- 
 ced init as you have made this for to caft forthonce, foyoumaymake 
 another^ caft forth twife, as I have formerly Ihewed you for the wa- 
 tcc ball. The forme is reprefented in the is Figure, by the letter D. 
 
 Fa CHAP. 
 
<zdrtificiall FireAVorJ^. < 5 ? 
 
 C h a p. L I X. 
 
 How to compofe a fbip of fireworkes, which being once fired) di- 
 vers motions fhaOprefent themjelves. 
 
 tufe a mould to be made fo, as you may cake off the 
 upper dcckc, to place fomc worl ej underneath, 
 where you (hall have a fircwheclc placed with a 
 fere won thcaxcltree; this whecle (hall bee placed 
 in thefternc,and (ball turne a rowler, on which 
 (hallbetwo girts placed, which (ball pafleon each 
 fide of the mainemaft, and runne on to the fore- 
 Ihipjin this whcelc there (hall be a hollow fpoake 
 and axeltree, as I have formerly (hewed, which (hall be fo ordered, that 
 the whcele being (pent, it may convey fire to a tier of gunnes lying round 
 about, which (hall be fired with a clofc conveyance, and having patted 
 that, it (hall take bold of another conveyance, which (hall give fire to cer- 
 taine rockets, being placed in the bodies of fomc figures reprefenting 
 Mariners, and (hall be fo fitted, that they may have a cane joyned to the 
 bodv to guide them, fo that they may runne up from the top of the deck, 
 to the top of each matt: this and many the like may bee performed with 
 great facility. The forme of this is reprefented in the 1 6 figure A . 
 
 A Reprefents the Jbip ready finijhed t with all things in motion. 
 
 B The fire w bee/e which moveth the rowler^and carry eth the girt whereon the 
 figures are placed. 
 
 C The figures placed on the girt being in motion. 
 
 D D D D The tier of guns which fire as the wheele beginneth to ft and ftill . 
 
 E E The figures which ftand ready to runne up the cords; alfoyou may fee 
 Jome in their motion halfe w ay ,and others being got up to the top of the mafts. 
 
 CHAP. LX. 
 
 Ho'V to make the Siren or Mermaid, playing on the water . 
 
 [is is to be formed divers waits, according to the 
 magnitude of the figure* ifyou will make one of an 
 ordinary length, which is five or fixe foot, pro; 
 ccedas foffowethi Let the body bee made of light 
 rods.fuch as basket-makers ufc, and in the center 
 of the body, let there be placed an axeltree, having 
 too whceles comming into the water; yet fo as they 
 may not be feenc 5 theft whceles muff be made hoi. 
 low,toconrainc a quantity offand or water* the ufc of it is to keepe the 
 Sirene upright, and alfotofinkeitfofarrcinto the water as is needful I, and 
 likewife tomakc itgoemore ftcady* note that tbefe wheeles muff bee 
 loofe, and the axeltree fafti in the midft of this axeltree, place three or 
 
 F i foure 
 
‘Pyrotechnic or, 
 
 foure great rockets* one by another with their raouthes all one way,y« 
 fa provide, that there may be fuch a diftancc betweene each rocket, that 
 there may come a vent from the raile of the firft, to the mouth of the fe- 
 cond, and from the fecond to the third, and to the end that it may con* 
 tinuc’the longer in motion, you may place divers lights about the body, 
 to make it more beautiful!; every of each light extinguifhing, fhall give 
 a report, and fo conclude. The forme of this is reprefented in the 1 7. Fi- 
 gure by the letter B> 
 
 f X " 1 * . 1 u 
 
 B Reprefent s a Siren on the water. 
 
 C T he wheeles which are loofe on the axeltree , being hollow , and filled halfe 
 with fand or water. 
 
 D D The rocket t placed in the axeltree which isfafi. 
 
 There are many other workes to be performed on the water, by ma- 
 nual art, or the hclpeofthe hand : fomeof which I will fliew, the reft I 
 Qiall leave to theiudgementof judicious workemen in that arr 5 in regard 
 there arc fe* fights, which are performed by gallics placed on the water, 
 with thehelpeofMaiinersa&cdjand likewife Caftlcs placed both oa 
 the water, and on the fhoarej all which doe reprefent fome former fto- 
 ry of the like * yet know this, there are many motions, to be wrought by 
 hand, after a more fecrct manner, which will caufc more admiration, and 
 is done by certainc lines placed under the fupcrficics of the water, the 
 ground of which I will fhewyou. 
 
 < CHAP. LX I. 
 
 How to reprefent a Dragon ijjuing out of a C a ftb> which /hall 
 fmmme thorow the water , and be incountred by a bor/eman 
 from the (hoare. 
 
 | Aufe a Caftle to be made on certainc timber, fo as it may flotc, 
 if it be in a flowing and ebbing water, snd let the botromeof 
 the doore of this Caftle, with the ground plar, be two foot 
 under the horizon of the water (the rcafons follow ) and 
 at a foot high within the Caftle, let there bee a certainelinetyed, which 
 may'paflethorow the body of the Dragon, and may bee fattened neere 
 the (hoare, where you (hall have a floatc likewife funkc fo farre under 
 water, that the line may not be perceived, then faften on your Dragon, 
 as 1 have formerly (hewed you for the line, but fo that the head of this 
 may alwaics be above the line, where that was under: then when the 
 time appointed comes, there (hall be one ready within the Caftle to fire 
 thofe parts of the Dragon which is requifitc, which being done by the 
 hclpe of thofe pullies, (hall paffe it thorow the water, which fo fbone as 
 it prefents it feife, Neptune (as being difplcafed to fee (0 monftrous a 
 creature within his bounds) (hall come and encounter the (aid Dragon, 
 
 ztnd 
 

 
 'm i /Ml/tH 
 
 j>atv 66 vtd (fj 
 
<zA rtifciall Fire4Vorl<es. 6 1 
 
 and at laft (ball overthrow him:you tnay order your work fo.that which 
 you pleafe (ball have the viflory, for that which keepeth fire longeft, is 
 fuppofed to have the beft, and that which is fooneft {pent, to have the 
 word. Many rare things may be done in this for the pleafure of Princes, 
 which are to be a&cd on the water, which for brevity fake I omit : onely 
 I (hall (hew you the order of compofing two forts of workes, the one to 
 be a£cd on the land, the other on the water. The forme of this workc is 
 reprefented in the 17 Figure, by the letters C D. 
 
 G Reprefenting the fatt/c floating on the water, out of which the Dragon 
 iffueth. 
 
 E The Dragon comming forth of the Caflle. 
 
 D Neptune comming towards the faid Dragon to encounter him. 
 
 F The fully which caufeththefe motions by meaner of drawing them to and 
 from each otheri the manner offafiening the line for drawing them, I have 
 f jewed you before in the 3 3 Chapter. 
 
 CHAP. LXII. 
 
 An order for agenerallpieceof fireworks for land, and is for 
 t be pleafure of 4 Prince or fome great perfon. 
 
 S Aufc a frame to be made of wood, which let be eight 
 fquare, or more properly eight fided (which is the 
 beft figure for this purpofe) and let ic bcc forty 
 yards from one fide to the other, there place two 
 Cattles the one oppofitc to the other, which Ga~ 
 
 I files (hall be eight foot fquare, thefe Cattles (ball 
 1 be fitted with motions, as I have formerly (hewed 
 you, fome comming outagaintt others, fome mo- 
 vingonthe walks* all which may bee performed by the hclpeof large 
 fire whcclcs, which muft beat the lead fixe foot diameter, with large 
 Rockets fot the fame purpofe, as I have formerly (hewed you : then on 
 the fourc adjacent fidcs, you (hall place fourc other wheelcs, two run- 
 ning horizontal, and two vertically and on the other two (ides you (hail 
 place rockets, fome dying upright, and others circular; at each angle or 
 corner, there (hall be placed a torch of a beautiful! (ire and (low; fo much 
 for the (ides: now you (hall come to fill up the vacuum bctwccnc the 
 fidcs, alwaies noting chat from one Cattle to the other, patteth a frame of 
 wood, the ufc whereof I havcformcrly (hewed, then before the midtt of 
 this frame, there is placed on the one fide, two fquare cafes of rockets, 
 and betweene thefe cafes toward the bottome, and fome what before, 
 there is placed anticke motions, and to the angles of each Cattle are pla- 
 ced two lines, with runners which take fire, and pa fie to and fro; note 
 theendofthofclincsmuftbepcrfc&wycr,or elfcthc fire would burne 
 them, then on the fame fide behinde the motions, (hall (land aloft a frame 
 with the Kings name or the like; then on the other fide of the frame, 
 
 within 
 
<58 
 
 Tyrotechnia , or. 
 
 within the vacuum, (hall be placed three (landing whcdcs, whereof the 
 one (hall caft forth rockets into the ayre, the other two are for reports 
 and fifgigSi thefe three whccles (hall (land in a triangular forme, and 
 (hall have a frame pa(Te from the one to the other* and betwcenc the an- 
 gles ofthefe whcclcs, (hall be placed two mortar pieces, which (hall bee 
 to caft fire bats, with divers workesin them. The manner of this is repre- 
 sented in the 1 8 Figure. 
 
 CHAP. LX I II. 
 
 Another order for ageneralhoorkey and is to teamed 
 on the boater. 
 
 JAvinga place appointed for your worke, (which 
 muft bcinfome fpacious River) you (hall feeke 
 the moft convenient place on the (hoarc for pla- 
 cing a Caftlc, which (hall bee made to reprefenc 
 fomc City or Fort lying on the water jthis Caftlc 
 (hall befurnifhed with all manner of workes, as 
 well fire bals, as rockets, with divers (mail Ord- 
 nance to give a more grace to the worke; this be- 
 ing provided, you (hall alfomakc another Caftlc on the water,on certain 
 boats chained and lying at anchor, thefe (hall bee fet at a reasonable di- 
 ftance trom the other, about twenty feor'e, or as your place will permit: 
 in this Caftlc like wife you (hall provide workes, as in the other, onely 
 this Caftlc may not be fo big as that on (hoarc, then you (hall provide 
 divers fmall (hips, which (hall be ready to makea fea fight: thefe (hall be 
 fo divided, that the greater part may belong to the (tnallcr Caftleon the 
 water, and likewife for furprifing that on the land; likewife you may 
 have motions paffing from one Caftlc to another, as I have formerly 
 (hewed you for the water; amongft the reft you (hall have fome fmall 
 fire (hip, fuch as I have (hewed you, which (hall have divers motions: 
 now there are many a&ions to be performed by thefe workes, as cafting 
 bals from one Caftlc to the other, with the mortcr pieces, likewife fen- 
 ding backe rockets to each other, with divers onfets on each fide for fur- 
 prifa!s,all which I leave to the diferetion and appointment of the Judi- 
 cious workeman; and becaufc I will not trouble you with prolixity, l 
 will conclude this my Pyrotechnia; onely I will at laft impart that which 
 is not the leaft, which is the making of cerraine Engines for trying of 
 powder, of which I (hall (hew you fourc, with the ufeof them in thecn- 
 fuing Chapters, and fo conclude. 
 
 Chat, 
 
I 
 
e Artificiall Firc-Wor\s. 
 
 CHAP: LX IV. , ,, 
 
 Of the ufe of certain Engins for the trying ofthegoodnejfe 
 or fir ength of powder. 
 
 Fore I come to explainc the manner of making thofc 
 Engins, I will fhewyouthe commodioufncflc of 
 them, efpecially in thefe works j for hee that will 
 make a good rocker, muft be certain of the ftrength 
 ofjhis powder, which if it bee too ftrong, will 
 break . if too weak, it will not rife to that heighth 
 it (bould ; which, I muft confefle, hath been a great 
 loflc of labour to me, as well as to other men, yet 
 ifmen will be fo carefull and take that paines for the trying their pow- 
 der, they may make rockets infallible ; therefore I advife every man that 
 will work fare, firft to take his powder, be it what it will, and allay it ac- 
 cording to the rules preferibed, then take a quantity of that mixrure,and 
 put it into your Engin being cxa&iy weighed to a graine,then drive your 
 rocket, and be fare to follow the former rules preferibed in driving your 
 rockets, which being fini/hed, with his works upon his head, you may 
 fire it, which if you /bail finde to bee too violent, you may allay by put- 
 ting thereto a proportion of coalc, and fotryitagaiiytill fuch timeyou 
 finde it to be the beft, then note that proportion fofaH rockets of that 
 fize, and fo do for all others; and ifyou finde your mixture yet too weak, 
 adde thereto a fmall quantity of roch peter till you make it of fufEcient 
 ftrength • and thus doing, you fhall have a certain and infallible rule for 
 your proportions : I could fet down the proportions according to my 
 Engins, but that would prove an abfurdity, in regard every Engin may 
 have a greater or Icffcr ftrength added to his. %ings, or the like, as you 
 fhall perceive in the next Chapter/ 
 
 Chap. LXV. 
 
 The manner of making the aforefaid Engines for trying 
 the ftrength ofpowdtr. 
 
 HE firft is made in a circular form, with a~neck 
 comraing from the circumference, which ferves for 
 a lid to the powder box, which box (hall bcc‘ made 
 to hold the quantity of a dram of powder, or there 
 about, fo that being covered with the lid, and fired, 
 will blow, according to the ftrength of the powder, 
 and moving, will turn about a circle of braffc, which 
 is divided into certain equall parts, and fo willfbcw the ftrength accor- 
 ding to the part it cuttcth ; for the greater the degree is that it is blown 
 
 up 
 
7 * 
 
 < lArtifciall Firc4Vorkes. 
 
 up to.the Qrongcr is the powder, and contrary. The form of this is re- 
 prefented in the twentieth Figure, by the letter A. 
 
 A reprefenting the form of the whole Engin. 
 
 B the powder box , which mu ft be filled to the top. 
 
 C the lid, which mu (l be put on the fayd box, it being filled. 
 
 D the circle of brajfe to which the lid is faftned, which is divided into de- 
 grees, and runneth upon the pin £, puffing thorow the center, with a fererw to 
 Jet it harder or eafter. 
 
 CHAP. LX VI. 
 
 Mother Enginfor trying of powder. 
 
 E lid of this fecond fore is made to rife in a 
 ftraight line, and hath for his guide two fquare 
 pillars of brafle , divided into degrees , with 
 fpringstokcep it fteaddy in this motion; this 
 muft be made on a fquare pcccc of brafle, with 
 the fmall box in the midft, and two fquare pillars 
 on each fide, with a pecce of braile to Aide up 
 and down by thofe pillars, and muft ferve for a 
 cover for your powder box ; this pecce of brafle muft have fmall fprings, 
 which muft go to each fidcof the fquare to guide it fteaddy in the moti- 
 on. The form whereof you (ball finde in the twentieth Figure, by the 
 letter B. 
 
 B the whole frame, with bis parts adjoyned. 
 
 C the fquare plate of brajfe, on which all itfaftned. 
 
 D the powder box, {landing in the midft of that plate. 
 
 E E the two fquare pillars of brajfe, /landing on this foot, and may bee made 
 to fererv off and on at pleafure . 
 
 F the lid to the fire box, which is made to /tide up the two fquare pillars. 
 
 G G the fprings, which arefaftned to the lid, to make it move more fteaddy. 
 The divifions io, 20, &c. few of what ftrength the powder is, for the 
 higher that the lid rifeth, the fir onger is the powder. 
 
 C HAP; LXVII. 
 
 A third Enginfor trying the ftrength of powdet . 
 
 ; E third fort are made fomewhat after the manner of the 
 former, which is to rife up ftraight, only it hatha cover 
 hollow as big as the box, and on each fide of the cover 
 is a fmall hole for a wycr to pafle thorow, and on one of 
 the (ides arc little peeces of fteele or brafle, fo fitted, that 
 they will rife with a touch, and give way to the rifing 
 of the lid, and fo foon as it is paft, will hold it there, and will not fuffer 
 
 it 
 
Jz Tyrotechnia , or, 
 
 it to paffe down any further ; this I bold to b7c7hcbeft of the three, in 
 regard that the fprings in the former are fubieft to grow foule with life 
 and fo will be very ftiffe, every time more and more • but this will not* 
 The forme of this is reprefented in the twentieth Figure, bv the let- 
 ter C. J 
 
 A the footwherem the E is gin fiandeth. ' 
 
 B the powder box, which hath two fmall wyers faffing from each fide to the 
 top , to guide the lid. 
 
 D the lid, which hath alfo two holes on each fide for the wyers to paffe tho- 
 row. J t * 
 
 E the fide which u divided , on which is placed at every degree, one of thofe 
 peeces to fide tip and catch the lid. 
 
 F F the forme of thofe catches, being either offieele or hraffe. 
 
 G G the two wyers which guide the lid of the box, and mttfi bee put into a 
 little pee ce of brap at the top , which may bee [crewed higher or lower at plea- 
 fur e, for the firaightning of the fame. 
 
 H the ferew which firaightneth thofe wyers. 
 
 CHAP. L X V 1 1 1. 
 
 Mother Engin for trying tbejlrength of powder by water. 
 
 H E fourth, and moft certaincft way of all, is by 
 water, and is thus $ caufc a fmall veffell to be made 
 of braffe, and very fight, foas it may containe a 
 pintc of water ; let this veffell bee made in a cillin- 
 dricall form, and from the top of this veffell let 
 there bee made a pipe of braffe, which (hall turne 
 like the fiphon.and fhall have a ferew atthelowcr 
 end, to ferew intoa box of braffe i all which (hall 
 ltandon a woodden frame : now when you wilufe this, you fbalfil this 
 great veffcl halfc ful of water, at a pipe which fhal come from the bot- 
 tom,and comeup tothetop winding, then fhal there be like wife another 
 veflel underneath for a receiver, fo that putting a quantity of powder in. 
 to the final box, and fere wing it on, it isready . then fire the powdcr.and 
 you fhal fee it fend forth a quantity of water, which you (ball weigh, and 
 fo keep the weight of it, by this you fhal know what quantity of pow- 
 dcr of fuch a goodneffc wil fend forth fucb a quantity of water 5 this I 
 hold to be the ccrtaincft way, although the roof! troublcfomc. Thcform 
 of it is reprefented in the twentieth Figure, by the letter D. 
 
 A representing the veffell of water, which Jhallhe alwayes filled one halfe. 
 
 B the pipe of braffe which paffeth fromthe powder box to the veffell of water. 
 
 Cthe powder box , being ferewed to one end of t he f aid pipe, 
 
 E the receiver x to receive fuch water as is forced out. 
 
 G the pipe which convey eth that water into the receiver. 
 
 F the bottom being ofwood t with a plate of braffe let into it. 
 
 FINIS. 
 
TREATISE OF 
 
 geometry. 
 
 Containing fundry Definitions and Problemes, 
 
 botbjplcafurable and ufefull, 
 
 1 Eomccry is the arc of mcafuring well. 
 
 A point is that which caanot be divided, and is 
 the leaH imaginary thing, as this • 
 
 ' A right line, is that which hath oncly length 
 
 without bredth, whofc termination is two 
 
 points,' * • )' '• > *" ‘ n - ’ 
 
 and is the flhorteft betweene the points. 
 
 5 A crooked line is that which being deferibed, a 
 
 {hotter line may bcedrawnc betweene the two 
 points, as this, R , 
 
 T I • f • ^ ~ C 
 
 * < '"‘sCun i 8* ah*i 4 irhu; 
 
 A fuperfice is that which hath length and A & 
 
 bredth oneIy 3 thus, 
 
 <7 
 
 ■r. : - d : - ■ 
 
 U^jn 
 
 F' : 
 
 A Collide, is that which hath lengthy bredth, y f~ 
 , and thickneflfe, as this figure. a t t k T 
 
 Jii j}- ■■■ 
 
 Cr 
 
 J 
 
 k i : 
 
 JC 
 
 ..f 
 
 An angle is the inclination of ,fi*oe liaises? 
 concurring in one point, thus: of which feme xroTT^r* 
 are right angled, and fomexsbliqoe: ; '7 iJS?. -a. 
 
 I; :ii 
 
 
 S 
 
 
 \ 
 
dA TreatiJeofCjeometry . 
 
 A right angle, is when one line falleth perpendicu- 
 lar upon another, thus: the perpendicular being A B, 
 let fall upon the line AG, it being right angled at 
 A. 
 
 B 
 
 An oblique angle, is cither acute, or obtufe* acute 
 when the angle is leffe than a right angle, as A. A 
 thus, it being acute at A. 
 
 An obtufe or blunt angle, is that which is more 
 than a right angle, thus, it being obtufe at the point 
 A. <. . A 
 
 A circle is a figure determined with oncline, which 
 is called circumference, as A E B. whole dia- 
 meter is the largeft right line within the circumfc. A 
 -fence. 
 
 •a 
 
 Afemtcircte,i$ balfc a circle, parted by the diameter, ai A EB. 
 
 A cord, is a Ihortcr line than the femediameter: as the line F G. 
 
 An arch, is that portion of the circumference, whichcomprchcndcth 
 the cord line, as EF G. 
 
 A triangle is a figure containing three tides, and of thefe figures there 
 are divers forts, fomc right lined, and feme oblique : of right lined trian- 
 gles there are alfo divers forts, fomc right angled, and fomc oblique; 
 
 A right angled triangle is that which hath 
 one right angle, and is called OrtktgMttm* 
 
 An oblique angled triangle, is laid to bee ei- 
 ther obtufe or acute. 
 
 An obtufe angled triangle, is that which 
 hath one angle obtufe, and the other two a- 
 cute, and is called AmbUgtnium^ obtufe at 
 theanglcA. 
 
 An acute angled triangle, is that whole 
 three angles are (aid to bceaciite 9 and iscalled 
 Ox'tgsnium, and if the three (ides be cquall (as 
 in this figure is manifeft) it is then called an 
 equilatCK 
 
 A ' A 
 
 ti a x - 
 
 lO 
 
 But 
 
<zA Treatife of Geometry. 
 
 ? 
 
 But if oneljrtwo fides bee equall, and the third /\ 
 unequal!, then it is called Ifo/cbe/ts, as you may here &/ \ Q 
 
 fcc,whcrc the two fides arc cqualJ,andbafc unequal. / \ 
 
 / _N 
 
 ^ 10 
 
 Andifall three fides be unequal!, then it is called 
 Schdcnum, as in this figure appeareth. 
 
 10 
 
 There bealfofoure fided figures, which are cal- 
 led quadrangles, and of thofc there arc diversforts, 
 Tome of which arc gcometricali fquares,whofcfbure 
 fides arc all equall, with equall angles thus, 
 
 do 
 
 ▼ 
 
 •orv; 
 ■ sn 3i 
 
 Others, whofefoure fides are equall, and oppo* 
 fite angles equall, which arc called Rombtts^ ordia» 
 mond like formes. 
 
 ■ ■ O !vV; 
 
 There are others which have their oppofite fides, , 
 
 and oppofite angles equal!, and are called Rombol 
 
 Apt. thne ^ U \- 
 
 40 
 
 desy thus, 
 
 There is a fourth fort which is called Trape&iu, 
 or table formes; andthofe arefuch as have neither 
 equall fides, nor equall angles, and of thofe there 7j 
 aredivers formes, of which here is oneforme. 
 
