THE FORTIFICATIONS BVONAIVTO LORINI FLORENTINE NOBLEMAN NVOVATELY REPRINTED, Correct & Expanded everything that was missing for their perfect accomplishment, WITH THE SIXTH BOOK. Where it shows, with Science, and with Practice, the order to Fortify the Cities, and other places, with all the tools, that can most benefit, for the safety of the Fortresses, C I O E, In the First Book. Yes, it is about the Science around the rules to form the Fortress Plates, with the knife file. In the second one. Yes, it shows the Practice with which to build the Fortress in Royal work. In the third one. They describe the diversity of the Plants, with the electrine of the best defenses. In the fourth. The diversity of physic, and how they should fortify. In the fifth. It is about the Mechanical Sciences, & the easy order of the Factory all the formicate & machine artifice that polonium make rebel in time peace as of war as fi profane with little force dominate great lime pace, In the 6th, & last. Yes, it is about the defense of the Fortresses & fi show all those spells, with which the defenders can defend us, with that greater advantage, that fi purr of the Fortress; & in addition to that filo between the Order of measuring cowardice & king Je Painted with other particular necessary to do what is proposed. WITH PRIVILEGES. IN VENETI A M D C. IX. Francis Rimpazzisco. A L L I SERENISSIMI PRINCES OF ITALY. LORDS AND MASTERS Always Colendissimi. And True Most Serene and Most Glorious Princes, that man has been by nature, or rather by God formed, with the obligation that as much as he can, and be so much a pistol wings other man, so that in such They are swollen by the other, depending on the other, even though they have an anumaranaÕs number, they are nevertheless full of love. photo j. Ada with those oil still, who with every pious affection wine, & with every pious ardent zeal all agree "laugh and hurt their Princes; because they sewed from God made, not following Princes, but Affori & Padre commune de' popoli, then who piously of the others profane and make, o also pili de gli altri fon fatui e prudenti, Tfr atti a han han to hold and swear; And yet they deserve the title of Viceregents of God; and the knowledge that I have of the amends of these debts, and in particular of the last one, has made me continually fatigued with every power in the fluids of the Athematics, with the means of which equal ephedra arrived at the attic and is it necessary to fortify the Cities the other places, & hard among beautiful, t5r of good all over the world, has in Italy 'together in the harvest. Serenijjimi Incipri , my forty years of continuous work, part confined by me learned to Gentlemen from such prophejj“onc to mean you, yes in France as in flanders : I have freed the time at the Circuits of the Sereni signed Republic of Venctia, learned of the continuous I have made Fortezze: And if I know myself well of the mimes of those who deal with the Fortifications; I hope, however, to write about them with such order, that no fake fruit will make my book quietly read: Already in the years p afati ^ne fi out a van fola part of the prefinite Opera to all the Most Serene Princes of Italy dedicated, with so much liberality oJe ne moji ali i fidi sfatti, che Pm 7“on vip de detrare ; hora ella fece intera a 'voi medium. afiiente dedicated the E although I was born in Fiorente , & besides the Serenijfimo Grand Duke of Tofana , of whom I am by nature and will njajjal'o , and wounder ; I feel the Screnijji“na Signoria of Veneti ^ that already for a long time I am pleased with my Phoenicia : I am still drunk at all the A /L W. SS. de detrare , O* procrare ogni grandezza & felicitˆ i II che (fero chiuso , con qualche comune sodisfattine effettuare , mani per pende /a/iurta Delli Stati ^ ^ deltlmperíQ d'Italia y i qual cosa le A. W- SS. will happily contribute with r Art of manufacturing est Fort'^^^e i0* then in the d' fender le , rotten with That, easy that fi, will aim in the ftoro , & 'last Book : And much more, Turi[ima ima mente tal difesa accadva y fa apre de! fortify (Ile conferred iter year 'together with that concord O* 'union of souls, which hora^hjedj ejfere between tutf njoi Serenijfimi Trincipi , for lacuale Italy rejoices , (S^ as Garden of the Adondo will produce all quŽ' more delicate & pntioj“frutti, which is foBta prodnrre > which first will make not fola laconferuatione , but Caccrefimento of the Sacrosanct Chrij“iana Religion'. With all those other pious and excellent virtues, which will make the benefit of the human and human confession, which will please the Chriflo nojtra Redeemer & Lord to make it worthy, t^ to the AA. VV - SS, grant all those great ^ZS “ & perpetual happiness, which they will defer. of Venetia on the 25th of February, 1609. Some A's. VV. SS. Humilissimo Seruo Good help Lorini TO READERS. HAVING several times between me fteflb confided to me the tnarauigliofo order of the Natural clearly seen not efler created with any imperfect indeed all (conforming to the genus fuo) perfect files, & in order to bring in commodo, & vtile to the man, who effectuating invoice, & image of God, and for So to speak, brother of Nature, and father of Art; I was inclined to believe that he is entirely obliged to imitate