 10 
 
 > 
 
 Aa 
 
 Such 
 
 I 
 
zA Treatije of Geometry. 
 
 4 - 
 
 Such figures as have more than fourc (ides, arc 
 generally called Folligons , which if their (ides bee 
 equall, arc called Regular PaUigons\ of which fome 
 are five fided, and arc called Pentagons. 
 
 Thole who have fixe fides, are called Hexagons. 
 
 A quadrant is the fourth part of a circle, and is 
 made by letting two lines concurrc of equal! length, 
 and making a right angle; and from that angle, dc- 
 feribe fuch an arch as may touch at the other end 
 of each Une, thus; £ 
 
 N O w to know how to make thefc figures, and divers others, it is 
 tequifitc that vre know what it is to let fall a perpendicular on a 
 line affigned ; of which there are divers wayes and formes, fome 
 of which I will Irnwyou. 
 
 Problem i« 
 
 To ere ft a perpendicular on the end of aground line. 
 
 F Irfi, open the points of the CompafTcsto any diftance, letting one 
 foot in the end oi the groundline.and with the other deferibean arch 
 of a circle, interfering the ground line* that done, fet one foot in the 
 point of interfe&ion, and from that point fet 
 off the femidiameter of that arch twife, and 
 fetting one foot of the Compaflcs in each 
 point, with the other make an interfering 
 arch, and from that point of interfeftion to . 
 the end of the ground line, draw another j 
 line which lhall be a true perpendicular to that 
 bafe. F 
 
 Example. 
 
 Let the line given be A B.on which it is required to ere& a perpendi- 
 cular, which lhall be from the point B. Firft, I open the Compares ta 
 any difiance, deferibingthe arch C D. interfering the line A B. in F. 
 then fetting one foot in F. I fet off B F. from F to C* and from C to D. 
 that done, I fet one foot of my CompaHes in € and D, and with the 
 
 other* 
 
<tA Treatife of (jeometry. 
 
 other, deferibe the intcrfcaing arches at E^andfrom the point of inter- 
 feaion, I draw the line E B, which is the perpendicular required. There 
 are divers other waics, which for brevity I omit. 
 
 Prob. j. 
 
 To divide a line given, into equal! parts, at a right angle , 
 
 O Pcn your Cotnpaffc to a greater diftancc 
 than halfc the line, and Petting one foot 
 thcrcofinoncend of the line given, with the 
 other deferibe a part of an arch both above and 
 beneath, then the compares unaltered, re- 
 move one foot of the compares to the other 
 end of the line, and with the other foot croffc 
 the others and from the place of interfettion, 
 draw a right line, which (hall cut or divide 
 the line given into two equail parts. 
 
 *4 
 
 B 
 
 Example. 
 
 Let A B, be the line given to be divided; Ifeeonc foot ofthcCom- 
 paffe in the point A, opening the other fomewhat beyond one halfe 
 with which I deferibe two arkes, as C D, then removing my Gompafles 
 to B, with the foot of the Compares unaltered, Iobferue where the in 
 terfe&ion is made in thofc two former arches; and from one interferon 
 to the other, I lay my rule, and draw the line D C, which cuttcth the o* 
 thcr into two equail parts at aright angle, which was required. 
 
 Prob. 5. 
 
 Amber way to divide a line intotvo equal! parts, althoueb the 
 Compafleftand atlejjethan balfe di fiance. & 
 
 OEt one foot of your Com- 
 ^pafles at one end, and with 
 the other, deferibe an arch a- 
 bove the line, then your 
 Compaffes unaltered, fet one 
 foot at the other end, and de- 
 feribe an arch under the line; 
 then lay a ruler till it touch the 
 wetreame part of each arch, and 
 draw a line from the one to the other; for where that intcrlc&cth ia the 
 line given, that is juft the middle, & foconicqucntly it is equally divided. 
 
 Example . 
 
 Let A B,be the line to be divided: open your compare to any di- 
 ftance, as A F, then letting one foot in the point A, delcribe an arch, as 
 CF, removing your compallesto B, deferibe the arch CD, under the 
 
 A 5 !ine a 
 
6 <$A T reatife of (feometry . 
 
 line, then laying your Ruler to touch thetwo arches in D and C, draw 
 a line, which will cut in E, which is the middle of your line A B. 
 
 . ' * lllk ! 
 
 Prob. 4. 
 
 To make one angle equal! to another aligned. 
 
 f\Pen your Compaffc to any diftance, Petting one foot in the angular 
 ^'pointaffigned, and with the other defer ibe anarch, then with your 
 Compaffe* unaltered, Pet one 
 foot on your line afligned, 
 
 and with the other dclcribc ^ + 
 
 an arch, which being done, 
 with your Compaffes, take 
 the fartheft diftance of your ^ 
 arch (deferibed in the firft) b 
 between the two lines, and 
 
 fet it off in the fccond, then laying down your Ruler, draw a line from 
 that point to the center, fo have you another angle equall to the angle 
 given. 
 
 Example. 
 
 * * ■. a , . ' '.tS 
 
 Let A B C be the angle given, I open my Compaffes to a diftance, and 
 deferibe the arch ED» Petting one foot in A • then do I draw another 
 line, which is F K, and Petting one foot of my Compaffes in the point F, 
 with the other I deferibe the;arch I K equal! to the arch ED; which 
 done, I take off the diftance E D, and fet it over from K to I, then laying 
 the Ruler from the point I, to F, I draw a line I F, which make an angle 
 of the fame quantity as the former* 
 
 . r ■ . • ' / 
 
 , ■ «, Prob. 5. 
 
 How> to draw parallel 1 lines '. 
 
 |7Irft open your Compaffes to the length of your line, which Pet down, 
 *■ and draw that line, then knowing the diftance that you would make 
 your parallel], open your Compaffa to that diftance, and Petting one foot 
 inthccnd ofyour lincaffigncd, dcPcribc anarch, and with the Com- 
 paffes unaltered, fet one Pootin the other end, and dePcribe another arch, 
 then lay your Ruler Po, that itmay touch each arch without cutting ei^ 
 thcr, and draw a line, which will be parallel! to the former. 
 
 B 
 
 Example. 
 
<iA Treatife of (geometry. 
 
 Example.' 
 
 Let ABbcthclineaffigned,to which I would make a parallel! whofc 
 diftance (hall be A C, fetting one foot of the Compares in the point A 
 and opening them to the diftance C, Ideferibe that arch, then fetting 
 one foot in B, the Compaffcs unaltered, Imake the arch D, and from C 
 to D do I lay my Ruler, touching only one partof each arch, and from 
 thence do I draw thelineC D, which is parallel] tothc former, the thine 
 required, 6 
 
 Prob. 6. 
 
 To draw a parallel 1 line, without f lining the Compares, 
 from the diftance given* 
 
 XJ Irftopen your Compares to the diftance given, then fetting one foot 
 in the end of your line affigned, deferibe an arch which may touch 
 your line, and fetting the foot ofyour Compares on that place deferib" 
 an arch which may cut the other . this done, do the like at the other end" 
 and then lay your Ruler on the interferons, and draw a line fo have’ 
 you a parallel! at one opening the Compaffcs. 
 
 E ■ 
 
 
 / \ 
 
 -y^TJS 
 
 
 
 
 
 Example . • 
 
 Let A B bee the line given, to which I would make another parallel!, 
 lopenmv compaffcs to thcdiftance, and deferibe the arch EDF;then 
 the fo.)t remay nmg in F, I deferibe the other arch AD Gj this done, I 
 remove my corapaffes to B, and do the like ; which done, I Jay my Ruler 
 that it may cut both the interferons, and then I draw a line from the 
 point of interferon in the onccnd, till it touch the extreme part of the 
 archat the other cnd,and fo have EDC paralcll to A B. 
 
 Prob. 7 . 
 
 To divide a line given 9 into equall parts. 
 
 AT one end, on the upper fide, make an ingle at all adventures, and 
 on the under fide at the other end, make another angle equall to the 
 former by the fourth problem of this fame . then open your Compaffcs 
 to lome fmall diftance, and fet off your parts upon the two parallel! lines, 
 and To laving the Ruler from the laft divifion of one to the firft of the 
 as you pj dfawingalinc, itftuil divide it into fuch proportionall parts 
 
 Example . 
 
\ 
 
 <*A Treatife of (geometry . 
 
 Let AB reprefentthe line, which I would have divided into ten e- 
 quall parts; 1 fir ft lay downe the line A B and from one end, I draw a 
 line, which let be A G, making an angle with the other line A B • and on 
 the other end 1 draw another line parallel to the former, which 3 let bee 
 B D ; then opening my Compaflc to any diftancc, I fet it down in the 
 lines A G and B D, from the angular point, and fo laying my Ruler from 
 one aBglc to the other, I draw certain parallels which cuttcth the line A B 
 into fo many cquall parts, as I defire. 
 
 ’ . Prob. 9. 
 
 To finde a meant proportion between any two lines preferibed* 
 
 T Et the two lines bee A and B, and it is required to finde a meane 
 •^proportionall line between thefe two ; firft ioyn thofc two lines fo 
 that they both may make one ftraight 
 line, and fixing one foot of your Com- 
 paffe in the midft of that line, extend 
 the other foot to the extreme parts, and 
 defenbe an arch of a circle, then rayfe a 
 perpendicular on the place of concur. 
 rence,and let it be extended to the arch; 
 which line (hall be a meane between the 
 two lines given. 
 
 Ex 4m fie. 
 
 Let A B the two lines given bee fo ioyned together, that they make 
 both one line, which let be the line C D E, then dividing the line CFG 
 intotwo cquall parts, in the point F deferibe the arch C GE • and rayfe 
 a perpendicular on the point D, till it concurre with the arch in the 
 point G, you have the line D G, which is a meane proportion between 
 the lines A and B, which was required. 
 
 V ' > 
 
 Prob. 9 ' 
 
a A Treatife of (jeome try. 
 
 Prob. 9. 
 
 In any right angled triangle > the mo conteyning tides being 
 giyen , to finde the fubtendent . 
 
 I N a right angled triangle, I call them the , 
 contayning fides which do contayne the 
 right angle, and the line fubrending the right 6 
 angle, I call the fubtendent, of which any two 
 being given, you may finde the third* 
 
 Example. 
 
 Let the fides (E Dand C D) bee given, and the fide E C is required 5 
 to do this Geometrically, i» no other then making a right angle of the 
 two fides, and from the extreme part of one to the extreme part of the 
 other, to draw a right line, which (hall be the fubtendent, which (hall be 
 double in power to the two contayning fides. 
 
 c *\ • ' V' 1 * < 
 
 Othermfc Arithmetically . 
 
 Letthe fide E|D be g, and the fide CD d, and I defirc to know the fide 
 AC* firft 1 fquare each fide, faying, $ times 8 is 64, and d times 6 is 3d, 
 which added, makes 100, out of which I extract the fquare root, which 
 is 10, and that is the fide required : Contrary, if one fide bee given with 
 the fubtendent, and the other fide be required, I fquare each, alwayes 
 fubtra&ing the fquare of the fide from the fquare of the fubtendent, and 
 the remainer is the fquare of the other fide, whole fquare root is the fide 
 required. 
 
 Example, 
 
 The fubtendent E C is to, thebafe E Dis 8, and there is required the 
 perpendicular D C ; firft multiplying 10 in it fclfe gives 100, and ,8mul- 
 tiplyed in it fclfe is 64, which fubftra&cd from 100, refts 3d, whofe 
 fquare root is the fide required 5 fo that from hence is gathered, that the 
 fubtendent is double in power to the two concaying fides, which is a 
 maine propofition, on which doth depend a great part of Geometry. 
 Ettclide 1. propofition 47. 
 
 Prob. 10. 
 
 To finde the center of anjarch of a circle prefiribed. 
 
 L Et there be an arch of a circle wbofe center ils required j firft I divide 
 the arch into twocquall parts, and then fetting one foot of the Com- 
 pares 
 
I o 
 
 <$A Treatife of (jeometry . 
 
 paffcs in the extreme parts, I open the 
 other foot fomewhat more than one 
 fourth, and fo deferibe an arch above 
 and beneath , and then removing my 
 Compares, I fix one foot in the midft,and 
 mark where it interic&cth in the other 
 arches, then I draw two ftraight lines 
 thorow the interfering arches, and where 
 thole two lines cur each other, that is the 
 center. 
 
 Exitnplc. 
 
 I v I » j 
 
 Let A. C D bee the arch of which 
 I dividcit into rw© equal! parts, in the point C, then fetringone foot 
 at A, I extend the other iomewhar more than j between A and G, and 
 there deferibe the intcilefting arches above and beneath, which are mar- 
 ked withD F and DF ; fo ukewife I do the li-ke from, the point D, 
 then I draw two ftraight lines D E and D F interfe&ing each other in the 
 point B, which is the center ot that arch required; 
 
 Prob. ii. 4 
 
 To finde out the chord lines in a circle , from the 
 third to the tenth . 
 
 L Et A B be the diameter of the circle, out of which the chords arc to 
 be found, firft havipg drgwn thediaroeter,andyourCompaffc9ftand- 
 ingatthefemidiamctct, fetone fbotin A, extending the other thereof 
 both above and bcpeqtj), till it interfc&in 
 the circumference, notethofe interfe- 
 rons which here are C, D, drawing the 
 line C D, which (hall bee the third chord, 
 that done, crofle the diameter at right an- 
 gles in the center with the line F G, and A 
 from A to F draw a line, which fhall be the 
 fourth chord : now to finde the fiftchord, 
 fer one foot of the Compares in E, and ex- 
 tend the other to F, fetting off the fame di- 
 ftance from F to H, which fhall bee the fife 
 chord ; the fixe is the fetnidiameter I F, the feventh is halfe the third 
 chord, which is C E or D E * for the eighth chord lay your Ruler by the 
 center I,and the interfettion K, and note where it cuttcth the circum- 
 ference in L j then draw the line A L, which is the eighth chord $ then 
 dividethearchlineCDimo three equall parts, as the line DM, which 
 the ninth chord ; laftly, the line I H is the tenth, fo have you the chords 
 from i to i o, which was required. 
 
 I defire to finde the center. 
 
 Prob. 
 
<t A Treatife of (jeometry. 
 
 li 
 
 Prob. 12. 
 
 Tofinde out thechordes above the fourth another way. 
 
 plrft, make anequianglcd triangle, then from one angle thereof daw a 
 perpendicular, cutting the bafe, which line (hall be increafed beyond 
 the angle, then divide the perpendicular of the triangle, into five equall 
 parts, and continue thole divifions on the line according to what nutn* 
 ber you plcafc: then may you by this figure fo provided, findeoutany 
 chord ofa circle appointed in this order. Firft lay downe the circle, 
 whole chord is required, and draw thereunto a diameter, which incrcafc 
 at length, then fet one foot of the Compares in an angle of the triangle, 
 and extend the other to one divifion Idle than the chord required, and 
 fetting one foot in the center with the other, make an arch, beginning it 
 from the diameter j that done, put the fidcs of the equilater,trianglcfrom 
 theimcrfe&ion ofthe diameter, and the (aid arch laft preferibed, asfarre 
 as it will reach in the arch, then lay your ruler by that interfeftion, and 
 the center, and draw a line, noting where it cutteth the circumference of 
 the given circle, and from that point to the end of the diameter, draw a 
 line which fliall be the chord required. 
 
 Example* 
 
 Let H be a circle giuen, wherein a Heptagon is to be in&ribcd:firft the 
 feventh chord is to be found, therefore draw the diameter F G, which in- 
 creafe in length towards O, then fee one foot in the angle A, of the pre* 
 pared figure, extending the other to the fixtb divifion; fb the Compaf- 
 fes nnaltcred»iet one foot in the center of your circle H, and with the o- 
 thcr make the arch I K., that done, take the fide of the triangle A C, and 
 fet it from I cowards K, and note where it endeth in L, then draw the 
 line L H,and note where it cutteth the circumference in M, and draw 
 thcline I M, which is the feventh chord,and will be found feven times in 
 the circumference, and the lines being drawne, will include a Heptagon 
 which was required. 
 
 * To 
 
12 
 
 dA { Treatife of (geometry 
 
 > To meafure the Area or fuperficiall content of any Geome - 
 
 tricall figure* 
 
 Defim. To meafiire the Area or fuperficies of any figure, is to fhew 
 how many fcverallfquarcs are therein contained, according to the icale 
 affigned. 
 
 Prob. 1 3. 
 
 To meafure the Area, fuperficies , or content of a fquare, 
 
 T O meafure aGcometricall fquare is nothing clfc, but a 
 multiplyingthefidcin itfclfe, let A 6C D, be a geo 
 metrical fquare, whofe fide A B, is 20. which multiplied in 10 
 it fclfc, produceth 400. the content of that figure. 
 
 Prob. 1 4. 
 
 Arithmetically tofindethe meane proportion betyteene 
 typo numbers. 
 
 T He meane proportion is found by multiplying the two numbers to- 
 gether, and out of thcprodu&extra& the fquare root, which fhew- 
 cth the demand. 
 
 Example: 
 
 Let the two numbers given be 3 2 and $0. which multiplied together, 
 produce 160. whofe fquare root being extra&cd,is 40. which is the 
 meane proportion betweene thofetwo numbers. 
 
 Prob. 15; 
 
 The fide ofafquare being ghen to find the length of the Diagonal 
 
 L Ec A B C D, be a fquare given, whofe length of the Diagonall A D, 
 is required.* firft, you (hall fquare A C, which is 20. fa. 400. which 
 double alwaics in this cafe, fa. 800. the fquare root whereof is the Dia- 
 gonal! A D,now forafmuch as 800 is a furde number, and hath no ‘per- 
 fc& root, therefore finde the root in fourths, (o (hall you findc the root 
 thereof to bee 113 fourths, and taking the £ of that number, is 28$ for 
 
 the length lot the Diagonall. A D, as appcarcch in the former Diagram. 
 
 ' 
 
 it jv ji ;; 
 
 Prob. « 6. 
 
 ciguqaH s ibsilwii 
 
 To meafure a long fquare . 
 
 meafure the content of a long fquare, is to multiply the length in 
 1 the bredth, the produft givech the content required. 
 
 Example. 
 
<t A Treatije of (jeometry. 
 
 a 4- 
 
 B 
 
 Example, 
 
 \ 
 
 Let A B C D, be a piece of ground, containing 50 perches in length, 
 and to perchcsin brcdth,and I defirc to know the content, firft Imul- 
 tiply to with 50 fa. 1000 which is fo many 
 
 perches, that this figure containeth: now if A ' ,3 
 
 you pieafe, you may reduce the fame into r ~ 
 acres by dividing the wholefumme (by 160 ) 
 which is the content of one acre, Co the con- 
 tent in acres will be found 6 and 40 perches C 
 which is ^ofan acre. 
 
 Prob. 17. 
 
 To meafure a (Regular Rhombus, 
 
 Eth^b f^° m k US ,s meafured by multiplying the perpendicular in 
 
 Example. 
 
 Let A B C D, be a Rhombus given to be mea&rcd, whofc fides (hall 
 be 24. and let the propofition be to call up the content thereof.* foraf- 
 much as the Rhombus confifteth of two 
 equilatcr triangles, therefore a pdfpendi, 
 cular let fall from one of the obtufe angles-, 
 as A, (hall divide the fide E D, whereon it 
 fallcth into two equal! parts intoE, then is 
 CE 12. Then may you by the 47 propo-^ 
 frion of the firft of Euclid^ finde the length 
 of the perpendicular A E, which is after this manner, fquare C E, which 
 is i2 fa. 144 alfo fquare A C, which is 24 fa. 57 <$ fubtraa theleffer, 
 which is C E, 1 44 from A <3,576 refts 452 whole fquare root being 
 extracted, is >4 $2 necre rational] 20 1. which multiplied by *4 produ- 
 ccth the area ofthe Rhombus 498 which was required. 
 
 Prob. iS. 
 
 To meafure anirregular Rhombus . 
 
 L Et A B C D, be an irregu- 
 lar Rhombus, whole fides 
 (hall bcaif. and let the propo- 
 fition bee to caft up the content 
 thereof : firft let fail the perpen- 
 dicular BE, which applied to 
 the fame fcale from whence the 
 fide A B, was taken, will be found to be 9 ~ which if you multiply by the 
 fide 2 ii.it gives you the content ofthe Rhombus, which is 205 1. that 
 divided by 60. giveth one acre 45 perches; 
 
 B ' Prob, 
 
 / 
 
 y tlj/ 
 
 A 
 
 t/ 
 
 /...J 
 
 B 
 
 D 
 
 ao 
 
oJ Treatifeof (geometry . 
 
 Prob. 19. 
 
 To meafure a ^hombqydes. 
 
 pVcry Rhomboidesis meafured, as long fquarcs and Rhombus arc 
 A-'mcafured, by multiplying the perpendicular in the bale. 
 
 Let A B C D, be a Rhomboides to be meafured, whofe fides are 49 f. 
 and«5 e firft let fail the perpendicular EC, which being applied to the 
 fame leak (from which the other fides were taken) it fliall bee found to 
 containc 31 which multiplied by the bafe 49 ,* produceth 1559 which 
 being reduced to acres, as I have mewed, is 9 acres 1 19 4 perches! 
 
 4 i !•/ i ■ ' ' 
 
 , Prob. 20: 
 
 To meafure a right angled triangle. 
 
 A LI triangls whatfoever confifting of right lines, 
 
 **are meafured by multiplying* the bafe with B o 
 
 the perpendicular, or halfc the perpendicular with 3 
 
 thcbafc,orclfemultiplyingbothtogcthcr,andtake J 
 halfc that produft Cheweth the content, wherfore A aa c 
 ifyou multiply 1 5 by 10 which is halfc the bafe fa. 
 
 150 for the contcntof the triangle ABC, which, was required. 
 
 Prob. 21. 
 
 To meafure an Equilater triangle without fndingtbe length 
 of the perpendicular, 
 
 \JVltipIy ; ofoncofthc fides in itfclfe, and that 
 ^-■produft againe by the *, that number multi- 
 plied in halfc the perimeter, and from that produ& 
 the fquare root cxtra&cd, anfwereth the demand. 
 
 , Ai 
 
 Ex &tnple. 
 
 Let A B C, be an equilater triangle to bee meafured, whofe fides are 
 *0, which being halfcd is 10, whofe fquare is 100. which multiplied 
 againe by 10 fa. 1000. and being multiplied by \ the perimeter, which is 
 
 30.fa. 
 
 20 p 
 
<zA Treatife of (geometry. 
 
 — 
 
 30 fa. 30000. whofc fquare root being extra&cd is >173 for the content 
 of the triangle ABC, which was required. 
 
 Prob. 22.’ 
 
 The dimeter of a circle being green to finde out the 
 circumference. 
 
 E Very circumference is more than triple his 
 diameter, by fuch proportion as is more 
 than and Idle than'^. but the neareft rati- 
 onal! proportion betweene the diameter and 
 circumference, is as 7 to 22; A 
 
 Example; 
 
 Let A B C D, be the circumference given 
 whofe length is required, and let A C, the 
 diameter be 28. I demand the length of the circumference 5 multiply 
 alwaies the diameter by 22; and divide that product by 7. you have 
 your defire; fb 2 8. by 22. fa.6x*. which devidedbyz. the quotient is* 
 88. for the circumference required. 
 
 Prob. 2 3. 
 
 To meafurea circle . 
 
 . • ..O' • i 
 
 D 
 
 C Very circle is of the fquare made of his 
 E' diameter, therefore fquare the diameter, 
 which (hall be 28. fa. 784. which multiplied 
 alwaies by 1 f . and that fumme divided by 14. 
 the quotient will be 616. for the area or con- 
 tent of the circle, ABC D. 
 
 B 
 
 A 
 
 C 
 
- - ■ - ■ — " - - - 
 
 <iA Treatije of Cjemetry . 
 
 — ■ m — ■ — ■ ~ " 1 
 
 Prob. 24. 
 
 To give the extenfion of the arch line. 
 
 L Et B C D. bee an arch line gi- 
 ven, whofe length is required : 
 firft,draw the cord line BD, which 
 mud be alwaies divided into foure 
 equall parts, as you fee numbred, 
 
 1, 2,3, 4. then take one of thofe 
 parts, and fet it from D to E, upon 
 the arch line* That done, draw a 
 line from the point E, tothefirftB 
 divifion, which (hall beiE, this 
 line is halfe the length of the arch 
 line, BCD. 
 
 Arithmetic 
 
 Let B C D.bean arch lirfe, whofe length is required ; firft finde out 
 the center (by the tenth propofuion) to that circle whereof B C D, is a 
 part of the circumference. Then take A B* or A D, and apply it to fome 
 fealc, to findethe length thereof, which let be 14. then is the whole dia- 
 meter 28. whofe circumference will be 88. then finde the quantity of the 
 angle BAD, which you (hall doc after this manner : take the femidiame- 
 ter, and fit it on a corde of 60 degrees, then take off the line B D, in the 
 fame corde, and you (hall finde it to be an arch of 120 degrees. Laftly, 
 fay by the rule of 3. if 360 were 88 parts, what (hall laofa. ap f. the 
 length of the arch line which was required. 
 
 ' Prob. 25. 
 
 To weafure a jemicircle ; 
 
 The*r» EVeryl. Circle is equall to that 
 ■■-'long fquare which is made of the 
 femidiameter and halfe the arch line, 
 therefore multiply halfe the arch 
 line by the femidiameter, and the 
 produft fheweth the content of that q 
 halfe circle; 
 
 Example. 
 
 Let G B H, be \ a circle to be meafured, whofe diameter G H, is 28, 
 the whole circumference is found to be 88. and confequcntly the halfe 
 is 44. which is G B H, halfe which is 22* multiplied by the femidiame- 
 ter 14 fa. 308 for the area of the femicircle, which was required* 
 
 $D' 
 
 Prob. 
 
<tA Treatife of (jeometry. 
 
 Prob- 26. 
 
 To me afar e any portion of a circle. 
 
 N Oca: You muft undcrftand 
 that 6 forts of portions of cir- 
 cles may be given to bemeafured, 
 and the realon of all thefeemcafu. 
 rings, is grounded on this Thc- 
 orme following. 
 
 Thco. Every portion of a circle 
 which is contained under twofe- 
 midiameters, and one arch line, is 
 equall to that long fquare, whofc 
 length & bredth is equall to the fe. 
 midiamerer, 5 c j the arch line, ther- 
 forcin any fuch portion, multiply 
 5 the arch line by the femediame- 
 ter, and it fbeweth the Area or 
 content thereof. 
 
 Example of the fit fa 
 
 «gS3£S}ggf**> r *• 1 *- 
 
 Example oft be ftcond. 
 
 be a portion of a circle to be mcafured, now for that it is 
 not included I wuh tvvo femediameters and an arch line, therefore you 
 muft draw the two femediameters A D,and B D,fo (hall you included 
 triangle A B D, more then the cantcll A B G,now firft mcafure the whole 
 figure A C BD, by thelaft propofition, whofe Area will be y 1 82. Then 
 mcafure the Ifofcheles triangle A B D, whofe Area will bee y 72 Q2 and 
 
 neerc rational!, 84 1 which taken from i8i.leavethp7 *. for the Area of 
 the Cantcll A C B. 
 
 Example of the tbirb. 
 
 Let A B C, be a portion of a circle, whofe Area is required; now for 
 that the wholcconfiftcth of an arch line, anda chord line; therefore 
 firft Undo our the center D, then dray the two femidiameters Da and 
 pC.andfindethecontentofthefigure CAD, and B, by rauhiplvi!e 
 5 thcarchhne A BC, which containeth 140 degrees, and lb confeoiirn? 
 
 iy is 58 j whole ; multiplied by 14. the femediame“r!"he wili 
 
 b . 4 1 0 , for the area of A B C and D, to which the triangle being added 
 wnofe area is y 7105. and ncere rational! *4 > maketh 495 x for the 
 whole area or portion of the circle ABC, which was required. 
 
 ® i Exam - 
 
<$A 'Treatife of (feometry. 
 
 A 
 
 Example of the fourth i $ 
 
 Let A B CD, be a portion Qfa 
 circle to be mealured* now for. that; . 
 the perimeter thereof confiftcth of 
 two arch lines, arid two chord 
 lines ^therefore firft the center is to A. 
 befound, which let bcE,then draw 
 the fourc femediameters, (o flaall 
 you reduce that figure or portion 
 of a circle like unto the firft Exam- 
 ple, all which foure figures being 
 meafured, as hath bcenc taught, 
 you (hall finde the content of the 
 whole figure to bc‘41 1 . $§.\ 
 
 Exmplt of the fifth. 6 
 
 Let A B C D, be a portion of a circle to be meafured, being inclofed, 
 in which arc two chord lines, and two arch lines, but whereas in the o- 
 ther Example, Jaft before the center was in the figure, in this the center 
 is without, yet as in all the reft, fo in this the center is to be found, which 
 let be E, then draw the fourc femediameters, fo (hall you reduce the 
 figure A B C D, and E, into three figures like the firft example, and one 
 Ifofchelcs triangle E B C, thefe three figures arc to be meafured, as hath 
 becne before taught, and from thefupcrficies thcrof, the triangle A D E, 
 is to be fubtra&cdjthc remainder (he weth the area of the figure A B C D, 
 which was required. 
 
 i . . , * V \i . < 1 * • * ' . . , 
 
 Example of the fixth . 
 
 *> ’ 
 
 Let A b C D, be a figure given to be meafured, firft let the center bee 
 found, then draw the femediameter A E,andE C, fo (hall you include 
 a figure like ro that in the full example, that done, mcafurc the content 
 
 of 
 
<iA Treatife 0/ (Jeometry. 
 
 of the antic A B C, by the fccon.d Example, to which content the fuper- 
 fiefrs ofthe Tnwgle A D C being added, makeih the arch of the whole 
 figure A B C D which was required, and fo much flrall fuffice for meafu- 
 ring of fcperficiall formes for that no fupe.ffcics can be made , but muft 
 bcfubjc&tofomcof thofc formes. 
 
 How to performe ( Reduction , Addition, Sub- 
 ftraftion, Multiplication , and Divifion, with the 
 Rule of Proportion) by Geometries and fir ft 
 for ReduBion. 
 
 Eduaion is aconvcrfionof one Geomctricall figure into ano- 
 cner, and yet to keepethe fame fuperficial] content. 
 
 — Prob. 27. 
 
 How to make a Geometrical! fquare of two lines , "whether 
 they be equal! or unequal! m 
 
 T?“ is done as I have formerly (hewed you.Problemeeighih, by fin- 
 ding the meant proportion betweene the two lines given , which 
 meane proportion is the fide of the Geomctricall fquare. 
 
 Example , 
 
 Let the Lines A B be giuen , I 
 ioyn them to gether in the point E 
 then finding the centre fas I haue 
 fhewed) I deferibe the arch CGD 
 fo ere&ing the perpendicular E 
 G, it is the fide of the Geometricall 
 fquare anfwering to thofc rwo lines 
 
 A B, to performe this arithmetical- C I 
 
 !ffupcrnuOTs r toncat f cofihc(imffg^inc r0PO ^ , '° n *^* 3CrC ^ OrCri ' >inlce 
 
 Prob. 2 8; 
 
 Hot> to reduce a long fquare into a Geometric 
 call fquare y 
 
 THc operation of this is the fame with 
 the other, for ifyouadde together the 
 length and breadth, and on that line de- A 
 fcnbea femicirclc, and from the concur- 
 ring point crc& a perpendicular till it cuts ^ 
 
 the arch.the length of that line (ball be the & «. M 
 
 tide of the Geomctricall fquare containingthe long fquare. 
 
 Example 
 
20 
 
 <sA T reatifeof (geometry. 
 
 Example* 
 
 Let the long fquare ABC D.bc reduced into a Geometrical! fquarc.I 
 addc the breadth to the length, & extend the line to E;thcn defcribing the 
 arkc GCE.I ere* a perpendicular , from the point D, which extended 
 to the Circumference, cuts it in F, fo is D F the fide of the Geometricall 
 fquarc C H F D : containing the long fquare A B C D, to performc the 
 fame arithmetically, multiply the length in the breadth* and from that 
 extras the fquare Root which is the fide required. 
 
 Example* 
 
 Letthc length A B be id the breadth A C 4> whichmultiplied together 
 produce 64, whole rquare Root is 8. the fideof the Geometricall fquare, 
 which was required. 
 
 Prob. 19* 
 
 How to reduce a Qeometricahjquare, into a long fquare, 
 ■whofe length or breadth U given. 
 
 Example, 
 
 Let the Geometricall fquare A B C D be given , to be reduced into* 
 
 long] fquare whofe breadth lhall be D M, firft I ln "8* * e ' * ,l 
 towards K thenfetting downe the breadth from DtoG, I draw the 
 line G B.whicb I divide into twoequall parte in the point H,*nd 00 that 
 I "reft the perpendicular, extending it till it concurre in the point I.which 
 
 let be the centre of a circle, ^ - 
 
 fo that letting one foot in a 
 the point i , and extending 
 the other unto G, dclcribc 
 the arch G B K , and from 
 DtoK is the length of the 
 long , whofe breadth was c 
 
 throng fquare^L h/ch equalltothe Geometricall fquatj: A BCD, 
 which was required to be done, 
 
 Arithmetically. 
 
 Becaufe as it aforefaid the fide ol the Geometricall fqunre isamean pro- 
 portion between the two fides of the long fquare. Therefore j. A 
 1 which is here tenne, fa. io», and dividing the produft by the fide 
 D M, which lhall be 8, there comtneth 10 the quotient 1 » ; for the length 
 ol the long fquare , whofe breadthisi. andWig multiplied together 
 will produce too, which is equal! to the Geometricall fquare A BC D. 
 
f 
 
 <L/f c TreatiJe of (geometry. 
 
 19 
 
 Prob. $b. 
 
 To reduce a Triangle into a Geometricall Square* 
 
 L Et there be a Triangle given , to be re- 
 duced into a Geometricall fquarc, find 
 the raeane proportion betweene halfe the 
 perpendicular and the bale, and itfhall 
 give you the fide of the Geomctricall 
 Square. 
 
 Example. 
 
 In the triangle A BG the perpendicular is BD, whofe halfe I Set off 
 from C towards E, then taking the midft of that line I fet one foot of the 
 compaffe, and extend the other towards A , describing the arch AFE , 
 then railing the perpendicular from the point C, Iobferucwhereit inter- 
 feds in the arch which is in the point F, fo that C F G is the fide of the 
 Geometricall Square containing the Triangle. 
 
 Arithmetically . 
 
 Multiply the pcrpcndicular,in halfe the bafc,and from that fumme, ex- 
 trad the Square Root, which fhall be the fide of the Square required. 
 
 Example . 
 
 Let the perpendicular B D be foure , and the bale A G fixe 1 , multiply 
 the perpendicular foure by -of the bale which is three fa. i a whole 
 Square Root is y i a neere Rationall 3 \ which is the fide of the Gcomc* 
 tricall Square F G equal! to the Triangle A B G which was required. 
 
 Prob; 3 1. 6 
 
 How to reduce a Rhombus into a Geometricall Jquare • 
 
 A Rhombus (as I haue flhewed you in my definitions) hath equall 
 fidcs, wherefore if you open your compaffes to the length eft any 
 one fide, and toitaddethc perpendicular, the mcane proportion 
 between thole two fhall be your defire. 
 
 Example . 
 
 Let there begiuen'the Rhombus A B 
 C D to be reduced into a Geometrical! 
 
 Square, I lay downe the fide A B, and 
 to it I adde the perpendicular D E , 
 which makes the line A F, then on the 
 point B, I eted the perpendicular G B, 
 which is a meane proportion betweene the bafe and perpendicular, and is 
 the fide of a Geomctricall fquare, containing the Rhombus , which was 
 required. 
 
 Arith- 
 
aA Treatifeof Cjeometry. 
 
 22 
 
 
 Arithmetically . 
 
 Multiply the fide of the Rhombus which is 34 with the perpendicu- 
 lar, which is here 21, and the produft is J04 whofe fquarc Roote being 
 extracted, gives the fide of the Geometrical! fquarcG H,and is nccre ra- 
 tional! 22 
 
 Prob. 32'. 
 
 To reduce a Rhomhojdes into a Geometrical! Jquare. 
 
 I N this you muff let fall the perpendicular , as in the former, and find a 
 mcanc proportion, betweene that and the fide whereon it falleth, and 
 that fhall be the fide of the Geometrical! fquarc. 
 
 Example. 
 
 Let A B C D be the Rhomboi- 
 des G D,thc fide on which the per- 
 pendicular falleth B E the perpen- 
 dicular , which joyned together 
 make the line C F , then from the 
 point G raife a perpendicular inter- 
 fering the circumference in I, fo 
 that G I is the fide of the fquare containing the Rhomboides which was 
 required; 
 
 Arithmetically . 
 
 You (hall workefor this as you did the Rhombois , for letting fall the 
 perpendicular, and finding the mcane proportion, betweene that and the 
 bafe whereon it falleth, is the fide of a Geometricall fquarc , anfwerablc 
 to the Rhomboides. 
 
 Example . 
 
 * 1 
 
 Let the fide A B be ten, and the perpendicular foure, which two being 
 multiplyed together make fortic, whole fquare Roote is >40, and necre 
 Rationail is 6 f which is the fide of the Geometrical! fquare C I , which 
 was required. 
 
 Prob. 33. 
 
 To reduce a Trapezium into a Geometricall fquare. 
 
 I F in a Trapezium, a line be drawne from any one angle,and of that line 
 a parallelogram be made comprehending the Trapezium , and parallcll 
 to the line fo drawne, halfc that parallelogram is equal to the Trapezium, 
 fo that finding the mcane proportion betweene the two (ides of the long 
 fquare, you (hall have the fide of a Geometricall fquare. 
 
 . Ex, 
 
Treatife of (jeometry. 
 
 
 K.\ 
 a \ 
 
 
 
 
 G » 
 
 H 
 
 Example , , 
 
 Let thercbe given the Trapezium 
 
 A B C D , firit draw the line A C, 
 then by the Angles B D, draw two 
 lines parallel to A C, and from thc^ 
 
 extreame partes of one to the other ^ — \ ^ 
 
 draw the lines F H E G.fo haucyou g *> H 
 
 a parallelogram double to the T ra- 
 pezium, which if you cut in halfe by the line I K,you have the parallelo- 
 gram equal! , fo that finding the me 3 nc proportion between* the two 
 fides, you (ball have the fide H F , which is the fide of the Geometricall 
 fquare as was required, and drawing the line EH, have a Triangle con- 
 raining the lame proportion which is E G H, equall to the faid fquare. 
 
 lA ritbmeticdlly. 
 
 This may be reduced Arithmetically by making the p3rellclogran> s 
 comprehending the Trapezium, which is E F G H 
 
 Example, * 
 
 Let theTrapezium A B C D be given firft,I draw the lines E F G H pa« 
 rallcl to AC, which I find to be fixtic, & from the extreme parts of one to 
 the other, I draw the lines E G F H, which 1 find to be 31, which being 
 done I multiply \ of the one by the whole of the other , fothatitprodu- 
 ccth 930, for the fuperficiall content, whofe fquare Root is y 9 \o neerc 
 Rationall 30 * which is the fide of the Geometricall fquare equal! to the 
 Trapezium, which was required. 
 
 Prob. 34. 
 
 ' 1 1 . * * I 
 
 I . t • r*\ 
 
 To reduce any \egular Pofligon-, into aGeometri- 
 call fquare, 
 
 A Regular Polygon is that which hath all his fides equal!, whether 
 it be Pentagon , Hexagon, or Heptagon , now to reduce any of 
 thofe figures, there is agenerall Rule, which is this, find the mean 
 proportion betweene the Serriiperiraetcrand the perpendicular, and that 
 is the fide of a Geometricall fquare containing the (aid Polligon. 
 
 Example, 
 
 Let there be given the Hexa- 
 gon ABCDEF , firft I lay CL 
 
 do wne the Semi perimeter K H, X / \ 3 
 
 and to that I adde the perpendi- 
 cular G H, which makes the line 
 K M,fo that I make that the dia- 
 meter to the fcmicircle K A M, 
 then I raife the perpendicular 
 
 from 
 
2^ Treatife of (feometry. 
 
 from the point H, till it cut the circumference in N , fo that H N is the 
 fide of the Geomctricall fquarc required, note that in all regular Poliigons 
 the long fquarc made of the Semiperimeter , and the perpendicular is c- 
 quall to the faid Polligon, as appeares by this figure. 
 
 Arithmetically, 
 
 Firft find out the perpendicular G H which you (hall find to be neere 
 8 j , then multiply that in the Semiperimeter, which is thirtie,fa.2 jy,for 
 the content of the figure, whofc fquarc Root is 2 5 j, and neere Rationail 
 fixtcen,for the length of HN, the fquarc whereof being made , Chall be 
 cqualltothe Polligon given, which was reqaired. 
 
 Prob. 35: 
 
 To reduce a Circle given into a Geometrical! fquare. 
 
 U Aving deferibed a circle, draw a diameter, which let be divided into 
 *• •* fourteen parts , & on 1 1 of thufe parts cre& a perpendicular, which 
 extend to the circumference a and from the point of interfe&ion draw a 
 line to the extreame part of the diameter , which line fhall be the fide of 
 the fquare containing the proportion of the circle. 
 
 Example* 
 
 Let the circle given be A C B A,the dia- 
 meter A B being divided-into fourteene 
 parts , take 1 1 of thofe parts which is at 
 D,and ereft the perpendicular C D,then 
 draw a line from the point G to the extrem 
 part of the diameter which is to A, fo the 
 line A C is the fide of the fquare propor- 
 tionable to the circle which was requi- 
 ted. 
 
 Arithmetically 
 
 Firft, let the diameter given to 1 8, which fhall be multiplycd in it felfe, 
 and that produ& by 11, then divide the whole by fourteene, the quo- 
 tient anfwcrcth to your queftion. 
 
 Examfla 
 
 Twenty eight multiplycd in it fclfc produccth 784, that multiplycd by 
 II is 8*24, which divided by fourteen * the quotient is 616 , whofc 
 fqaare Root is she length of the line A C y 6t6 t neere Rationail 24 J , a 
 fquarc whereof being made will be cquall to the circle given. 
 
 Prob. f 
 
<$A Treatife of (geometry . 
 
 Prob. 3 < 5 . 
 
 To reduce a Geometrical! fquare into a circle. 
 
 H Aving laid downc a fquare to bcc re- 
 duced into a circle, take any fide of it, 
 and divide it into n. parts, deferibing a 
 fcraicircle to the laid diameter, then on 
 eight of thofc parts, erc& a perpendi- 
 cular, which extend to the circumference 
 of the fcmicirle, then draw a line from the 
 extreame part of the diameter, interfering 
 the perpendicular in the circumference of D 
 the circle, and continue th2t line till it 
 touch tlhe fide of the fquarc, fo that line will bee the diameter of a circle 
 anfwcrablc to the fquarc. ^ 
 
 Example; 
 
 Let the fquare A B C D, be given, making C D, the diameter* I de^ 
 feribethe femicircle C FD, then having divided the diameter into n 
 cquallparts, I take eight of thofc parts, and there I ere& the perpendi- 
 cular E F, then I draw a line (from the extreame part of the diameter) 
 which interfe&cth the perpendicular in the circumference, which being 
 continued,»gives the line D G, the diameter of the circle required. 
 
 Arithmetically. 
 
 Firft fquare the fide of the fquare given, which is here 10. fa. ioo; 
 which muft be multiplied alwaies by 14, and produceth 1400. this pro- 
 duft like wife muft be alwaies divided by 1 1, which make 123 f the fquarc 
 root whereof is y 1*7 and ncere rationall ii?.. for the length of the 
 line D G, fo that a circle made, whercol D G, is’the diameter, is equall to 
 the fquarc ABC D, which was required. 
 
 Of Addition Geometrical!. 
 
 De finttio. Addition is the producing of many figures in one, and to 
 rctainc the fame quantity. 
 
 Prob. 37. 
 
 To adds Ptoo fquares together . 
 
 TT Aving the fidcs of two fquares, make thereof a right angle, and from 
 ^thc two extreames, draw a right line, which (hall bee the fide of a 
 fquarc, containing the other two. 
 
 Exam- 
 
aA Treatife of Cjeometry 
 
 Example. 
 
 Let A B, be the fidcs of two fquares to bee 
 added, and let C D E, be the right angle made 
 of both thofe lines, then fhall the line C E,be 
 cquall in power to both the lines, C D, and 
 E D, which was required. 
 
 Arithmetically. 
 
 Square the two lines A B, adding their two fquares together, and 
 from that fumme extra# the fquare root, which fhall be the fide required. 
 
 Example, 
 
 Lct'the line A be 6 . which fquared, fa. jtf.againc the line B, fhall bee 
 8. which fquared, (lull be 64. chcfc fquares being added, fa, loo. from 
 whence extracting the fquare root, fa. ia which is the fide of the fquare 
 equal 1 to the other two fidcs given, and is the line E O. 
 
 Prob. 38. 
 
 To adde divers fquares together . 
 
 L Et A B C D, be the fevcrall lines whiph 
 reprefent the fidcs of feverall fquares; 
 firft, I make a right angle which is E F G,; 
 and from the point G, to H, I fet off the; 
 
 line A, and from the fame point toward I, 
 
 I fet off the line B, then I draw the line H I, 
 which contained both thofe fquares, then 
 fetting off that line from G to L, and the 
 line C from G to K, I draw another line & 
 from thofe two points, which is K L, and 
 doth containc thofe three fquares, then I take that line K L, and fet it off 
 as I did the former, and the line D on theother fide, and draw the line 
 M N, which containcth the fourc fquares made of A B C D, which was 
 required. 
 
 M K II 
 
 Arithmetically, 
 
 Square each line or fide particularly, then adde thofe fummes together, 
 and from the whole, extra# the fquare root, which fhall bcc the fide of 
 a fq j arc, containing all the other* 
 
 Example. 
 
 Let the fide A be ^whofe fquare is 9. aga'nc the line B fhall be 4 C 
 5 and D 6. the fquares of each being 9, 16, * 7,36. which added together, 
 
 make 
 
<tA Treatife of (jeometrj. 
 
 
 27 
 
 make 8 6. the fquare root whereof is y %6. and ncere rationall 9 for the 
 line M N, which is the fide of a fquare equall to the fidcs ABC D, which 
 was required. 
 
 Prob. 39. 
 
 To aide two circles together m 
 
 I N all circles the diameters arc in proportion as the fidcs of a fquare 5 
 wherefore if you take the diameters, and vrorke as you doc for the 
 fqaarcs, you fhall have your defirc. 
 
 Example; 
 
 Let there bee two circles, 
 namely A B, which I would 
 addc together, I take their 
 diameters C D, and E F,and 
 fet them off in the right an. 
 glc G H I, and from the two 
 points K L, (which is the 
 length of each diameter) I 
 draw a line which is the dia- 
 meter of a circle containing 
 both’the former, which was 
 required to be done* ^ 
 
 Arithmetically 1 , 
 
 Square the diameter of each circle, adding their fquarcs together 1 
 and extra&ing the fquare root from the fumme, it (hall be the diameter 
 of a circle, containing the other two. 
 
 Example. 
 
 Let the diameter of A be 10. which fquared, fa. ioo.likewife the dia- 
 meter of B, fhall be 13. which fquared, fa. 1 69. which added Co the o- 
 thcr, fa. 269. the fquare root whereof is y a 69. ncere rationall f 6 j which 
 is the diameter of the circle.* containing the other two, which was 
 required 
 
 Prob- 40. 
 
 To addc two long fquare s together, l 
 
 pirft, reduce your long fquarcs into geomctricall (quarts, as I have 
 (hewed you 9 and then proceed according to the two former propofi- 
 tions. 
 
 Prob2 
 
z8 
 
 <iA T'reatife of Geometry. 
 
 Let A B (5 D, be one of the long fquarcs, and let H I K L, bee the o- 
 thcr. I reduce them into the two geometricall fquarcs, DEFG, and 
 LMNO, then I fet one fide of the leffer fquare from Qjo T, 
 and the other from Qjo S, and draw the line TS, which is the fide 
 of the fquare V, equall to both the long {Squares, which was required. 
 
 r Arithmetic illy s 
 
 Reduce the two long fquarcs into two geometricall fquarcs, by the 
 twelfth propofition, and then adde them together by 2 1 proportion. 
 
 Example , 
 
 Let the fide A B, be 4o,and the breadth thereof {ball bee 10. which 
 multiplied together, fa. 400. the fquare root whereof is to. the fide of the 
 geometricall fquare anfwerable to the fame, but if you take the content 
 of the other long fquare, and adde it to this, and from the whole, extra# 
 the fquare root, it fhall be the fide of a fquare, containing both the other 
 fo the fidesofthat being 40 and 13. which being multiplied together, fa! 
 520. which added to 400. the content of the other fa. 920. whofe fquare 
 root being extra#cd , is y 9 10. and nccre rationall 30* which isthc fide 
 ofa geometricall fquare, containing both the long fquares, and is the 
 fide S T, which was required* 
 
 Prob. 24< 
 
 To adde diners figures together . 
 
 L Et there be a fquare, a triangle, and circle to be added together; firft 
 I reduce them into one forme, and then I proceed as before. 
 
 ■. •• - ■ 
 
 Exam* 
 
<iA Trcdtife of Geometry. 
 
 *9 
 
 Example, 
 
 Let A B C D, be the fquarc, E F G, the triangle, and MON, the circle, 
 
 I reduce the triangle firft into a long fquarc, and then I finde the racane 
 proportion bctwccnc the two (ides, which is the fide of a geometrical! 
 Iquare equall to the triangle* then I finde the fquarc anfwerable to the 
 circle by a Former proportion, which having done, I make the right an- 
 gle P Q R, and fet off the Gdc of the fquarc ABCD, from Qjo P. and 
 the fide ofthc fquarc KL, I fet off from QtoT, then I draw the line > 
 P T, equall to thole two fqaarcs, then I fee off that line, namely from 
 Qto V, and alfo the line MO,f the fide ofthc other fquarc) from Qjo 
 W, and draw the line V W, which is the fide of the fquarc X YZO, 
 and is equall to the three former figures which was required to be done* 
 
 Arithmetically. 
 
 Firft I finde the content of each of them feverally, then adde all thole 
 contents together, and the product (hall be the torall to the demand, the 
 fquare root of which fumme being cxtra&cd, lhall be the fide of the ge- 
 ometricall fquare, containing the fame quantity of all the other; 
 
 Example . 
 
 Let the fide of the fquarc A B, be *o. then is the content 400. like wife 
 the triangle EFG, being reduced, the fide of his fquare is found to bee 
 14. whofc content is 196. and the circle MON, being like wife reduced, 
 the fide of his Iquare is 13. which produceth for the content, 1 69. thefe 
 three liimmes being added, fa. 7 ^.whofe fquarc root being extracted is 
 y 7 6y. and is neerc rationally * for thefide of the fquarc WX, which 
 is equall to the three other figures. 
 
 Prob.42/ 
 
 jtgenerall way for adding all forts of figures whether 
 regular or irregular . 
 
 L Eft here be given what irregular figure you pleafe, you fhall firft draw' 
 it forth into triangles, and then dbferve this, (that the mcanc proper- 
 
 C 3 tiott 
 
1 ° 
 
 <tA Treatije of (geometry. 
 
 lion bet wcene halfc the perpendicular and the bafe) is the fide of a geo* 
 metricall fquarc anfwetablcto that faid figure, fo having reduced them, 
 you may proceed according as I have formerly (hewed. 
 
 OfSubftra&ion geomctricall. 
 
 Subftraftion is a taking of the lefler figure from a greater, and to give 
 the remainder in the third figure. 
 
 Prob. 43. 
 
 How to fubflraft one line from another , and to give the 
 remainder in a third. 
 
 \ 
 
 J^Et A and B be given to fubftraft the lefler out 
 of the greater, let A be 10. and let B be 6 . then 
 is Cthe remainder, which is 4. for 6 fubftrafted 
 
 B. 
 
 io 
 
 6 
 
 c — 4 
 
 from io. there refts 4. Co the two lines B C, are equall to A which was 
 required to be done. 
 
 Prob. 44. 
 
 To Jubftratt one {quart from another 1 and to give the remainder 
 
 in a third. 
 
 L&A B C D, and E F G H, be two fquares, it is required to fubftraft 
 the fquarc E F G H, from the fquarc A B G D, to doc this you muft 
 firft make a right angle, and fee off the fide of the lefler fquarc from the 
 right angle on any fide, and fetting one foot of your compafles in that 
 point (being opened to the difiance of the fide of the greater fquarc) ci- 
 tend the ether till it cut on the other fide, and looke where the point of 
 interfeftion is, for from that point to the right angle, is tbe length of the 
 third line, or the fide of a fquare remaining. 
 
 A 
 
 I 
 
 Exdmple. 
 
 Let A B C D, be the greater fquare, E F G H, the lefler to be fub ft ra- 
 fted from the greater, I make the right angle M N O, and (et off tbe fide 
 of the leffer fquare from tbe right angle at O to T, then opening the 
 Compafles to the fide of the greater fquarc A B, I take the hoc 
 thereof a B, and fetting one foot of the Compafles in tbe point T, and 
 
 with 
 
dA Treatife of (jeometry. 
 
 with the other foot I interfe# the point Qfo the diftanccfrom O to Qjs 
 the fide of the fquarc I K L C which is the remay ncr, the letter fquare be- 
 ing fubftra&cd which was required to be done. 
 
 ' i^iritbmetkally. 
 
 Square the fide of each Figure, fubftraaing the fquarc of the letter from 
 the fquare of the greater , and of the remay ner extras the fquare Roof, 
 which anfwersyour demand. 
 
 Example* 
 
 Let the fide of the greater fquarc A B be 20 , which multiplycd in it 
 felfc fa. 400, and let the fide of the letter fquarc EF be rvrcluc. which 
 fquared fa. 1 44* and being fubttrafted from 40©, the greater fquares retts 
 25 6 whole fquare Root extracted is fixteen for the fide of the remayning 
 fquare, which is I K, which was required. 
 
 Prob. 45. 
 
 Another way for working of tie fame , 
 
 O N the length of the longeft fquare defcribe an arch t and let that 
 line be the diameter of the fcmicircfe , then open your compafles 
 to the letter fide , and fetting one foot of them at the end of the diame- 
 tcr,with the other cut the arch, and from that point of inrerfe&ion to the 
 ether end of the diameter draw a line which (hall be the length of the 
 third line , or the fide of a fquare remayning , the other being fub- 
 ftra&ed. 
 
 Example* 
 
 L Et A B bee the fide of the grea- 
 ter fquare, open your compattcs 
 to the (cmidiameter of the line, and 
 defcribe the fcmicirclc A G B, then 
 open your compattcs to the bredth 
 ot the fquare to bee fubftra&ed , 
 and fet it off from B to G , then 
 draw the line A C which is the fide of the third fquare or remayner* 
 which was required. 
 
dJ T reatife of Cjeometry 
 
 Prob. 4 6, 
 
 To fubflraft one Qrcle from another. 
 
 L Et A and B be two circles, 
 the propofition istofub- 
 Ara# the lefler from the 
 'N greater, to doc this and the like, I 
 
 j doc as to the fquarc, that is, I fee 
 
 J off the diameter of the leffer circle 
 B from the end of the greater dia- 
 meter to the point E, which is the 
 interfe&ion of the arch , then I 
 draw the line E C, Which is the diameter of a third circle containing the 
 remay ne which was required. 
 
 Arithmetically . 
 
 Square the diameter of each circle , fubftrafting the leffer fquare from 
 the greater, and extra# the fquare Root of the remaync , which (hall be 
 the diameter of the remay ni»g circle. 
 
 Example. 
 
 Let the diameter of the greater circle be ao his fquare is 400, alfothe 
 diameter of the leffe (hall be fifteene , Whofe fquare is 115, which being 
 fubftra#ed from 400 the greater fquare , refts 175. The fquarc Roote 
 whereof is y 175, necrccra&ionall 13 which is the diameter of the rc- 
 mayning circle. 
 
 Prob. 47. 
 
 To fabttratt a triangle from a fquare . , 
 
 F ir ft, reduce your triangle into a long fquare, then reduce that long 
 fquare , into the breadth of your other fquare , fo have you the 
 length and breadth of a fquare to be fiibftraftcd, which is perfor- 
 med as followeth. 
 
 Example. 
 
 Let A B C D be a fquarc from 
 which I would fubftra# the 
 triangle E F G , firft I reduce 
 the triangle into the fquarc T F 
 G H , then I reduce that long 
 fquare into a long fquar, whofe 
 fide is given namely A B G, I 
 find the breadth thereof to be 
 KF, which fet off from D to N 
 
 I* 
 
 and 
 
■iA Trtatife of Cjeometry. 
 
 33 
 
 and from C to M, and draw the line M N , fo that the fquare C D N M 
 is the long fquare anfwerable to the triangle given , which being fubftra- 
 &ed from the fquarc a BCD, leave the fquare ABMN, which was re- 
 quired^ 
 
 Arithmetically . 
 
 Call vp the content of the fquarc, and caft up alfo the content of the 
 Triangle,which having done, fubftra& the content of the Triangle from 
 the content of the fquare, the remayner is your defire. 
 
 Example* 
 
 Let the fide of the fquare A B be ten , the whole content whereof is 
 i oo, and lctthefidesof the Triangle EF and F G be fix, then the con- 
 tent of it will be found to be eightecne, which fubftra&cd from ioo,rcfis 
 78, which was required. 
 
 Prob. 48. 
 
 To jubftraSb a long fquare from a triangle giyen, 
 
 I Et A B C be a irianglc fr 5 which I would fubftraft the long fquar 
 DEF G, which I reduccjinto another long fquare containing 7, 
 -rfehc fide A C, for his breadth whole length is found by the fore- 
 going propofition to be L D, which line I draw^parallel to A C which is 
 N P, and cutteth the line A B in O , fo have you the Triangle A C O e- 
 quall to the long fquarc given, which being fubftra&ed from the Trian- 
 gle A EC, then refis the Triangle C BO, which was required. 
 
 Of Multiplication. 
 
 Vltipli^ation in Geometric, is nothing elfe , then of lines given to 
 ■**v-l.i n ak ea fq UarCj w hofearcais called the produd of the Multipli- 
 cation. 
 
M- 
 
 <tA Treatijeof Cfeometry 
 
 
 Prob. 
 
 0/ lines given to make afquare by Multiplication* 
 
 L Et the line A B be given to be^ 
 multiplied by the line G D, 
 it is nootherwifethen to produce g 
 the long fquarc EF GH, whofc 
 area or content is the produft re- 
 quired , and fo much for Mulci-ao 
 plication. 
 
 4-o 
 
 go 
 
 D 
 
 4-Q 
 
 zo 
 
 4-0 
 
 Of Divifion. 
 
 D Ivifion is no|othcr then' to know how many times one Figure is 
 contained in another, and is wrought after this manner , firft reduce 
 the dividend and divifor, both into one length or bredth , then by mea- 
 furing it with your compaflc, you (hall finde how many times the leffer 
 which is the divifor, is contained in the divident, which produccth a 
 
 ' ,UOt,em - ’ Prob, jo.' 
 
 lo divide one long fame bj another ; 
 
 Let ABCD bealongA B 
 
 fquarc given, and let the pro 
 pofition bee to divide the 
 fame by the long fquarc E F 
 GH, firft, I reduce the long 
 fquarc E F G Hinto a long 
 fquare, whofc fide is A B, T 
 and 1 find it to be K E,then 
 I mcafure that breadth in 
 the fide E D,and 1 find it to 
 bee contained foure times, 
 which is the quotient required. 
 
 Pro. 
 
qJ Ifreatife of (jeometry , 
 
 
 K 
 
 
 Prob. $i. 
 
 To divide a Circle by a triangle . 
 
 L Et A be a circle gi- 
 ven, and let thepro- 
 pofition be to divide 
 the fame by the trian- 
 gleB CD. Firft,Jetthc 
 circle A be reduced .in- 
 to a fquarc , by the 19 
 propofition, whole fide 
 is found G H s and fo G 
 H I K. is the fquare 
 made equall to the circle , then is the Triangle 
 brought into a long fquare, whofc length D M 
 is equall to the fide of the fquare G H , the 
 breadth of the long fquare is alfo found to be 
 j OC, which I fee off, in the fide Of the fquare 
 from Hto I, which is found to be contained 
 
 therein five times. 
 
 J r 
 
 To perform the Rule of three , or the rule of 
 Proportion, 
 
 'He Rule of three is, of three numbers or three ftraight lines given, to 
 find afourth in proportion, that is fuch ajine or number, that may 
 bcare fuch proportion to the fecond, as thethird doth to the firft. 
 
 Prob. 
 
 Three lines being given to find afourth in proportion . 
 
 L Et A B C be three lines given, and let 
 
 the propofition be to find a fourth in iA _ 
 
 proportion , firft the angle D E F is b 
 drawne, then is the line A fet from D to I, c 
 and the line B is fet from D to K, then is the 
 line I K drawne , afterward I fee the line C 
 From D to G , and by the point G is a line 
 drawne parallel to I K, whichcuttcth theo- 
 ther fide of the angle in H, and fo the line G 
 H is found to be the fourth line in proporti- 
 on, and as the line A is to the line B, fo is the 
 line C to the line G H , which was required 
 to bt done. 
 
 F Oraftnuch as in the performance of thefe Rules in thisTreatife, and 
 their dcraonftrations, the power of lines is of great ufc, you fhallun- 
 
 derftand 
 
 20 
 
 10 
 
<*A Treatifeof Cjeometry. 
 
 dcrftand what the power of lines is,* which by the third definition of the 
 tenth Booke of Euclide , is faid to be the fquare thereof , or any plaine fi- 
 gurecquall to the fquarc thereof, as when the line is in length fiuc, the 
 fquare is as, lb that the power of the line is faid to be a 5 , bccaufc there 
 will be 15 fqaarcs contained within the fame. 
 
 Prob. 55. 
 
 To tike any fart of the power of a line. 
 
 T O find out any part of the power of a line, is to find a line , whereof 
 a fquare being made, the fupcrficies thereof, flialibeare the propor- 
 tion afhgncd to the fuperikics of a fquarc made of a line given, as the two 
 given termes bear£ one to the other, therefore to takeany part or parts of 
 the power of a line, doc thus. On the line given deferibe afcmicircle, 
 then divide the diameter into as many equall parts as the greater tearmc 
 given containcth unites, 2nd on fo many parts as the IcfTer rerme contai- 
 ned! unites, raile a perpendicular, till it cut in the arch line, audnotethe 
 interfedion in the arch linc,for from that point to the end of the diame- 
 ter, where the part begantobenumbred , aline bcingdrawnc fballcon- 
 taine the proportional! parts required. 
 
 Example. 
 
 Let A G be a line given, now the 
 queftion is to find a line that (ball 
 be in povfecr | of the fame. Firft, on 
 the line A C is deferibed a femicir- 
 c)c, then is the fame line divided in- 
 to eight equall parts ( according to 
 the number of the greater terme gi- 
 ven) and on five parts thereof (according to the lefler tearmc given ) is 
 raifed the perpendicular B D which cutteth the circumference in B, then 
 arethelincsABandBCdrawne. Now for that, by the 31 propofition 
 of the third Booke of Euclide , the angle B is a right angle; Therefore by 
 the 33 Thcorcmc of the firft of the fame, the lines A B and B C arc equal 
 in power to the line A C. Then for as much, as by the thirteenth of the 
 fixth booke of Euclide , the line BD is a mcanc proportion, betwixt AD 
 andDG. Therefore I conclude.thatthe line A Bis £ of the power of the 
 line A C, and the line BC is | of the power of the line AC, and in this 
 manner you may take any part or parts of the power of aline , that is a 
 greater proportional! power given to findcalcfle in any proportion re- 
 quired. 
 
(lA Treatife of (geometry. \l 
 
 Prob. ap. 
 
 To inlarge a line in power according to any proportion given* 
 
 T Otalceanypartor parts of the power ofa line, is to produce alcfle 
 linetocontainealeffcrproportionall power, fo to inlarge aline in 
 power, is reproduce a linctoconcaineagreater proportional power, and 
 as the propofition before was to take | of the power of a line .* now the 
 propofition fhal be to make a line in power to aline given, as 5 to 2. Now 
 for that the power of the 
 line to be produced, muft con- 
 taine the line given twice, and 
 3, for that 2 is contained in 
 5 twice, and i. Therefore firft 
 deferibe a right angled trian- 
 gle, whofc obtaining fidcs fhal 
 be the length of the line given; 
 and draw the third line, 
 which fhall bee double in 
 
 power to the fame line given; then take halfc the power of the line given, 
 by the laft propofition before taught, and raife the perpendicular of that 
 length oathe end of the laft found line, and then draw the line which 
 fubtendeth the right angles, which I conclude by the 3 3 Theorems of the 
 jaft book of Euclid* , to beare that fuperficiall proportion to the line 
 given, as 5 doth to 2 , 
 
 Example. 
 
 Let A B, be the line given, and let the propofition be to inlarge a line, 
 that it may have fuch proportion, to the line given, as 5 to a. Firft ere& 
 the perpendicular A D,cquall in length to the line given, then deferibe a 
 fcmicirclcon the line given, as A E B, then divide the line given into two 
 cquall parts, and on the mid ft crcftthe perpendicular E C, then draw 
 the fubtendent line D B, which by the 47. of the firft of Euelide , is dou- 
 ble in power to the line given, then with your Compaffes take the length 
 of E B, and crc& the perpendicular on the line D B, of the fame length as 
 B F,and laftly,draw thcline D F, which fhall have fuch proportion to the 
 line given as 5 to 2, 
 
 Prob. 55. 
 
 To cut offfrom a triangle any parts , as and with a line if- 
 
 filing out of any angle . 
 
 ^ Akc 1, *, or what you pleafe, of the fide oppofite to the angle affig- 
 ncd,and from that point draw a line to the angle affigned, fo fhall you 
 have a new triangle to rccaioe the parts required. 
 
 D 
 
 Example 
 
*8 
 
 <±A Treatije of (geometry. 
 
 Example. 
 
 Firft, the* of the line A B, 
 being oppofitc to C, is taken 
 or found, which endethin D, 
 and then the line CD, is 
 dravvnc, fo is D C A , ^ of the 
 triangle A C B, which was re- 
 quired. ' 
 
 Arithmetically , 
 
 Let the line A B,be given 42. which is oppofite to the angle affigned; 
 now* of 42 is 10 1 which is the diftancc from A toD. then the line 
 C D, being drawnc, cnclofcth the triangle A CD, cquall to ; of the 
 whole triangle given, which will appeare more plainely ifyou caft up the 
 content of the whole triangle, which you flsall finde to bee 336. thc£ 
 whereof Being fubftra&ed, which is 84. gives your defire, and is the 
 content of the triangle CAD, which was required. 
 
 Prob. 5 61 
 
 To cut off from a triangle any parts with a lineiffuing out of 
 
 an angle aligned. 
 
 F irft meafure the area 
 of the whole triangle, 
 then multiply the fide op- 
 pofite to the angle aflig- 
 ned by the parts to be cut 
 off, and divide the produ £ 
 by the area of the whole B 
 triangle , the quotient 
 fheweth how much you 
 (hall cut from the line, to make a new triangle, retaining the parfs 
 required. 
 
 Example . 
 
 Let A BC, be a triangle given, and let the propofition bee to cut off 
 84 parts, with a line iiluing from the angle C,and falling on the line A B, 
 and making CB, one of the fidcs of thenew triangle: firft the whole 
 content is found to be 33 < 5 . which having, proceed thus, let 84 bee the 
 numerator, and 33 6 the denominator, which being abreviated thus, 
 
 £ a. you fhall finde it to be* of the content, then proceed in all rcfjpe&s 
 as you did in the laft propofition, and you {half finde the triangle BCD, 
 containing 84 parts of the triangle ABC, which was required. 
 
 Arithmetically, 
 
 Firft, the content or area of the triangle being found to containe 3 35. 
 and the line A B, is 41. then fay by the rule of proportion, as the whole 
 
 area 
 
%A \Treatife of (jeometry . 
 
 area is to 41. foisthe lefier area 84. to a third number, which will bee 
 found to be io j. in the fame parallel, which fet from B towards A, iten- 
 deth in D, then draw the line C D, and the triangle BCD, doth con- 
 taihc 84 parts, the thing required. 
 
 Prob.57, 
 
 To cut off from from a triangle or any other parts with a 
 
 parallel to any of the fades afrgned . 
 
 plrft fquareoneof the (ides in which you would have the parallel to 
 - cut, then workc thus by fhc rule of proportion, as the greater terroe 
 given is to the fquare of that fide, fo is the lefier terme to a fourth num- 
 ber, whofe fquare root being extra&cd, and fet off in the fame line, pa. 
 rallel to the other fide, you (hall findc a triangle including the parts re- 
 quired. 
 
 O f I IO li ~ u 1 4 t ; wl 
 
 Exemplei 
 
 Let A B C,be a triangle from < 
 whence | is to be cut off with 
 a line parallel to A G, fo that 
 BG, may bee one of thefides 
 that the parallel rauft cut; firft 
 deferibe a femecircleon the line 
 A B, then divide the line A B, 
 into five equall parts, accor- 
 ding to tbe greater terme given, 
 and one three ofthofe parts the 
 lefier terme given, raife the per- 
 pendicular D E, which cuttetb 
 the arch line in E.thcn draw the 
 line B E, and fet itofF from B to F,and from F draw a line parallel to A C, 
 which cutteth rhe line G B io G, fo the triangle F G B, is f. of the trian- 
 gle A B C, which was required. 
 
 ' I - l ; . * * 
 
 Aritbmeticdlly . 
 
 Square the fide C B, which is 34. fa. 21yd, which multiplied by 3: 
 fa. 3458. which divided by 5. the quotient is 69 4 * whofe fquare root is 
 y 693 ? neerc rational! 2 6\ which is fet from B towards C, and endeth in 
 G, from whichjpoint draw a line parallel to A C, and it cutteth the line 
 A B,in F, fo is the triangle G B F of the whole triangle, the thing re- 
 quired. After this manner you may reduce any plot into any proporti- 
 on greater or lefier at your pleafure.] 
 
zA 'Treatife of (feometry . 
 
 Prob. 58* 
 
 To cut any number ofmeafuresfrom a triangle as 1 0.40.60 Aficl 
 in a triangle proportional! to the triangle given with a line 
 parallel to one of the fdes appointed . 
 
 p Irft meafurc the whole trianglc.thcn fquare any of thole (ides in which 
 you would have the parallel to cur, that fquare number multiply by 
 the parts given to be cut off, and divide the produft by the area of the 
 whole figure, out of which quotient extraft thefquareroot, and it (he w- 
 eth how much you (hall take of that fide of the triangle, to make a new 
 triangle, with which mea Cures found, worke as in the laft propefition. 
 
 Geometrical). 
 
 Let A B C, be a triangle from 
 which 1 12. is to be cut off with a 
 line parallel to the line AC, the 
 triangle being meafured & found 
 to be 33 6: put 1 12 over for the nu- B 
 mcrator, and 336 underneath for 
 the denominator, and abreviatiftg 
 it, you (hall findc the fame to bee 
 y then having dcfcribtd the fc- 
 micircle on the line AB, divide 
 the line A B, into three equall 
 parts, dod on one of them, cre&the perpendicular D E, then take the 
 diftance from B to E, and fet the fame from B towards A , which endeth 
 in F, by which point, draw a line parallel to A C, (b the triangle BGr, 
 doth containe 112. which was required. 
 
 Arithmetics//). 
 
 Firft, fquare the fide B C, which is 20. fa 400. then fay as 33 6 . is to 
 400 the (quare of that fide, fo is 1 12 . to 1 3 3 ' r whofc fquare root being 
 cxtra&cd, is y 13 3 f neere rationall i 1 j. which is the diftance from B to 
 G, fo if you draw from that point at G, aline parallel to A C, you have 
 thctriatigle B F G, which containeth lit. which was required. 
 
 Prob. 
 
 To make the parts cut off in a trapezium*, if there be a proportion 
 givenjbetweenc the parts to be cut offhand the whole figure* 
 
 S Vbftraft the lefler terme given, from the greater, and with the remain- 
 der worke as before is taught,! 
 
 Exam- 
 
f 
 
 <iA Treatije of Geometry. 
 
 41 
 
 Example. 
 
 Let the triangle A B C,bc given, 
 from whence ; is to be cut off in a 
 Trapezium; firft, on C B, deferibe 
 a fcmicirclc, then diuide C B, into 
 five equal! parts, and on three of 
 them, from B, creel a perpendicu- 
 lar D E, then fetting one foot of 
 your Compares in B, extend the other to E, which diftance let off front 
 B, towards C, which endeth in F, by which point draw a line parallel 
 to A C, fo I conclude the triangle G F B,to contained of the whoIe,and 
 confequently the trapezium ACF G,doth contafne ) of the fame, which 
 was required. 
 
 Arithmetically. 
 
 Firft, taking | from the whole, the remainder will bee* then by th® 
 rules afore taught, make the triangle G F B, to containe and then it fol~ 
 lo weth, that the Trapezium A G F G, muft containe of the whole tri* 
 angle, which was required to be done. 
 
 Prob. 60. 
 
 To cut off from a fquare any parts ajftgned, and to make t be fe parts 
 into a triangle , therein you muft note that the parts to be cut off 
 may not exceed * the fquare , for if they be y then the remainder 
 •spill be a triangle. 
 
 T O worke this, firft draw a Dia- 
 gonal! line to the fquare, that 
 being done, the fquare is reduced 
 into two right angled triangles, 
 then may you from either of thofc 
 triangles, which is affigned, cut off 
 any number of meafures therein 
 contained, by the rules concerning triangles afore going, either with a 
 line iftuing out of an angle, or with a line parallel to any of the fidcs. 
 
 Example . 
 
 From the fquare A B G D, let there be cut | of his area, with a line pa- 
 rallel to the diagonal^ firft the diagonall B C, is drawne, then muft you 
 note the \ of the whole is ; of the halfe,thetefore the proportion ftandeth 
 thus from the triangle A G B, let there be cut? with a line parallell to 
 B C, which is found by the 57 pfopoficion to bee the triangle A E F, 
 which is - of the fquare A B C D, the thing required; againe, the fquare 
 G H I K, being found to be 400. I defire to cut off 1 50. parts with a line 
 iffuing out of the angle K,and falling on G H. 
 
<t A c freatijeof (geometry. 
 
 ing of the menfuratf 
 
 on of Geometricall Solids. • 
 
 Prob. i , 
 
 How to meafurethe Soli ditie of the Cube. 
 
 He cube is a body comprifedof fixe fquare fupcrfi- 
 cicsbcingof cquall proportion , and is accounted 
 one of the five regular bodies , being named of the 
 Greeks Exaedron^ and is meafured in manner fol- 
 lowing. 
 
 Fir ft having found the fuperficiall content of or.c 
 of the fquares, by thc4p propofitionrof the firft 
 book, and multiply thatlumby the fide of the fquare, and that produceth 
 the cube, other wife niultiply the fidcin it fclfe cubically , and it worketh 
 the fame cfFeft. 
 
 Example, 
 
 ' Let the cube ABC D be given to bee mea- 
 fured, the fidcs whereof (hall be five inches, the 
 fquare whereof is found to be 25 inches, and that 
 againe multiplyed by the fide or root, produceth 
 12J , which is the content of the cube in inches, 
 which was requited. 
 
 Prob. 2. 
 
 How to tneafure the Crafsitude of an Oblonge. 
 
 T His is performed aimoft with the fame facilitic as the precedent, 
 for if you multiply any of the fupcrficies terminating the fame 
 figure, by one of the fides which falleth on the Laid fupcrficies at 
 right angles, it giveththe content required. 
 
 Example. 
 
<iA Treatife of Cjeomctry. 
 
 Example, 
 
 Letthcfolide Oblonge bee EFGH, the fide g 
 of which EFisfix inchesf t ahd the fides F G isfbure & 
 inches, which multipiycd together fa. i4.that muh 
 tipiyed by the length, which is eleven inches, fa.204 11 
 for the folidttie of that figure. 
 
 6 H 
 
 Prob. 3; 
 
 How to meafure a Rectangular figure being hollow. 
 
 T His Figure is meafured as the former, only the lefTcfollid muft be 
 fubftra&cd from the greater, which leaves the right content. 
 
 Example, 
 
 Let the fquare which is given be Q R S T, the R- . ap- 
 
 breadth of Qjt being eight foot , and the length ^ 6 
 
 R S being ten foot, the heigth feven foot, and let 8 , 
 the breadth of the intrinfique of the concavitic V 
 X be foute,thc length X Y,fix foot,& of tfie fame 
 heigh: with the reft. Firft, 1 meafure the whole 7 
 asafolid, faying, ten by eight makes 80, that a- 
 gaine by feven makes 550, afterward I meafure 
 the concave as a folid, faying, fixe by fourc is 24, 
 which multipiycd by feven, produceth 1 68, which I fubftraft out of the 
 whole content, and the remaync is your defire. 
 
 Prob. 
 
 4 - 
 
 How to find out the Crafsitudeor Solid content of 
 a Cibinder . 
 
 pfrft find out the diameter, and by the 23 propofition of the firft book 
 find out the fuperficiall content of the circle, that done, multiply that 
 fumme by the length, gives your defire. 
 
 Example. 
 
<iA Treatife of (fesmetry, 
 
 44 
 
 l Example* 
 
 Let the cillinder given be ABC the diameter 
 whereof A B is (even, then is the fuperficiall con- 
 tent of it 38 j , which raultiplyed by the length 
 B C which is 1 z produceth 4 6i, for the content 
 of the whole cillinder, which was required. 
 
 Prob. 5. 
 
 How to me afire the trilaterall figure calledtbe Prijma. 
 
 T HePrifma is terminated with twocquall and cquilate rail Triangles 
 which being meafured by the 2 1 Propofition of the fiift bookc , and 
 that fummcmultiplyed in the length, giveth the foliditic of the fame. 
 
 Example. 
 
 Let the figure given to be meafured be D E F, which 
 is terminated with two equilatcrall Triangles,thcfides 
 whereof arc found to be fix inches, and by the 21 Pro- 
 pofition of the firft, the fuperficies will be 15 h which 
 raultiplyed in the length E F» which is 12 fa. 187} for 
 the whole content. 
 
 j 
 
 Prob. 6 . 
 
 How to find the {olid content of a Prifma Trapezium. 
 
 T His figure is terminated with two equall Trapezians, Co that finding 
 the content of the Trapezium by the 33 Propofition of the firft 
 bookc, and multiplying that fumme by the length , gives the foliditic of 
 
 the whole. 
 
 Example 
 
<iA Treatife of geometry. 
 
 Example, 
 
 G r 
 
 Let the Prefma Trapezium given be G H I , the 
 bafts of which are two Trapeziums , cquall to each 
 other, the fides equall are foure, the leffer fide three, « 
 and the greater (even 4 and the height thereof is 1 1 , 
 the fuperficics given of the Trapezium will bee 
 found by the 3 3 of the firft to be 17 ;, which mul- 
 tiplycd in the length which is 1 1 fa/ 1 $i\ for the fo- I 
 lid content which was required. 
 
 4i 
 
 Prob. 7. 
 
 To find out the Qrafsitude or [olid content of an 
 ExagonaU figure. 
 
 A S in the reft fo in this you muft firft find out the fuperficial! con- 
 tent of the Exagon, comprehending the figure, which multiply ed 
 in the length giveth the foliditic. 
 
 Example, * 
 
 • r Yj‘ 7 U* t ^ U • v *0 *•- 
 
 Let the Figure given bee KLM , the height 
 whereof (hall be 1 6 Foot, and the fides of the Exa- 
 gon (ball be fix foot , then will the fupef fides of this 
 Exagon, bee found by the 34 of the firft to bee 9 g 
 which multi ply cd in the length which is fa.140 
 7 y for the folid content of the Hexagon which was 
 required. 
 
 Prob. 8. 
 
 How to tneafirethe filid content of a concave Ci Hinder. 
 
 F Trftmeafure the whole as a (olid Cillinder, by the fourth propo- 
 rtion of this booke,HkewHe meafure the concave as a folid , which 
 lubftrad: from the whole, leaves the conteoc required. 
 
 Example 
 
aA Treatife of (geometry. 
 
 Example, 
 
 3 § m 
 
 Let the concave Gllinder given bee R S T , the 
 diameter of the exteriour being nine inches , and the 
 diameter of the intcrionr or concave fhaibc fix inches, ; 
 the length whereof (ball bee ten inches, by the 13 
 propofition of the firft booke the fupcrficiall content 
 of the whole . circle will bee found 6 3 , and the fu- 
 pcrficics of tfye concave or leffer circle will be found 
 a8; ( then multiply the greater 63 ,|by ten the length 
 fa. 6^61 like wife multiply 2 8 \ , the leffer fuperficies 
 by ten fa. 282 1 , which fubftra&ed from the whole 
 6 ^ 6 \ refts 353 which is the folid content orbicu. 
 lar of the concave cillindcr required, and after this manner may yon mea- 
 fure any of the aforegoing Figures being concavous, or hollow. 
 
 Prob. 9 . 
 
 How tofintl tbe folid content of a Cone. 
 
 T His is done by multiplying the fuperficies of the bafje by the 
 third part of the height of the Cone, for every Cone'isjpf a 
 cillinder, confiding on the fame bafe, and being of equal height. 
 
 , Example, 
 
 Let the cone given be A B C, the height where- 
 of A C is twelve, and the diameter of the bafe being 
 ten, fir ft the fuperficies of the bafe is found , by the 
 2 3 propofition of the firft to be made 98 , which 
 multipiyed by fourc, the third part of the perpendi- 
 cular fa.3 14 i for the folid content. Now it refteth to 
 find the perpendicular, which is after this manner, 
 firft fquare the fide of the cone which is here thir- 
 teene,fa. 1 69, likewife fquare f the diameter, which 
 is five fa. 2; , then fubftrad the leffer fquare from the 
 grcatcr.fa* 144, whofe fquare Root being extra&cd 
 is twelve, the length of the perpendicular required , and after this man- 
 ner are all pyramidall Figures meafured. 
 
 [Prob. 10: 
 
 - • / . • ' - . •. " r - •“ 
 
 ■ , jTo find the Cvafsitude or folid content of aSpbeare. 
 
 ■ ... . 
 
 T His is done by cubing tbe diameter, which multipiyed by eleven, 
 and divided by 2 i, gives the folid content, for every cube is in pro! 
 portion to his Spbeare, as 21 to eleven, every globe is to his cube 
 as eleven to 21. 
 
 •Vv ,«*. .,1 x 
 
 Example 
 
+7 
 
 aA Treatife of Cjeometry. 
 
 Example. 
 
 There is a globe whole diameter is fourtccne 
 inches, and I defire to finde the craffitudcofit, 
 
 Firft I cubciburtcen fa. 1744, which I multiply 
 by eleven fa. 301 84, that divided by twenty one, 
 is 1437 t the foliditie required, to findc the fu- 
 perficiall content of any Sphearc is only multi, 
 plying the diameter by the circumference in this 
 example, the diameter being fourtcenc , theeir* 
 cumfcrenc, is forty fourc, which multiplyed in each other, produce 6*6 
 the fuperficiall content of the Spheare required. 
 
 1, 
 
 The third Part , contayning divers and fundry 
 wayes for meafuring Altitudes, Longitudes, and 
 Profundities,afwell inaccefsible as accefsible-fome 
 performed Geometrically, fome Arithmetically, 
 and other Mechanically, and firft for meafuring 
 of Altitudes. 
 
 The forme of the Geometricallfquare^with the ufiofit > "which 
 ferves for meafuring of Altitudes , Longitudes 
 and Profundities . 
 
 I N meafuring with the Gcometricall fquare it is to be noted, [that one 
 fide of the fquaremuft alwayes (land parallel to the Horizon , and 
 like wife your eye mart come dole to the centre, on which the Index 
 playcth,if you meafure with a moveable Indcx,but if you meafure with a 
 Thred and Plummet which will alwayes hang perpendicular to the 
 Horizon, then it will be contrary , butlapproovc of the Geometrical! 
 Square, with the Index before the Quadrant, with a plummet, efpccially 
 for thefc rcafons, firft, bccaufe the Square may be fet on any Horizontal 
 plane, where the other cannot, and fecondly , becaufe the holding of the 
 Quadrant cannot be fo ftcady but it will caufe fome errour, and the third 
 reafon is in regard that this may bcufed as a Quadrant at pleafure , and 
 laftly this may be ufed flat when that with a plummet and thred cannot, 
 wherefore I approve this as the beft; For the grounds of this inftrument 
 it is taken from the fourth propofition of the fixth booke of Euclide t 
 where he fayes, that of equiangied Triangles , the fides which are about 
 theanglesare proportional I, wherefore I will notfland upon thar,onIy I 
 will lay downc the forme of the inftrument in the Diagram or Figure 
 following, and then will come to ftiew the ufe or application of ir. 
 
 The 
 
! 
 
 Treatife of (jeometry. 
 
 The forme of theOeometricaU Square. 
 
 B C and C D being divided each into fixtie equall parts. A being the 
 centre, on which the moveable index playcth. B D a Quadrant di- 
 vided into ninetie degrees and minutes, which is placed within the 
 
 Square; 
 
 Tbeufe of the GeometritaU fquare in finding the height of a 
 To we or Caftle which is accefstble. 
 
 F Irft holding one fide of your fquare parallel to the Horizon , with 
 the centre next to your eye , move the index upward , till through 
 the fights thereof you perceive the top of theTowrc or Caftle, 
 then lookc what parts is cut by the index,and what proportion that hath 
 t© the Horizontal! fide , fuch proportion is there betwccncthc bafe and 
 altitude required. 
 
 E%mfle. 
 
<L // ' Treatije of ( feometry . 
 
 Example; 
 
 Let there bea tower, whofe height is required, wh ch (hall bee A B, 
 and the diftanccfrom the bate to my ftation, B C, being 100 yards : to 
 workc this, I place my inftrument, with the fide whereon the index iy- 
 eth, parallel to the horizon, moving the index upward, till it eating 
 parts of verted ftiadow, that being done, I fay as 60 the whole fide is un- 
 to 40. the parts cut,fo is iooyards,thediftance B C, to 66 \. which is 
 the height required, namely A B, but if it fall in 40 parts of right (ha~ 
 dow, then I fay as 40 the fide cut is unto 60 the whole fide, fo is the di- 
 ftanec D B, 44. to the height AB, 66) the thing required. 
 
 By the Geometrical! Jquare to finde the height of any Tourer 
 
 beinginaccefible, ' 
 
 IF you would take the altitude of any Tower, Wall, or other edifice 
 "which is unapproachable, either in regafrdof the enemy lying bc- 
 tweene, or by the hindcrancc of fomc River or Ditch, you (hall proceed 
 asfollowcth. Fim, approach to rhcncareft and moil convenient place 
 for your purpofe, where placing your inftrument, and obterviog the 
 parts cut in your fquare, you muft then goe back ward in a ftrait line, ac- 
 cording to the commodioufncfte of the place, and make a fccond obfer- 
 vation, noting likewife the parts cut in your fquare, which will be either 
 on the right or verted ftiadow: if they fall both on the verted fliadow, 
 ( which mod often doth happen, in regard of many impeachmcnts)ycu 
 (hall divide the fide of the fquare fevcrally by departs cur, and fubftrad 
 the leffer quotient from the greater, and by the remainder, divide the 
 tcrrcftriall difference bctweenc the two Rations, to that adde the height 
 ofyour eye from the horizon, you have your defire. 
 
 Example. 
 
 Let the height be A B, which cannot be approached in regard of fomc 
 river, firft I make choice of a place tofetmy inftrument, which is H, 
 then railing the index untill I fee the top of the tower thorow my fights, 
 I note the parts cut, which is 45 of verted flbadow, then falling backein 
 
50 
 
 <iA Treatife of Cjeometry « 
 
 aftraight line, I make choice of 
 another ftation which is ten yards , 
 diftant from the firft, and obfer- 3 * 
 ving there I finde my index to cut 
 in 30. which being done, I divide 
 the whole fide of the fquare, 
 which is 60 . by thefe two fums E 
 fevcrally, and I finde the one to be 
 1 j . and the other 3. fo that taking 
 the lefle from the greater, the re- A 
 mainder is ^by which number I divide the tcrreftiall difference of my 
 ftations, which is to. and the quotient is z 5 . to which adding the height 
 of my eye from the ground, being fiue foot, the whole will bccfixrcene 
 yards and two foot for the height of the tower, A B. 
 
 Othervtifi. 
 
 Take the leffer number of parts from the greater, and by the remain, 
 der, multiply the fide of the fquare, and that product pit in the firft 
 place in the rule of three, the product of the parts multiplied together 
 in the fecond place, and the difiance of the two ftations in the third. 
 
 > Ex aw fie. 
 
 Take 30 from 45. the remainder!*! 5; which multiplied by the fide 
 of the fquare, which is 6o* fa. 900. which produft put in the firft place, 
 then multiply the parts together, which is 44 and 30. fa* 1350* for the 
 fecond, and the difiance of the two ftations, which is tenne yards for the 
 third, fo the rule ftandeth thus : 
 
 As poo is to 1350.(0 is xo to 15. 
 
 10 
 
 4 1 35(09 
 
 09 
 
 So that the quotient being 1 5. anfwereth the demand, and is the height 
 of the tower A B, which was required. 
 
 How to performs the fame, when tbeparts cut fall on the 
 right tbadow. 
 
 IF the parts cut in each ftation bee of right tbadow, which is very fcl- 
 *dome,(ubftra& the lefier number of thofe from tbegreater, and put that 
 in the firft place in the rule of three, that fide of the fquare in the fecond, 
 and the ftationarie diftancc in the third Example. 
 
 Exam- 
 
<iA Treatife of Cjeometry. 
 
 Example. 
 
 Let A B,be the height re- 
 quired, and let the parts cut 
 be 30 and 55. of right (ha- 
 dow, fubftraft the lefler 
 from the greater, the re- 
 mainder is 25. which (hall 
 be put in the firft place in 
 the rule of three, 'the fide of 
 the fquare being do. in the 
 fecond,and the diftancc bc- 
 t wcene the two ftations which is 10. (ball bee the third, fo the rule ftan^ 
 deth thus; as the difference of parts cut is to the whole fide, fo is the dif- 
 ference of ftations to the height required, or thus, 
 
 As 2 5 to do. fo 10 to 2 4, 
 
 V IO 
 
 - ■ 
 
 (3 - 600 I 
 
 600 (24 \ 
 
 er 
 
 How to take an altitude by the fquare, yben the parts cut are 
 of different fbad'oyoes* 
 
 IF the parts cut in the neareft ftation.be of right ftiadow, and the fartheft 
 * ~e of contrary ftiadow, they fliall be both reduced to one (hadow, after 
 this manner fquare the whole fide, which is do. and deuide that produft 
 by the parts, cut off the verfed ftiadow, and the quotient (hall give the 
 tight ftiadow, that being done, lubftraft theleffcr (hadow from the grea- 
 ter, and the remainder (hall be the firft place in the rule of three, the di- 
 nance bctweenc the two ftations (hall be the fecond, and the fide of the 
 fquare the third. 
 
 Example - 
 
 Let the parts of right and verfed ftiadow be both 30. and I defire to 
 bring them to be both rights firft I fquare the whole fide, which here is 
 60. fa. 3 600. that produft I devidc by the parts cut of verfed (hadow, 
 which is 30. the quotient is 1 20. from which fubftrading 30. the lefler 
 right ftiadow, the remainder is 90. for my firft termc, the diftancc be- 
 t wcene my two ftations being 2 1. is the fecond termc, and the fide of the 
 fquare the third, for the ruleftandeth thus. 
 
 As 90 is to a i, fo is 60 to Id; 
 
 60 
 
 E% 
 
 * 
 
 ( 1 4 
 99 . 
 
 1260 
 
 Otberwife 
 
5* 
 
 aJ Treatife of geometry. 
 
 Otherwifc ■without reducing one [badote to another. 
 
 \ A Vltiply the parts cut in each other, and fubftra& the prodoft from 
 iV^thc number gathered by multiplication of the fide in it fclfc, putting 
 the remainder for the firft terme in the rule of three, the produtt ot the 
 multiplication of the parts 
 touched in the verfedfha. 
 dovr, by the fide of the 
 fquarc for the fecond li- 
 terate , and the difiance be- 
 tweene the two ftations for 
 the third. Example of the B 
 former, where the parts cut 
 of right (hadow,are 30. and the farthefi difiant as much of verfed £ba- 
 dow; the difference betweene the two ftations being xt. multiply the 
 parts cut in tbcmfelveSjfa.joo. fubftra&that product from the fquarc 
 of the whole fide, which is ^oo the remainder will be 1700. which thal 
 be put in the firft place in the rule of thrcc s the produft of the multipli- 
 cation of the parts, cut of the verfed fhadow by the fide of the fquarc 
 which is 1800 (hall be put in the fecond place, and thediftance between 
 the two ftations being 2 1. (hall be the third place, the rule ftandeth thus, 
 As*70oisto 1800 fo is ai to 14. 
 
 21 ¥ 
 
 ■ — 0 
 
 1800 Z ?%00 ( 14 
 
 3 6 00 Z 77 O 0 
 
 ■ — 1 z 
 
 3 7800) 
 
 To take the height of a Tower or Caftleflandwg on a bill. 
 
 T O per/orme this, you muft firft take the height of the hill, at two fta- 
 tions, as a thinginacceffible, & after the fame manner cake the height 
 ofthe tower and the hill together, which being done, fubftra&chc 
 height of the hill from the whole, the remainder will bee the height of 
 she tower. 
 
 Example , 
 
 Let there be the hill E. F,on the top of which is erc&ed the Tower 
 F G, firft placing your inftrument atH, obfervethe altitude of the hill 
 F, and note the parts cut in the fq rare, which are 60. that done, goe 
 backe to the point K> and there make another obfervation, which is found 
 to be 40. that being done, divide the fide ofthe fquareby the parts cur 
 fcvcrally, and fubftraft the lefler quotient from the greater, and by that 
 which refts which is |,devide the ftationary diftance, whichis, 20 yards, 
 the quotient will be 40 yards, for the height of the hill E F. Now feeing 
 K H,to F : E, is in proportion as i to 1. in doubling the one and the other, 
 the proportion (ball beasi to 2. by the fifteenth proportion ofthe 
 fifth of Eucltde } fo that K H, being 20 F E, (hall be 40. 
 
 And 
 
Treatife of (yeorrtetry. 
 
 I N measuring ali forts of profundi- 
 ticsjthe fquare muft be placed contra- 
 ry to the aforefaid order ufed in taking 
 ofaltitudes.tbatis the fide devidedin 
 the fquaic,muft be turned downwards, 
 whereas before it was upermoft,to take 
 the profundity or depth of a Well, 
 place your fquare on the top, fo that it 
 may ftand horizontal!, and Jikcwife 
 that fide next your eye may bee cquall 
 with the fide of the Orifice of the 
 Well, then move the index, till through 
 the fights you fee the bottome of the 
 Well on the oppofite fide to your 
 fquare, that done, obferve the parts 
 cut in the fquare, which will be of 
 fliadow, and the rule will 
 as the parts cut are to the wnoic tide, to 
 is the diameter of the Orifice to the 
 depth of the Well. 
 
 And confequently 
 to have the height 
 E G,youmuftfollow 
 the precedent rules’ 
 by taking two obfer- 
 vations, the firft be- 
 ing at the point M, 
 the fecond at O, 
 which parts cut, are 
 36 and 30. devide 
 them feveraily as before, the fide of the fquare, by the faid parts and 
 fubfirad the lefler quotient from the greater, and by that which re- 
 maines, which rs ; devide the ftationarie diftance O M, which iscigh- 
 tecne yards, and you fhall have for the quotient, fifty foure yards the 
 height E G, from which fubftrafting the height of the hill E F, which is 
 fotty, the remainder will be fourtccne yards, the height of the tower 
 F G, which was required. 
 
 to meajure all forts of profundities Ij the faid fquare. 
 
 H&Am* 
 
o/ Treatife of (jeometry. 
 
 Example. 
 
 Let the diameter of the Well be two yards, and the parts cut being 
 
 found 24. 1 fay, 
 
 As24is to 6o(o is 2 to 5. 
 
 2 
 
 120 
 
 & 
 
 ZZ0 (s 
 
 Z# 
 
 So the depth found, will be five yards which was required. 
 
 How to take a diflance by tbefaidjquare ; 
 
 | N this cafe the fquaremuft beheld as in the foregoing chapter of ta- 
 lking a profunditudcj but note, that this ferues but for a fhort diflance, 
 wherefore place your inflrumcnt as high as you can from the horizontal! 
 line of your bafe to be meafuredj that being done, move your index till 
 youfccthecxtreamepartof the horizontall diflance at the bafe, and 
 note the parts cat in the fqaare, which will be in the verfed (badow,thcn 
 the proportion will bee thus, as the parts cut is to the perpendicular 
 height of the eye from the bafe, fo is the whole fide of the fquare to the 
 diflance 
 
 Let there be a River, whofe bredth I defire to know, I make choice of 
 a place for my Ration, where (landing on a banke, I obferve the fuperfi- 
 cies of the water on the oppofite fide of the River, and note what parts is 
 cut, which I finde to be 40.then I meafurc the perpendicular height from 
 my eye to the fuperficies of the water, and I finde it to be eight foot, fo I 
 fay as 40 is to 60. fo is 8 to i2.which is the bredth of the River required. 
 
 How 
 
A Treatife of (jeometry* 
 
 How to performs the fame by the Quadrant, -which is wrought 
 by thefquare , and firfifor taking the altitude of a 
 Towre hawing the diftance given. 
 
 T N meafuring by the Quadrant placed on your fquare, you arc to hold it 
 *in all refpc&s,asyou held icraeafuring with the fquare, fo that having 
 made choice of a ftation, placeyour inftrument, as I have (hewed you 
 for taking an altitude 5 moving the index till you fee the top of that you 
 defire to mcafure • then obfervethe degrees cut in the Quadrant, which 
 being found, the Rule ftands thus. As fine complement of the altitude is 
 to the diftance, fo is the right fine to the altitude required. 
 
 Example, 
 
 Let there be a Towre whofe height is required, namely A B, and the 
 diftance given B G being a ioo yards, I make my ftation at Q obferving 
 with my Quadrant the degrees of altitude, which I finde to be thirty de- 
 grees, whofe complement to ninety , or Radius is fixey degrees, then I 
 fay thus : 
 
 As Sine complement the altitude which isjtfo deg.Co. Ar ., 0614691 
 
 is to the fide given, which is zoo **,0000000 
 
 So is the right Sine 30 degrees, 9, 69 89700 
 
 to 57 li- 
 the height required namely A B. 
 
 ,1 > *9 7614194 
 
 To find the Altitude of a Towre orCaftle being inaccefsible, 
 by the Quadrant. 
 
 H Aving made choice of a place for your Reft ftation, obferve the 
 degrees of altitude cut in the Quadrant, then going backe ten 
 paces or yards make another obfcrvation , and note the degrees 
 cut, that being done you have a Triangle, in which is given the 
 
 angles 
 
<±A 7 reatije of (geometry* 
 
 angles wichonc fide which isthc ftationarie diftancc,then the Rule hands 
 thus : 
 
 As the Sine of the angle ©ppofite to the ftationary diftance is to the 
 faid diftance, fo is the angle laft obferved to the Hepothcnufall in the firft 
 Triangle, which being found, the fecond workc will be thus. 
 
 As Radius or the whole Sine being 90 degrees , is to the Hepothcnu- 
 fall.fo isthc Sine of the firft obfervation to the altitude required. 
 
 ~ j 
 
 Eximple, 
 
 Let the Towre whofc height is required, be A B , I make choice of a 
 place for my firft ftation at C where I obferve by my Quadrant, and find 
 the altitude to be 45 degrees, then falling back ward to D, I make another 
 oblervation which I find to be 27 degrees, fo have I in theTriaoglc A D 
 C the three angles, the obtufe angle C being the complement of 45 to 180 
 which is 1 3 5 degrees, which added to 27 degrees fa.i 61 that fubftrafted 
 from 1 80 gives 1 8 for the angle DA C, which being done, 
 
 I fay as Si 18 degrees, ocom.ar. 0,5*00 175 
 
 to io pa*— — — - 1,0000000 
 
 fo is Si. 27 degrees o * 9t 65 70468 
 
 to 14 -i* — —The Hipothenufall A G* t-i 670644 
 
 The fccond operation. 
 
 As Radius Si. 90 , * 
 
 To A C 14 -~i — 1, 1 670644 
 
 So is Si ^degrees, — 9,8494850 
 
 T 6 to fere — —1,0 1 65494 
 
 which is the height of the Tower A B. 
 
 lo find the Longitude or diftance of any place inaccefuble , . 
 
 by the Quadrant. § 
 
 r/rJL .J6- 
 
 Q Vppofea Gaftle placed at A, whofc diftance I defire to know in re- 
 Ogard of placing my Ordnance, to makea battcrie again ft the fame, Firft 
 T make choice of a convenient place for my ftation , which is B , where 
 
 . placing 
 
<tA Treat ife of Geometry. 
 
 placing my inftrument I bring the index to the edge or no degree in the 
 Quadrant, and fetting it to fome noted place which is the point A then I 
 move about the index my inftrument handing quiet till I brinp it to the 
 extreame part of the Quadrant.that done,! obfcrvc thelinc B C in which 
 Imeafureoutahundred yards or atpleafure, then bringing my inftru- 
 ment to the point C , f make that my iecond ftation , where I place rov 
 inftrument, in filch manner that the edge (where the divifion beginnes to 
 be numbred, may be parallel to the line B C, turning about the index un- 
 trll I lee the point A thorow the fight , that done , I obferve the degrees 
 cut, n. he Quadrant, and findcthemtobclevcnty degrees, no minute, 
 which I note, and lay thus: 
 
 As fine complement B C A feventy degrees no minute , is to B Ca 
 hundredyards, fo is Si.feventy degrees to B A, the difiance required 
 
 AsSi 20 degrees o.Co.A r .- 0,4659480 
 
 is to 100 yards ~ 2,0000000 
 
 ioisSi. 70 degrees *o —51,9729858 
 
 to A B *744 : — *2,43889338 
 
 To meajure a diflance at one flatten in a Hori^tntaU 
 plane , by the Quadrant. 
 
 0 Vppofe a Ca- 
 ^ftlcftandingat 
 F whofcdiftance 
 
 1 defire to know, 
 Firft, I make 
 choice of a place 
 for my fiation at 
 E, where placing 
 my inftrument 
 as high as I can, 
 I make obferva- 
 tion to that part 
 of the Caftle 
 which is equal! 
 
 to 
 
58 
 
 (fj T mtijeof (geometry. 
 
 rn the bafe ot my fiatfe^hicb 1 findctobctcndcgtces.nominutc, vn- 
 dcr the Horizontal! line , and .he heigh, of m, eye from .he ground 
 
 ,0 Asfine'complOTenttheanglewken is to .he perpendicular heigh. of 
 my eye from the bafe, fo is fine 80 degrees © to the diftancc which is 
 
 45 00,, As Si. 6 AB io Co. Ar. >7 6 °3 2 
 
 Is to 8 ,903°9 
 
 So is Si.8o degreeso 9.99335 
 
 So that^hc^ftance oTihcThwre'?Bls4 7 rlsfeet which wasiequi. 
 red. 
 
 To find the Prof undine of any Well or Ditch by the 
 Quadrant. < 
 
 T Hi< i«; wrought after the fame manner as the aforegoing propofmon, 
 
 °n.heto P 0f,h '^t' O nltS 
 
 .heanglccut, from.hefuperficies.othebottome, 
 the Well or Ditch, and meanmng the hread.h.heRulc ft^nde.h.has 
 as the fine of .he angle cut ia to .he diameter of the Well, fois theline 
 complement to the depth required. 
 
 £x Ample. 
 
 Let the Well whofe depth I defire 
 to know, be E B GF , whole diameter 
 EB is two yards or fix foot, and obfer- 
 ving by my Quadrant, I find the angle 
 cut to be twcntic two degrees, I defire 
 to know the depth namely, E F, I fay. 
 
 As Si. 2 a degreeso co.ar.-o,^^* 4 
 Is to 6 foot 9> 77$i$ 
 
 SoisSi. 78* 
 
 -9,96711 
 
 T014H5 
 
 1— 17*73 
 
 fo that the depth of the Well namely 
 E F will be 1 4 & foot , which is five 
 yards fere » 
 
Treatife of (geometry. 
 
 Haying the heighth and difiance giyen to find the Diagonal Of 
 length of a fcaling Ladder. 1 
 
 ^ Und fi L C r by thc P rccecJcnt Rules, fquarc each fide ftve- 
 
 ihe fnuire R™? -uf k^V? 0, L rodu . a# ’ and from lh « fumrae extra# 
 ihc iquarc Rooty which (hall be the Diagonal! required. 
 
 Example* 
 
 Let the height of 
 the Towrc A B bee 
 thirtiefootj and the 
 difiance from the bale 
 of the Tower to my 
 Ration B C (hall bee 
 fortic, thefe two (urns 
 fevcrally fquared pro- 
 duce poo and Itfoo, 
 which being added, 
 fa,2yoowho(cfquare 
 Root being extracted 
 
 Which i, 'the fidc e AC f ' he Diae ° na,lor rcaling L,dderfor ** place 
 
 I I '* 
 
 Divers vayesfir taking Altitudes and diflancesy performed h 
 theplaine table, and firfl to find the Altitude by the %u- 
 ler on the plaine table. 
 
 X™ ? U,<:rs , wllCfc ^ *11 conclufionson thiiinflrumeot are petfotmed 
 
 ctluimcl h ,hcn ?, Wi ' h fiand ! n 8 fi 8 h ". others wkh a kj. 
 circle, and (omc with a channell or cover clofe to the edge, covered with 
 
 7 h tC ° F b f 2rd ’ thc laft ra ° a comm °nly received is that which 
 thTSfJi? 6 t0 /P eakc ° f * F,rft having got thc Horizontall diftance to 
 ^ e ^ arc - Thcnlheonc fi de of thc Ruler fianding upon the beginning of 
 the divifions , place the other fight on fo many divifionsasfieK- 
 Ranee to the bafe,that done, place thc table parallel to the Horizon which 
 is done by a plummet placed on thc fide of thc Ruler , and having fee thc 
 
 mcafurett ? * 8nd thc Vanc 00 tbc fu,,thcf % ht at (brae even 
 Jh n k Clh !? 8 nCCf l thc Vppcr cnd> notc lhc Parts whereon it Ran” 
 do ^T^c the ncerer fight to you, till through the hole 
 thereof, and the pins head of the farther vanc , you fee the top of the al 
 titude, and there Bote the parts cut by thc edge of that vanc whichmrre 
 
 which fc'!ll h° rC wl ?' K0 " th c fa [ lhcr vane ftandeth , leave’th a number 
 Ihen r,m fa '. CqU:l t0 ,he height required above the level! ofyooreyc, 
 hl n nX?^' T «“ T' u P*g* !ne - till thorow thc hole thereof and 
 
 hefrnarslTnf^"^' va " e >y°“ f “ ' he *>*& of the altitude, and note 
 thele parts cut for theparts whereon the farther vane ftandeth taken out 
 
<Jo 
 
 dA Treatife of (geometry < 
 
 of ihc pacts cut, (bail be cquall to that part of the altitude belo w the le. 
 veil of your eye, which added to the former (hall make the whole altitude 
 required. 
 
 Ex Ample* 
 
 
 
 A 
 
 
 
 / 
 
 ^ ] 
 
 2 
 
 / 
 
 oo yards 
 
 / 
 
 * 
 
 ✓ 
 
 ♦* 
 
 a AyurJis 
 
 S ..5s 
 
 / 
 
 ♦ 
 
 
 
 D 
 
 -- 
 
 <S-£yArds 
 
 — 
 
 Let A B be an altitude whole height is required , let C be the place of 
 nation, whole Horizontal! diftance being found twenty one yards- Sup- 
 pofcF H to be the Ruler placed on the plane Table , whole ncercr fight 
 placed oh the beginning of thedivifios isF G,thcn the farther fight being 
 D E, which is placed atfo many divifions, as is the Horizontal! difiancc 
 which is hccre twenty one yards, then let the farther vane be fet on fixty 
 cquall parts of the fight, fo doth K L I reprefent the line of levell 5 then 
 let theneerer vane bee brought downe till through the fight thereof 
 and the point L , you fee the top of the altitude A , then fuppofc the 
 parts cut to bee forty , which taken out of fixty lea veth twenty, for 
 that part of the altitude from I to A, ithen bring up the nccrer vane, 
 till through the fight thereof , and the point L you fee the bale of the 
 altitude B fuppofing thofe parts cut to bee 6 5 r » from whence ta- 
 king; fixty leavcth 5 *for the number of yards from I toB, which 5* 
 added to the height of I A being t wenty f 3. 2 5 r for the whole altitude re- 
 quired , the which is thus demon ftrately proved. Fir ft, the angle LFK 
 is equall to the angle L A I by the fifteenth Propofition of the firft of 
 Eucltde. All perpendiculars Handing or falling upon.or from one line are 
 parallel , therefore the line K F is parallel to the line I A , and therefore 
 proportionall thereunto , by the fecond demonftration of the eleventh 
 propofition of the fixth of Eucltdejn Hke manner might the fccond part 
 of the Work be dcmonftratcd,but that to the ingenious a word doth fuf- 
 ficc, and in this manner you may take any altitude or part thereof, or a- 
 ny depth, whereof might be fet downe divers Propofitions , though all 
 arc to be performed , as is before taught by this Propofition , wherefore 
 I will not trouble you with prolixitic , only I will fhew you in the next 
 the ufc of the degree fet on the Ruler. 
 
(tA Treatifeof (geometry 
 
 To take an angle of altitude by the degrees fit on the Ruhr. 
 
 having placed the table parallel to the horizon, by the former 
 -*• propoficion, then fee the fight next your eye on 90 degrees, and the 
 other from your eye on 45 degrees, and fee the farther vane on the he- 
 ginning of degrees: then is there double regard to bee had, viz whether 
 the quantity of the angle be IcfTc or more then 4 5 degrees, iflcflc, bring 
 downetheVane on the necrcr fight, till through the hole thereof, and 
 the pinnes head of the farther Vane, you fee the thing defired, then the 
 degrees cut by that Vane, ftieweth the quantiry of the angle.- 
 
 But if the quantity of the angle be greater then 45 degtce$,then let the 
 Vane on the fight next your eye, be placed at 45 degrees, the fight ftili 
 {landing on 90 degrees, and lctjchc Vane of the farther fight Band on 
 the beginning of degrees as before, then move forward the farther fight, 
 till through the fight of the nearer, and pinnes head of the farther, you fee 
 the thing defired, and then the parrs cut by the fight on the fide of the 
 ruler, fhc weth the degrees anfwering to the quantity of the angle. 
 
 Example. 
 
 Let there bee theTowre AB, whole height I defire to know, and 
 wouldfindcitby the angle of altitude: firft having placed my inftru- 
 mentand fomc knowne difiance, which I imagine too yards, I fet my 
 ruler which I direct to the place afligned, where obferving bv my eye, 
 I finde it to be an angle under 45 degrees, fo placing my fights at 90 and 
 4y degrees, I fet the farther Vancon the beginning of degrees, and move 
 down the nearer Vane,till through the hole thereof, and the pins head of 
 the other, I fee the point A, which donc,I obferve the degrees cut by the 
 necrcr Vane, and I finde them to be 30 degrees, which' is the angle requi- 
 red. the rule then (lands thus : 
 
 As fine complement the angle found is to the difiance given, which is 
 100. fo is the right fine to the altitude required. 
 
 As fine F A B, do deg. co. ar 06246 
 Is to IK too yards, 2,00000 
 
 So is fine F 30 deg. __ 9,69897 
 
 to 57 ?;»• which is the height required, namely AB. 
 
 
 
 K 
 
 
 / r 
 
 / aojanis 
 
 32V* l 
 
 ogyarfis 
 
 
 
 D 
 
 -H 
 
 
 
 B 
 
 f 
 
<±A c Treatifeof ( geometry . 
 
 To take the horizontal! difiance from any place afiigned to ano- 
 ther place within a view, at two ftations . 
 
 AT the place from whence the diftance is required to any affigned 
 **markc, there place your inftrument for your tirfl obfervation, there 
 appoint out fome place for your fecond ftation, being a convenient di- 
 ftance from the firft, which ought to bee at lcaft of the required di- 
 ftance, other wife it will makefuch acute angles in the points of interfe- 
 &ion, as will caufe great errour.Thcfc things being confidercd,ahd your 
 inftrument orderly placed, at your place of (landing, marke what degree 
 the fouth end of your needle doth cut upon the card in the bortomc of 
 the box, bccaufe refpeft is to be had there unto all your fecond ftation, 
 for the true crcfting and placing your inftrument; in that place make a 
 point upon your paper, which call the center ofyour firft ftation, from 
 which point firft draw a line to the marke, whofe diftance is required, 
 then draw another line to the fecond ftation, which line you fhall call 
 your ftationary diftance, and in that line from the point of your firft fta- 
 tion, fet offby fome (calc, the meafured diftance betweene the two ftati- 
 ons, and make there a point for your fecond ftation. Then take u p the 
 table, leaving a marke at your firft ftation, and carry it to the fecond fta- 
 tion, where having placed the fame in fuch fort, that the pricke of your 
 fecond ftatidn ftand dirc&ly over the marke whereuntoyou looked. 
 Lay the edge ofyour ruler by the ftationary line, turning about the ta- 
 ble till through the fights thereof you fee the marke fet up at your firft 
 ftation; that done, (crew faft your table, and if you have performed this 
 rightly, you (ball finde the needle in the boxe cutting on the fame degree 
 it did at firft , if not, you have wrought falfc 5 then from the point of your 
 fecond ftation, draw a line to the marke required, and note the place 
 where it intcrfe&eth the firft line drawne, meafuring that line on the 
 fame fcalc you meafured the other, and you (ball finde the right diftance 
 required, and in this manner may you take any horizontal! diftance 
 whatfbever. 
 
 Ex Ample. 
 
 Let A B be a diftance required, and letC be the place appointed for 
 the fecond ftation, which being meafured forty yards, I fet it off from D 
 to C,and make that my ftationary diftance, that done, I draw the line 
 DFjtcprefentingthe line A B, and removing my inftrument to G, I 
 make a fecond obferdation towards B, drawing the line C B, from the 
 point of my fecond ftation, to the point 
 interfering the line DF; that done, 
 
 I meafure the (aid line by the former 
 
 fcalc, and I finde it to be 93 f for the '***•••••.... 3 * 
 line DF, being c^uall to the line A B, j 
 
 the diftance required, and the line C E, • 
 
 is equal! to the line Q, B, which being 
 likewife meafured in the fame fcale,will 
 
 be found 90. the ground of this arifeth from the fourth propoficion of 
 
 the fixth of Euclid. „ 
 
(tA T rcatife of ( geometry . 6 $ 
 
 At oneflation or at one placing the inflrument > to give the 
 diflance betweene two defired market. 
 
 H Aving placed your tableat any didance, firft make a point reprefen- 
 ingyour ftation, from which point draw aline to each feuerall 
 marke, then meafurc the diflance to each marke feverally, and fet thofc 
 diftancesby the fcale upon thofc two lines, fetting each diftance on his 
 owne line, and from the extreame part of one, to the extreame of the o- 
 ther, draw a line, which being meafured on the fame fcale, will bee the 
 right diftance required. 
 
 Example. 
 
 Let A B, bee twomarkes, whofe di- 
 ftance one from the other is required, the 
 point C being theplacc of ftandmg, where 
 I placing my inftrument, I draw the lines 
 C G,and C F, that done, I meafurc the 
 diftances from my ftation to each marke, 
 and findetheone which is C A, 30. and 
 the other C B, 44 which I fet off by 
 fome fcale in the lines G G, and C F, 
 which I finde to bee in G and H, that 
 donc 3 1 draw the line G Hf, which meafured in the fame fcale, is found toi 
 be 2 6 ’ the thing required. 
 
 Divers mechamcall waies for finding the altitude 
 or diftance of any place defired, and firft for fin> 
 ding the diftance by the diagonall from the eye 
 to the bafe. 
 
 How to take a diflance without any inflrument » onely by the 
 brimmeqfthehat . 
 
 H Aving made choife of a place for your ftation, erc& your body 
 as (freight as you can, that done, pull downc the brimme of 
 your hat untill you fee the bafe from the borizontall line of your 
 ftation, that done, turneyour body about without ftirring your hat, and 
 note where it cutteth in the fame horizon, which being meafured, wilt 
 be found equall to the diftance required, for the body being the center, 
 and the brimme of the hat the circumference; and feeing all the lines 
 dra wnc from the center to the circumference, arc eq.uall;it folio w«th then 
 that thefe muft like wife be equall. 
 
 Fa 
 
 Example 
 
* 4 ■ 
 
 <t A Treatife of ( geometry \ 
 
 Example* 
 
 Let there be a Towre placed at A, whofe diftance is required^fuft I ob- 
 ferve the horizontall line from my foot 5 to fome port of the Caftlc, which 
 is theiine A B, that being done, I make B, the center whereon I Hand, 
 where ere&ing my body, I pull downe the brimme of my Hat, untill it 
 interfe&eth in A, that done, I move my (elfc about untill I perceive fome 
 part of the horizontall plane interfering the brimme of my Hat, which 
 is at C, then meafuring the diftance from BtoC, Ifindc it 100 yards, 
 which is cquall to the diftance A B, the thing required. 
 
 How to take a diftance "With a ioynt Ruler . 
 
 T His differs not much from the other, for in ftcad ofyour body per- 
 pendicularly ere&ed,you (hall make ufe of one of the limmes of your 
 ruler, which muft hang perpendicular to the horizon, the other being 
 opened to that angle which the diagonall maketh with the perpendicu- 
 lar*, that done, move about as you did in the former, and obferveagaine 
 what place of the horizontall plainc it cutteth,and to that meafure, which 
 is equall to the diftance required; 
 
 Example. 
 
 Let the diftance required be A b, and the pi ace of my ftation being B, 
 1 obferve the angle from my eye, which is at D to the horizontall bale at 
 B,and moving my inftrument about, I obferve againe where it cutteth in 
 die horizontall bafe, and I findc it to be at C, to which I meafure, and 
 findeit eo yards, which is equall to the diftance required, they being 
 both femidiameters to a circle. 
 
 Having 
 
<zA Treatifeof (jeometry. 
 
 Haying the diflance betweene two places , to finde the diflance of 
 each from any flation, performed by fcale and CompaJJe . 
 
 T Et there be two trees which are diftant from each other * o foot, and I 
 ’“-‘defire the ftationary diftanee to each. Having made choice of a place 
 for my ftation, with my Compaffcs in my hand, I ere& my body, exten- 
 ding my armc outright, and open the Compaffts till fuch time as I fee 
 the center of the two places intctfe&ed by the points of the Compafle, 
 that done, I mcafure the diftanee fro my eye to the points of the Coropas, 
 which I finde to be t wo foot, and the rule ftandeth thus* As the diftanee 
 of the two points are unto two foot, fo is the diftanee of the two places, 
 from the ftationary diftanee, alwaics provided that you place your ftati- 
 on proportionall tocach, that the center of the eyt may pafle betweene 
 them both in an cquall proportion, fo that the Coropalles being opened, 
 and found to be two inches, the diftanee will bee found 240 foot, the 
 thing required. The rcadieft way for performing this, is by a fcale which 
 may be calculated for that purpofe, which to fatisfic the curious Readers, 
 I have performed, being calculated according to finches diftant from 
 the eye. Theufc hereafter followeth. 
 
 The forme of the fcale with the ufe of the fame* 
 
 THis fcale confifteth offixe inches long, each inch being devided into 
 * fixtccac cquall parts, the ufe whereof is thus* having opened my 
 Compaffes, and placed them at a proportionall diftanee, I apply them to 
 the fcale, obferving what parts in the fcale it fals in, for fo many times is 
 the bredth given, contained in the diftanee required. 
 
 
 Example 
 
h°8* 
 
 66 dA Treatife of (geometry. 
 
 Example. 
 
 Let the diftance betwcenc the two trees in the former diagram bee 
 twenty foot, having placed my Compaffcs at thirty inches difbnt from 
 my eye, I open them till the points areequall with each tree, that done, 
 I apply the points of the Compaffc to the fcalc, fetting one foot in the 
 end where the greateft number of parts are, and obferve where the other 
 foot touchcth, which I findc to be in twelve, wherefore I conclude that 
 the diftance is twelve times more than the bredth bctweenc the trees, 
 which was twenty foot, fo that io multiplied by 12. fa. 240. the true di. 
 ftancc required. 
 
 Haying the diflancegiyen to finde the altitude of a Towre or 
 Caftle by the aforegoing rule, 
 
 T Et the diftance given be A B, 240. and the height of the Caftle A C, 
 •■‘•'required, firft having placed my fclfcatB 3 with my Gompaffes in 
 my band, I open them, extending my armc out right, till I fee the points 
 ofthe compaffc cquall with the bale and top of the Caftle which is 
 A G,that done, I obferve by my fcalc, the parts that the Compaffcs ftand 
 at, and I findc it as before to be two inches; that done, the rule ftandeth 
 thus. • 
 
 As the diftance from my eye, to the point of my Compaffc, which 
 is two foot, is to the ftationary diftance, which is 240. fo is two inches, 
 the diftance ofthe points of the Compaffc from eich other, to twenty, 
 the height required. 
 
 Ex<tn. 
 
it// 7 reatije of Geometry, 
 
 * 7 
 
 Example, 
 
 As BE, or BD, 24 inches 
 Is to DE, 2 inches. 
 
 So is B A, 240 foot, which reduced 
 
 to inches, is 2 8 So inches, 
 
 to A G, 140 inches, which is 20 foot. 
 
 Many more waics I might lay downe, which are mcchanicall , as the 
 ufeof the cinicall quadrant, with divers others, but I thinkc thefe fuffici- 
 ent in regard they cannot be wrought without errors, wherefore I doe 
 not approve ofany of thefe oncly for delight or curioficy, and partly to 
 fatisfie fome of my friends, I have the rather put them to publike view. 
 
 i x 
 
 THE 
 
aj Treatijeof Qeometrj. 
 
 ' 1 * I 
 
 THE VSE OF THE ENSV- 
 
 ING TABLES. 
 
 Forafmuchasfhave fometimes before made mention 
 of the Square and fquare %oot , f have thought it 
 not impertinent here to adioyn a table of the fquaret 
 of every number , from i to ijooo ,and of the fubes 
 of every number from ito \ooco.f cannot at pre~ 
 fent /hew the ample ufeofthofe Tables in fundrie 
 <tA Igebraicall , (geometrically and other o5\i at he - 
 maticall Troblemes : onely as an introduction to the 
 ufe of them, f have thought good. to annex thefe 
 Troblemes following. 
 
 ITob. I. 
 
 To find the jquare of any number, not exceeding 
 25000 , by thefe tables. 
 
 L Ooks vour number in the fir# colume beiag the colume of Roots, 
 and right again# il inltbe fecond colume being the colume of 
 fquares. you have the fquare of that number; 
 
 Thus I find the fquare of this number 65 7* K> be 43 1 S> 1 1 8 4. 
 
 Prob. a. 
 
 To find the Qube of any number by thefe tables > not 
 exceeding 10000 . 
 
 T Ooke yout number in the firft colume of Roots, and agffnfl it in the 
 L third colume, being the colume of cubes, you (ball find the cube of 
 
 that number. 
 Thus you may 
 
 283852461*48* 
 
 finde the cube of the forefaid nufnbcr, 6572 to bee 
 
 Prob, 
 
<$A Treatife of (geometry. 
 
 Prob. 3. 
 
 To find the fquare %oot of a fquare number not 
 exceeding 6 2500000000 , 
 
 L Ookc in the columc of Squares for the number given } and rightagainft 
 it in the firft colume being the colume of Roots , you have the root 
 of that number . 
 
 Thus I find the fquare Root of this number 43 1 9 1 1 84 to be 6572- 
 
 Prob. 4. 
 
 To find the Cubicke root of a Cubick number not exceeding 
 1000300000000 by thefe tables, \ 
 
 L Ooke in the coluracof cubes for the number propofed , and right 
 againftitintbecoiumc of Roots, you (half finde the cubit Root 
 thereof. . . 
 
 Thus you may find the cubick Root of theforefaid number 2 8385 24 
 <$1248 to be 6s 72. 
 
 CEeke in the Table for the fquare of the Numerator of your fra&ion, 
 ^and fetthat for Numerator , alfo the fquare of the Denominator for 
 Denominator. So is this new fra&ion the fquare of the former. 
 
 But if it be a fra&ion annexed to a whole number , and you defire the 
 fquare of that whole number and fraction , reduce it into an improper 
 fra&ion , and feeke the fquare both of the Numerator and of the Deno- 
 minator as is aforefaid. 
 
 Example, t: 
 
 Let there be required the fquare df this fra&ion I find the fquare 
 of its Numerator to be 431911841 which I fetior Numerator , alfo I find 
 the fquare of 87 61 the Denominator so be 76790169 , which I fet for 
 Denominator, and fol hauc this fra&ion being the fquare of 
 
 Example, 2. 
 
 Let there be required the fquare of this whole number and fra&ion 
 annexed namely 1764 \ , I reduce it into an improper fra&ion,and fo it is 
 whofc fquare will be found as before to be **t 9 .? 4 ** 
 
 3 i 9 
 
 ProbJ 
 
7 ° 
 
 <tA Treatife of Geometry. 
 
 Prob. 6. 
 
 To find the Cube of a fraction , or of a whole number ha- 
 ying a fraction annexed. 
 
 C Eckc for the cube of tbe Numerator of your fraction , and fct that for 
 ^Numerator, alfo the cube of the Denominator of your fra£Hon fet for 
 Denominator, fo is this new fra & Lon the cube of the former. 
 
 Example. 
 
 Letthcrc be required the cube of this fraction I find in the Table 
 
 thecubeof the Numerator to be 28385*461 248, and the cube of the 
 Denominatortobe<S729i 22 5°?47 therefore I fay the cube of this fra- 
 ction iS a ?? 8 *»4*H 48. 
 
 876} 671911*50947 
 
 But if there be a fraction annexed to a whole number , and you defire 
 the cube of that whole number and fra&ion , reduce it into an improper 
 fra&ion, and feckc the cube both of the Numerator and Denominator as 
 before, J ' 
 
 Example. 
 
 Let there bee required the cube of this whole number and fraction 
 27 64 j, which being reduced into an improper fra&ion is zi* 4 whofe 
 
 cube I fccke as in the former Example and find it to be 38 — 58 i ££ 84 
 
 Prob. 7. 
 
 To find the root fquare of a fraction. 
 
 L Ookcin the Table for the fquare Root of the Numerator of your 
 fra&ion, and fet that for Numerator , alfo the fquare Root of the 
 Denominator, fo is this new f ration the root fquare of the fracti- 
 on propofed. 
 
 Example . 
 
 Let there be required the Root fquafcof this fra&ion 1 finde 
 
 the fquare Root of the Numerator to be 6572 and the fquare Root of the 
 Denominator 8763 , therefore I fay gg is the fquare Root of that fra- 
 ction. 
 
 Example. 
 
iA Trcatife of Geometry. 
 
 71 
 
 Example, i. 
 
 Againe, admit there be required the fquare Root of this number $7 
 I reduce it to an improper fraAion, and foie is **, now the Root of 82 
 will be nine and fome what more, but the Root of three is more then one 
 1 and lefle then two. But for the more exa Anefle of the Root of this and 
 other (iich like fraAions, you may put both to the Numerator and De- 
 nominator, 2,4,6, or 8 Ciphers as the Table, will beare, as in this exam- 
 ple of putting to cither fixe Ciphers, it wilbe 8loooo °°, w h 0 fe Root 
 
 3000000 
 
 fquare we may find as before to be which is the Root of 27 7. 
 
 Prob. 8. 
 
 To find the Cubicke ^ oot of a fraction- 
 
 F ind in the Tables the Cubick Root of the Numerator, and fet that for 
 Numerator of the Root, alfo the Cubick Root of the Denominator, 
 and fet that for Denominator, fo is this new fra & ion the Cubick Root of 
 the former. 
 
 Example* 1. 
 
 As if there were required the Cubick Root of this fraAion 
 
 Wc fhall find it by the Tables to be as before 15 \ 
 
 ' 'j 7 876} 
 
 Example , a. 
 
 Againe , if there be required the Cubicke Root of this number 17 i I 
 reduce it to an improper fraction, and foitij and bccaufe I cannot 
 
 have exa A:Iy theRoots of this Numerator and Denominator, that I may * 
 come the more neerly to it, I put both to the Numerator and Denomina- 
 tor 3, 6, 0 or 1 2 Ciphers , as in this example I put to cither of them nine 
 Ciphers, and fo the fraAion is ^=225? whofe Cubicke Root wee fhaH 
 find as before to be 4i± 4 , 
 
 144* 
 
 Prob. 9. 
 
 Tofindnearely the fquare %oot of a number 
 not fquare, 
 
 T F you cannot find your number whofe fquaic Root yon defirc in the 
 icolume of fquares,take the next lefler number, and fetdowne the Root 
 thereof for the intcgrall Root of your number , and of the refidue make a 
 fraAton thus, fubftraA that number taken out of the Table from your 
 number given, and the remayncr fet for Numerator, whofe Denomina- 
 tor is the forefaid Root doubled, and one added thereto; 
 
 Example'. 
 
<t A 'Treatijeof Qeometry. 
 
 ' '' £ , 
 
 Example, 
 
 I Would find the Root fquare of this number 64280306, I find it not 
 in theTablc,butthcnextlelIcr is 64272289, whole Roore fquareis 
 8017, then I fubftra& 64272289 from 64280306, and there remayncs 
 801 7 which I make the Numerator of a fra&ion, then I double the fore- 
 faid quotient, and addc one to it being doubled, and fo it is 16035 which 
 I make the Denominator, and fo thefraftion is therefore the Root 
 required is 801 7 JL°I r , that is ncere 8017 i which is nearly the Root of 
 the number propofed. 
 
 Prob. 1 o» 
 
 To find nearely the Cubick Qfoot of a number 
 not Cubick, 
 
 T Akc in the colume of Cubes, the number that is next lefler then 
 the number propofed, the Cube Root of which number fet down 
 for part of the Root required, namely fo much of it as can be ex- 
 preffed in a whole number. Then for thefra&ion, fubftra& the faid num- 
 ber taken out of the Table from the number propofed, and the remay ner 
 fet for Numerator, whereto you may find a Denominator thus. To the 
 Root before found adde one, and t^at multiply by the Root tripled, and 
 to the product addc one, and that fet for Denominator. 
 
 Example, 
 
 Let there be required the Cubick Root of this number 9* 73 3 7 J2 93 80, 
 I find it not in the Table of Cubes, but the next lefle then it is 917144- 
 5P1751 whofc Cubicke Roote is 9751. Now for the fra&ion I fub- 
 ftrad this number found in the Table from the number given, and the re- 
 mayneris 19*637619 which I make the Numerator of a fraction, and 
 for the Denominator I adde i.to the forefaid Root 975 i,»ndfo it is 9751 
 which I multiply by the triple of the Root, namely by *92 j 3,6c the pro- 
 duct is 285275256,10 which adding one I have sthe '.Denominator, and 
 
 fo the fra&ion is i 9 therfore I fay the Root required is nearly found, 
 
 2*5275*57 
 
 namely $75 1 
 
 * * X 5 * 75*57 
 
 Prob. iO. 
 
 The Aggregate of the Squares of two numbers being given, 
 together with the fquare of their halfe furnm > 
 to find thofe numbers , 
 
 t . ft I* 
 
 FXOuble the fquare of the halfe furome,and fubfirad it from the fore 
 •■—'faid Aggregate, halfe theremayner is fquare of halfe the difference of 
 thofe two numbers by the 9 2. of Euclide, Or , 
 
 From 
 
<iA Treatife of (jeomctry. ■ 73 
 
 — - - 
 
 From halfe the aforcfaid aggregate, fubftrafl tbc fquare of the halfe 
 fumme, the remainder is the fquare of halfe the difference of thofe two 
 numbers. 
 
 Example, 
 
 As let there be given the aggregate of the Iquares of two Unknowhe 
 numbers, 104522890. and the fquare of their halfc fumme 41809 156. 
 
 I demand thofc numbers- 
 
 The halfc 0(104522890. is 52251445. from which fubftracling the 
 fquare 418091 5 6 , there remaines 10452289 whofe root fcjuarc wee 
 may finde in the table to be 3233. which is the difference of the two 
 numbers required from the halfe fumme: and feeing the fquare of halfe 
 their fumme is 4 1809 15^. whofe root fquare is 6466 ■ therefore 6466. is 
 halfe the fumme of the two numbers required, whereto adding the afore- 
 faid halfc difference 3235. the fumme is 9599. or fubftracling it, the re- 
 mainder is 32 3 3. therefore thele numbers 9 6 99 < and 3 23 3. ate the two 
 numbers required. 
 
 Prob. 12. 
 
 The aggregate of the fquares of two numbers being given, toge- 
 ther With the fquare of half e their difference , to finde thofe 
 
 two numbers. 
 
 F Rom halfe the forefaid aggregate, fubftraCl the fquare of halfe their 
 difference, the remainder is the fquare of the halfe fumme of thofe 
 two numbers, by the fame. 
 
 As let there be given the aggregate of the fquarcs of two unknowne 
 numbers, 103407444. and thefquarc of halfc their difference 423801. 1 
 would know thofe numbers. 
 
 The halfe ofi 034074 44. is 51703722, from which fubftra&ing the 
 fquare, 423801. there remaines 51279911. whofe root fquare wefindeto 
 be 7152. which is halfe the fumme of the two numbers required, and 
 feeing the fquareofhalfctheirdiffcrcnccis 4238 oi. whofe root fquare is 
 551. therefore 5 ji.is halfcthc difference of the numbers required, that is, 
 the difference of one of them above the halfe fumme, and of the other be- 
 neath, therefore if to the halfc fumme 71 61. we addc <>5 1 • the fumme is 
 78x2 the greater number, or if we fubft rad inhere remains 5510 the leflfer 
 
 Prob. 13. 
 
 The aggregate of the fquares of the halfe fumme , and balfe diffe- 
 rence of two numbers given, together with one of thofe 
 numbers to finde the other of them. 
 
 pRom theaforefaid aggregate being doublcd,fubftra£t the fquare of the 
 number given, the remainder is the fquare of the other number requi-. 
 red, by the fame, 
 
 G The 
 
74 
 
 <t A 'Treatijeof (jeometry. 
 
 The aggregate of the fquarcs oft he halfcfumme, and halfc different 
 of two numbers let be 5 170372s. and let one of thofe numbers be 6510. 
 I demand the other of them. 
 
 The aggregate 5 1703722. being doubled is 103407444. from which 
 fubftra&ing 42380*00. the fquare of $5 10. there remay .nes 61017344, 
 whofe root fquare we (hall finde in the tablctobc 7812. which is the o- 
 thcr number required. 
 
 Prob. 14. 
 
 The two f ides of a right angled, triangle given to finde the 
 hypothenufaU • 
 
 A Sin the triangle next following, Prob. \6. let the fide CD, be <55. 
 imparts, and the fide BD, 76 parts, there is required the hypothenufaU 
 BC. 
 
 The fquarcs ofthefidcs are equal! to the fquare of the hypothenu- 
 fa!l by 47. 1 Euclid. 
 
 Therefore the fquare of <>5. being 4225. and the fquare of 7c. being 
 5776. Iaddethem both togcther,the fumraeis roooi whofe rootfquare 
 is ico. and fomewhat more, therefore I fay the hypothenufall B C, is 
 100. parts, and fomewhat more. 
 
 Prob. 15. 
 
 The hypothenufall and a fide given, to finde the other fide. 
 
 A S in the triangle next following, let the hypothenufaU B C, be 100 
 parts, the fide C D, 6 j . and let there be required the other fide B D. 
 From the fquare of the hypothenufall fubfirad the fquare of the fide 
 given, the remainder is the fquare of the fide required. 
 
 Thus the fquare of B C, too is 10000. from which fubftrading the 
 fquare of C D, 6 5. namely^ 4125. there rcmaincs 5 77 5 . whofe root fquare 
 is almoft 7 6. which is the fide B D, required. 
 
 Prob. 1 6. 
 
 The three fides of an obtufe angled triangle being given, to finde 
 how far the perpendicular fals without the obtufe angle . 
 
 pRom the fquare of B C, fubftrafl: the fquares 
 of A B, and A C, and divide halfc the remain, 
 dcr by A C, the quotient is A D, by the 12 
 prop. 2 Euclid. 
 
 As let the fide A B, be 80 parts, the fide A C, 
 
 40. and B C,ioo, and let there be required A D. 
 
 The fquare of A B, 80. is 6400. and of A D, 
 
 40. the fquare is itfoo thefumme of thefetwo 
 fquares is 8000. which fubftra&cd from the 
 fquare of B C, 100. namely from 1 0000. there 
 remaincs 2 000. the halfe whereofis » 000. which 
 divided by A C, 40. the quotient is. A D, is parts.* Prob. 
 
 B 
 
Treatife of (geometry i 
 
 Prob. 17. 
 
 The three fades of an acute angled triangle 9 being given to finde 
 where the perpendicular fals. 
 
 pRom the famine of the fquares of 
 AB,and A C, fubftraft the fquare B 
 
 of 6 C, and devide halfc the remain- 
 der by A C, the quotient is A D, by 
 13. a Euclid. 
 
 As let the fide A B, be So parts, the fide A 
 B C,40. and A C, ioo.and let there be required A D. 
 
 The fquare of A B, 80. is 6400; the fquare of A G, loo. is 10000. the 
 fumme 16400. from which fubftra&ing the fquare ofB C, 40. namely 
 1 600. there rcmaincs 4800. the halfe whereof is 7400- which divided 
 by A C, 100. the quotient is A D, 74. 
 
 Prob. is. 
 
 Admit the femediameter of the earth to be 3436. miles , and that 
 there is a mount aine in height one mile : how farre may that 
 mountaine be feene upon plaine ground or at fia. 
 
 H Eretothe femediameter of the earth 3436. adding one mile for the 
 height of the mountaine, it is 3437*whofc fquare is 1181 zp£p.frotri 
 which fiibftra&ing the fquare of 3436* namely 11 80609 6. there re- 
 maines 6873. whofc root fquare is almoft 831 fo that that mountaine 
 may be feene at (ea almoft 83 .miles. 
 
 Prob. ip: 
 
 Admit the femediameter of the earth to be 3436 miles, and that 
 there is a mountaine jeene off at fea 83 miles 9 I demand 
 the height of that mountaine • 
 
 r ‘p He fquare of 3436*^ 1 1 $06096 the fquare of 83. is 6889. the fumme 
 ofthefe two fquares is 1 18 12985. whofc root fquare is 3437.^ 
 from which fubftra&ing the femediameter 3435. there refts 1 miles* 
 that is a mile and little more for the height of the mountains 
 
 Prob- ao. 
 
 The diameter of a circle given to finde the area of that circle] 
 
 I T is proved by Archimedes , that thcfquare of the diameter of a circle 
 ft in proportion to the area of that circle as 1 4 to 1 r: 
 
 As let the diameter of a circle be 2 1 inches* I demand the area of that 
 circle. 
 
 The fquare of 2 1 is 44 . 1 f3y then. 
 
 ' G 2 As 
 
<zA Treatife of Cjeomctry. 
 
 As 1 4to11.ro is 44 1 103461 which is the area of the circle required. 
 
 Prob. 2 1. 
 
 > 
 
 To divide a number bj extreme and meane proportion. 
 
 * % 
 
 A Vltiplv the fquare of your given number by 5. and devide the p.ro- 
 by 4. and from the fquare root of the quotient, fubflraft the 
 halfe of your given number, the remainder is the greater portion, which 
 fubftra&ed from the whole, leavcth the lefle part. 
 
 As fo divide this number 8117. fo proportionally I finde the fquarc 
 of it to be 66031876. which multiplied by $.the produttis 330159380. 
 which divided by 4. the quotient is 815:98 45. whofe root fquare wee 
 may finde to be 9085 from which fubftra&ing the halfe of 8127 
 namely 3 i. there remaincs joi 1 f&‘. the greater part being almoft 
 50»i£.which fubftra&cd from the whole 8127. leavcth 3io5^|the 
 IcfTer part. 
 
 Prob. 22 i 
 
 The dimeter of a circle given to finde tbe fides of the inferibed 
 equilater , triangle , jquarepentagon^ and decagon, 
 
 T Riplc the fquarc ofthe femcdiametcr, the root fquareof that product 
 is the fide of the triangle', double the fquarc of the femediameter^nd 
 the root fquare ofthe produft is the fide of the fquare. 
 
 Devide the femcdiametcr by extreame and meane pro portion, the grea- 
 ter part is the fide ofthe decagon, whole fquare added to the fquareof 
 the femcdiametcr, and of that torail the root fquare cxtra&ed is the fide 
 ofthe inferibed pentagon. Matter Digges of Geometricall follidcs, whofe 
 name is worthy of reno wne. 
 
 Example. 
 
 as let the femcdiametcr of a circle bee 21 00. the fquare thereof is 
 4410000. which tripled is 1 3230000. whofe root fquare is 3^37^. 
 which is the fide of the inferibed triangle- Againc, doubling ^41 oooo.it 
 is 8 8*0000. whofe root fquarc is 2 9^9 tJs’I* whfehisthe fide of the in- 
 feribed fquare 
 
 Sundry other problcmcs of this nature touching the infeription and 
 circumfcription of figures might bee propofed, which here wee pafic 
 overj 
 
e A Treatife of (jeometry . 
 
 Prob. 
 
 i 
 
 , If 1 45 00 be put into a fquare Battle, bow many 
 
 Will there be in ranke and b<to many in file. 
 
 Find by thefc Tables the fquare Root of <4900 to be 123, and there 
 remayncs fixteen, therefore I fay there will be 1 22 men in ranke and 
 as many in file and fixtecn men over. 
 
 Prob. 
 
 24. 
 
 There is delivered to the Sergeant Mai or 60 Enfignes , ineuery 
 Enfigne 160 Pikes 3 and (hort weapon. The Generals pleasure 
 is that he fb.aU put them in one mayne Squadron , and to arme ip 
 round with 7. rankes of Pikes , I demand how many Pikes, and 
 bow manyfhort weapons b*fb A n ufi to make the greatefi Squa- 
 dron, and bow many rankes (ball be fy that Battaile . 
 
 F Irft multiplying 1*0 by fix tireproduft is p* 9 o,which is the nura-’ 
 her of men delivered to be ctabatled , whofegreateft Root fquare 
 in integers is 517. the number of men in grantor Flank, and 1 91 
 men remayncs, now confidcring the Front oftfre fftort weapon muft be 
 fourteen leffc being armed round withfeven Rankes of Pikes , therefore 
 fubft rafting fourteen out of ninety feven, there remayncs eightie three, 
 vvhich is the number of the Ranksoffhort weapon ,whoftfcmai* is 6U 9 
 the number of fliorc weapon and t hat tobftraft ? d .from the fquare 
 
 Battle of nftrrie feven iftii tanke Ida ves 2 520 the number of Pikes. 
 
 Prob. 25. ' ", I 
 
 There is delivered to the Sergeant Maior^ob SouUiers wit fa 
 commandment that heeimbattle them, in fucb fort that euery 
 Souldier in fronts fland three foot difi ant from the other, and 
 every ranke from other feven foot , and this obferved to frame 
 of thefe men the greatefi battaile that may bee to make the 
 ground fquare y Idemandybow many war ankc, and how hany 
 rankes in that battdile. 
 
 B Ecaufe the diftance of the Raaheis to the diflance of the Files a* 
 (even to three multiply 8joo the number ofSouldierspropoVed 
 by 3-theprodua is 15J00 which I divideby feven the quotient is 
 3 C43 almott, whole Root fquare is fixty befides the retnayner which here 
 
 2 ? u ’PP eares ,h£rc wil1 bc Pn“y Rankes in that battaile, 
 which ttiultiplyed by feven, and the produft divided by three , the quo- 
 tient is 1 40, the number of Souldiers in every Ranke. 
 
?8 
 
 zA Treatife of (geometry 
 
 Prob. 2 6. 
 
 Experience teacheth that to incampe 6000 Footmen , and 600 
 Horfe commodioufly ^ith roomejufficientfcrthe flreets f Mar- 
 ket place ^munition : and other occafions.it U requifite the Camps 
 fhould be 6 40 paces fqu.ire. But there is delivered by the Ge~ 
 neraU 30000 Footmen * and 5000 Horfe • I demand vphat 
 fcope of ground the Lord High Marfball or Camp-mafter fhould 
 appoint to receive this Company lodging them as commodioufly 
 as the other. 
 
 F Orafmuch as 6600 men require 640 paces fquare of ground , that 
 is 409600 (quare paces of ground,! fay by the Rule of proportion. 
 As dloo men, to 409600 fquare pacesifo 33000 men, to 2048000 
 fquare paces, whofe|Root fquare is betweene 14.31 and 1432 paces, fo 
 that it appeares the fide of a fquare piece of ground of fufficicnt capaci- 
 citic to incampc commodioufly, 33000 men fhould be 143s paces. 
 
 Thcfc and fundry other fuchqucft ions fetdowne by Maftcr Them as 
 Digges in his Stratiotti$s l and by others treating of Military Difciplinc 
 may aptly and cafily be. performed byhclpcof thefe Tables whereof it 
 fbali fuffice here to h^egiven this tafte. 
 
 Prob, *27. 
 
 ..... ' v 1 ‘ 3; ’ 
 
 / Of a Jhip of 1 00 tuns be 44 foote long at the keek , of ■svbat 
 length l ball the keele be of a Ship of 2 00 tuns. 
 
 F Orafmuch as like Solids are in treble the proportion of their cor- 
 refpondent fidesor lines, therefore I feckc tbe cube of 44 and find 
 the fame to be 85 1 84. And fay by the Rule of Proportion; 
 
 As 100 tuns is in proportion to 85 1 84.(0 is 200 tuns to 1703 68 whole 
 Root Cube is ncare 55 the length of the kcclc required. 
 
 Prob. 28. 
 
 . :V *: nWi '<* -'3 ’ V *"«*r*\ '-y 
 
 \f a Jbip of 1 60 tuns be 44 foot long at tbe keele, of what burthen 
 [ball the like fhip be wbofe keele in length is 55 'fjootl 
 
 T He cube of 44 is 8*184 the Cube of 55 *7 is neerc as before 170368 
 I fay then by the Rule of Proportion. 
 
 As 8*184x0 1 70368 fo is 100 tons to^oo tuns , the burthen of the 
 fhip required. 
 
 
 Prob* 
 
Qji Treatife of (geometry. 
 
 Prob. 29. 
 
 ' \ 
 
 Ifafhipof 100 tuns be 20 foot broad, at the mid-flip beame t 
 of what breadth there /had the like [hip bee 
 of 200 tuns, 
 
 T Hc Cubeof-2ois 8000 1 fay then by the Rule of Proportion : 
 As 1 00 tons to 8000, foislootunsto 16000, whofc Cubicke 
 Root is 2^ / altnoft* . 
 
 Or if you will worke the fame in inebe^you may reduce 20 f 00t int0 
 inches,fo is it 240 inches, whofe Cube is 13 82 4000,1 fay then. 
 
 As 1 00 tuns to 13824000,10 is 200 tuns to to 2 7648000, whofc cubick 
 Root is altnoft 302 1 inches, 
 
 Prob. 30. 
 
 Jf a [hip of a 100 tuns be 10 foot broad at the midflnp bcame , 
 of what burthen [had the like (hip be, whofe breadth 
 there is 25 \foot . 
 
 T He cube of 20 is 8000, and the cube of 1 $ : i* 1 6003, 1 fey then. 
 
 1 As 8000 to 100 tuns, fo is 16003 to 200 £ tuns, the burthen of 
 that other (hip being moulded in all points like the former. 
 
 Trob. 31. 
 
 If afathome of rope often inches compaffe , weigh 17 pounds, 
 how much will afathome of S inches compaffe weigh* 
 
 nPHe fquarc of 10 is loo, the fquarc of 8 is 64 , 1 fay then by the Rule 
 * of Proportion. 
 
 As 1 00 is in Proportion to 1 7 pound, fo is 64 to 10 J| pounds. 
 
 Prob. 32. 
 
 Jf afathome of rope of 10 inches compaffe weigh 17 ponnds 
 of what compaffe [had the rope be; whereof 1 fa - 
 thyme weigheth 10 ,JJ pounds . 
 
 T^He fquare of 1 0 being 1 00, and 1 o reduced into an improper fra-} 
 
 &ion I fay by the Rule of Proportion. 
 
 As 2 pounds is in proportion to fo is ^ pounds in proportion 
 
 |Q I08800 
 I700* 
 
 Which reduced is 64 whofe Root fquarc is 8 inches the compaffe of the 
 rope required. 
 
 Prob: 
 
 l 
 
8 q <*A Treatije of geometry . 
 
 rn.r. m 11 ■■--- - 1 
 
 Prob. 33. 
 
 » > - ; . ( 
 
 Admit there he a Demicannon having its tore 6 ~ inches, and 
 that it (hoot a bullet weighing 3 2 pounds , I demand 
 the weight of that (hot that jeryes a Can- 
 non of Si inches diameter. 
 
 V 
 
 H Ere as the cube of the one Diameter is in proportion to the cube 
 of other/o is weight of one (hot to the weight of the otherrther- 
 fore I feeke the cube of 6 5 or ^ and find it to be '¥21 . Alfo I 
 
 feeke the cube of 8 \ or & and find it to be 4 2i|,I fay then by the -rule of 
 
 Proportion. v 
 
 As 1 ¥21 to ^i|»fois — pound to which improper fra&ion 
 
 reduced into its integers is 80 or 80 j pounds almoft. 
 
 Prolv 34. 
 
 Admit a (hot 0/31 pounds weight ferye a piece ,the Diameter 
 of wbofebore is C\ inches of what Diameter /had 
 the bore of that peece be which (hoots 
 a bullet of 80 i pounds, 
 
 r jpHc cube of 6 $ is !£f ±5 1 fay therefore, 
 
 As 32 pounds is in proportion to 80' pounds or • , fo is 
 to wbofe cubick Root is ncetc 8 \ the Diameter of the bore rc- 
 
 »i8 • « ' f 
 
 quired. L * 
 
 Sundry other queftions of like nature may be refolvcd in like manner, 
 all which together with the more ample ufc of thofe Tables in fundry 
 Algcbraicall and Geometrical Problcmes I muft at prefent pafle oucr, 
 contenting my fclfc with thefe few examples here (hewed. 
 
I tent. 
 
 R. 
 
 Sq., , Cu. 
 
 i \ 
 
 1 
 
 ' 1 
 
 1 4 ; 2 1 i ? i . 
 
 2 £ 
 
 4 ? 
 
 8 
 
 • C * 1 
 
 3 r 
 
 9 -? 
 
 5 27 c 
 
 4 \ 
 
 16 
 
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 25 
 
 12 5 
 
 6 
 
 36 
 
 216 
 
 7 : 
 
 49 
 
 343 
 
 8 
 
 £4 
 
 512 
 
 9 * 
 
 81 
 
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 IO 
 
 100 
 
 1000 
 
 it 
 
 121 
 
 1331 
 
 12 
 
 *44 
 
 1728 
 
 *3 
 
 169 
 
 2197 
 
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 196 
 
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 225 
 
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 256 
 
 4096 
 
 17 
 
 289 
 
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 324 
 
 5832 
 
 19 
 
 361 
 
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 20 
 
 400 
 
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 9261 
 
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 529 
 
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 24 
 
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 676 
 
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 19683 
 
 28 
 
 784 
 
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 29 
 
 841 
 
 24389 
 
 30 
 
 900 
 
 27000 
 
 
 961 
 
 29791 
 
 32 
 
 1024 
 
 32768 i 
 
 33 
 
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 35937 
 
 34 
 
 1156 
 
 393°4 
 
 35 
 
 1225 
 
 4*825 
 
 3 ^ 
 
 12 96 
 
 48656 
 
 37 
 
 1369 
 
 50653 
 
 3 8 
 
 1444 
 
 54872 I 
 
 39 
 
 1521 
 
 554*9 
 
 40 
 
 1600 
 
 64000 
 
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 1681 
 
 68921 
 
 42. 
 
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 74088 
 
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 1849 
 
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 1 Cent'. 
 
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 62 
 
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 274625 ’ r 
 
 1 66 
 
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 68 
 
 69 
 
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 287496 
 
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 329199*1 
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 72. 
 
 73 
 
 74 -: 
 
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 15041 
 
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 5476 
 
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 6084 
 
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 474522 . 
 493039 1 
 5*2000 • 
 
 81 
 
 82. 
 
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 86 
 
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 90 
 
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 7056 
 7225 
 
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 53 * 44 * 
 
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 592604 
 614125 v 
 636056 f 
 648303 ' T 
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 9 «*- ; 
 
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 94 : 
 
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 778688 
 
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 830584^1 
 
 8 57375 
 
 9 * 1 
 
 98 
 
 99 ? ? 
 
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 92 r6 
 
 94<59 
 
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 9801 
 
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 884736 1 
 915*73 
 
 941*92 
 
 97°*99 
 
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I 
 
 l 
 
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 I Cent. 
 
 !L 
 
 Sq. 
 
 Cu. 
 
 
 
 Sq. 
 
 Ctt. 
 
 101 
 
 102 
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 125 
 
 106 
 
 1 107 
 
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 1061208 
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 1124856 
 n 57625 
 
 
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 152 
 
 153 
 
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 3442951 
 
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 156 
 
 157 
 
 158 
 
 159 
 
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 1520875 
 
 
 161 
 
 162 
 
 163 
 
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 165 
 
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 167 
 
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 173 
 
 174 
 
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 177 
 
 178 
 
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 180 
 
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 183 
 
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 186 
 
 187 
 
 188 
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 190 
 
 34596 
 
 34969 
 
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 357*1 
 
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 6434856 
 
 6539203 
 
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 141 
 
 142 
 
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 144 
 
 145 
 
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 2803221 
 
 2864288 
 
 2924207 
 
 2985984 
 
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 191 
 
 192 
 
 193 
 
 194 
 
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 37*49 
 
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 200 
 
 38416 
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2 Cent. 
 
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 202 
 
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 3452164 
 
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 1861 
 
 1862 
 
 1863 
 
 1864 
 
 1865 
 
 1866 
 
 1867 
 
 1868 
 
 1869 
 
 1870 
 
 3463321 
 
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 1876 
 
 1877 
 
 1878 
 
 1879 
 
 1880 
 
 3519376 
 
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 3526884 
 
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 3534400 
 
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 6613913133 
 
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 1881 
 
 1882 
 
 1883 
 
 I 1884 
 
 1885 
 
 1886 
 
 1887 
 
 1888 
 
 18 89 
 1890 
 
 3538161 
 
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 6665900968 
 
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 6708494456 
 
 6719171103 
 
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 6761990971 
 
 6772724288 
 
 6783468957 
 
 6794224984 
 
 6804992375 
 
 6815771136 
 
 6826561373 
 
 6837362792 
 
 6848175699 
 
 6859000000 
 
 1891 
 
 1892 
 
 1893 
 
 1894 
 
 1895 
 
 1896 
 
 1897 
 
 1898 
 
 1899 
 
 1900 
 
 357P81 
 
 3579664 
 
 35^3449 
 
 3587236 
 
 3591025 
 
 3594816 
 
 3598609 
 
 3602404 
 
 3606201 
 
 3610000 
 
20 
 
 \ MX y * 
 
 
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 R. 
 
 Sq. 
 
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 R. 
 
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 1901 
 
 3613801 
 
 6869835701 
 
 
 * 95 * 
 
 38064OI 7426288351 
 
 190a 
 
 3617604 
 
 6880682808 
 
 
 I 95 2 
 
 3810304 
 
 74377*3408 
 
 1903 
 
 3621409 
 
 6891541327 
 
 
 *953 
 
 3814209 7449150177 
 
 1904 
 
 3625216 
 
 690241 1264 
 
 
 *954 
 
 38l8ll6 746O598664 
 
 1905 
 
 3629025 
 
 6913292625 
 
 
 *955 
 
 3822025 
 
 7 472058875 
 
 1906 
 
 3632836 
 
 6924185416 
 
 
 1956 
 
 3825936 
 
 7483550816 
 
 1907 
 
 3636649 
 
 6935089643 
 
 
 *957 
 
 38298,9 
 
 7495014493 
 
 1908 
 
 3640464 
 
 6946005312 
 
 
 *958 
 
 3?33764 
 
 7506509912 
 
 1909 
 
 3644281 
 
 6956932429 
 
 
 *959 
 
 3857681 
 
 75*8017079 
 
 1910 
 
 3648100 
 
 6967871000 
 
 
 i960 
 
 38416OO 
 
 7529536000 
 
 1911 
 
 3651921 
 
 6978821031 
 
 
 1961 
 
 3845521 
 
 7541066681 
 
 1912 
 
 3^55744 
 
 6989782528 
 
 
 1962 
 
 3849444 
 
 7552609128 
 
 1913 
 
 3659569 
 
 7000755497 
 
 
 1963 
 
 3853360 
 
 7564163347 
 
 1914 
 
 3663396 
 
 7011739944 
 
 
 *964 
 
 3857296 
 
 7575729344 
 
 1915 
 
 3667225 
 
 7022735875 
 
 
 1965 
 
 386/225 
 
 7587307125 
 
 1916 
 
 3671036 
 
 70337432 96 
 
 
 1966 
 
 3865 156 
 
 7598896696 
 
 191 Za 
 
 3674889 
 
 7044762213 
 
 
 1967 
 
 3869089 
 
 7610498063 
 
 1918 
 
 3678724 
 
 7055792632 
 
 
 * 968 
 
 3873024 
 
 7622111232 
 
 1919 
 
 3682561 
 
 7066834555, 
 
 
 *969 
 
 387696I 
 
 7633736209 
 
 1920 
 
 3686400 
 
 7077888 -DO 
 
 
 1970 
 
 3880COO 
 
 7645373000 
 
 1921 
 
 3690241 
 
 7088952961 
 
 
 * 97 * 
 
 3884841 
 
 7657021611 
 
 1922 | 
 
 3694084 
 
 7100029448 
 
 
 1972 
 
 3888784 
 
 7668682048 
 
 1923 ! 
 
 3697929 
 
 71 11 117467 
 
 
 *973 
 
 3892729 
 
 7680354317 
 
 1924 
 
 3701776 
 
 7122217024 
 
 
 *974 
 
 3896676 
 
 7692038424 
 
 1925 , 
 
 3705625 
 
 7133328125 
 
 
 *975 
 
 39O0625 
 
 7703734375 
 
 1926 
 
 3709476 
 
 7144450776 
 
 
 1976 
 
 3904576 
 
 7715442176 
 
 19271 
 
 3713329 
 
 7155584983 
 
 
 \977 
 
 3908529 
 
 7727161833 
 
 1928 j 
 
 3717184 
 
 7166730752 
 
 
 1978 
 
 3912484 
 
 I7738893352 
 
 1929 
 
 3721041 
 
 7177888089 
 
 
 1979 
 
 39*644* 
 
 7750636739 
 
 
 3724900 
 
 7189057000 
 
 
 1 980 
 
 3920400 
 
 7762392000 
 
 1931 
 
 3728761 
 
 720023745,1 
 
 
 1981 
 
 3924361 
 
 7774 * 59 * 4 * 
 
 1932 
 
 3732624 
 
 7211429568 
 
 
 1982 
 
 3928324 
 
 7785938168 
 
 1933 
 
 3736489 
 
 7222633237 
 
 
 *983 
 
 3932289 
 
 7797729087 
 
 1934 
 
 3740356 
 
 7233848504 
 
 
 1984 
 
 3936256 
 
 780953*904 
 
 1935 
 
 3744225. 
 
 7245075375 
 
 
 1985 
 
 3940225 
 
 7821346625 
 
 1936 
 
 3748096 
 
 7256313856 
 
 
 1986 
 
 3944196 
 
 7833*73256 
 
 1937 
 
 3751969 
 
 7267563953 
 
 
 1987 
 
 3948169 
 
 7845011803 
 
 1938 
 
 3755844 
 
 7278825672 
 
 
 1988 
 
 3952144 
 
 7856862272 
 
 1939 
 
 3759721 
 
 7290099019 
 
 
 1989 
 
 : 5956 l 2 I 
 
 7868724669 
 
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