Nature, and with Art to do all his good works, and first to the honour of God our Lord, and then to the benefit of the proflimation. Therefore, by dominating all the other earthly cultures, he is able to make them as perfect as he is, as much as he finds his nobility greater, as a creature of reason, and as a philosopher compared to a small world, we can only be able to make them perfect in another way, but it is good, that he is able to represent all the excellences of the world, as (the commodity God) they find in him. For which goddesses with every study he deals with in all those eflcrcitij, & in all those arts, that can bring more value to the world: Following the good inclinations of his wits, & increasing always that talent that God gave him. Wherefore those who are elected of the noblest arts, and profit from the comfort of human beings, shall do worthy of greater honour. Et fŽ fra tutte l'arti, iS(^ le fcienze (lafciando le facre lettere) la difciplina Militare tiene il primo luogo ^ fi potrˆ col mezo di qucfta afcendcre a tutti i maggiori honoris comedi ci˜ fi legge nell'Hiftoriede gh huomini illuftri cflere auenuto ˆ molti, Who was well born of bafla fortune, and of vile lineage, I am, however, aphcephic, because of this virtue, to the fupiemi degrees of Imperius jl, which he has done well. Because, I do not know which major son-in-law is the most suitable for mankind, who, in order to confer on us the freedom of our homeland, and to tell us of the infidels, and enemies of the Holy Roman Chiefa, has brought about so many misunderstandings and dangers of life, which bring the imperfections of war, and the violence in the high altitudes of the Fortresses, and in the armed forces. Beyond that I do not know which is the major, and the most important load, but that the commanding, and well faper gouernare an army, in froatedel fuo nimico, and particularly in making it march, 6 ^ lodge safely in the countryside, and in prefcntare with advantageous order the battle. Therefore, by reconcreating, he will be able to be intelligent, and to practise his quarrels, with all those comforts and inconveniences, which are the most polar and which will bring defencelessness to the enemy. And that the whole fi elfifies with the antiuedcr the offense, which can make an enemy efib, & appreflb with the readiness of parties, opening in advance in diucrfi ways to oppose him with the diefefe . And if it is a part of the niclticro of the war (that is to say, the fortified ones) founded by the Prefect Opera, they will give all those, 5 Which to this prophecy shall we devote, hauer not a little intelligence, and practice of the offcfc , That as an enemy elf couldfleroriccucre: but that from such an intelligence goddesses depends the praxis of the most secure, and real ftrada^ that ofleruar fi pofia, to determine, and with good order, to build the body of the Fortress, that is, with those members, and with those military proportions, that such Architecture requires, to defend not only a small one in the countryside, By other aliai inaggiore, and by more powerful forces, but the Ethiopian Cities, & Kingdoms, which is the noftrcT end \ preualendoci of the forms, & materials of the fiti, with such order, that the few defenfori fi pollano defend from greater number aliai, with the loss of time, on which depends the greater benefit; and so it does so with the half of the abundance of the typologies of the bitterness of men, and then with the transformation of the breath, and its material to the strength of the enemy, or the strength of the defenders, through the construction of the Fortress. The lesser Jion praise they have deserved from those who, with their ingccno fi fi do confirm the Statesj as much as the others who with the force they have made them acquillatiie much moreeficendo fciency of the Fortify founded joprabiii terms deinoftrabiii (as at your place fi will say) laquale feienza was not done by the ancient Ronani, but still then by the other powerful princes, not little appreciated, & vfata for their difefa, in accordance with the oftefe, that in those times they are made, as the tabrices of the ancient Rocche de Calli3& the new ones of the cictˆ, that in many parts of Italiaje outside of her see us. Confirming that Vitruuion the first Book of your Architecture, i.e. how diligently you have ordered the fabrications, 5;^ eilequite; then fcguendo lo ftef“b Auttorc the rules of architecture ciuile, to embellish the city in fabrication with real public decorations, priuate habitationi for the commodo de gh habitantis in which Architecture many then ef“'ercitatifi, Ci fono fatti famofi Architects ^ & have with their works reduced such fcienza to the highest degree of beauty. But of Military Architecture it seems that few hay horned those, who had wanted to, it was not possible to make the above rule, that is, from the offefe cauareleditefe, ei“endo quefto forf auenuto, for he did not delight so much in the thunder of the Artillery, with the rouine of the mines made by the enemy in the Fortresses cfpugnation, as did the proposal, the vagueness of the profpettiiiejimparate in the comfort and delitie of their own Chambers, Therefore, when two orders of Architecture are so necessary for the Union, the 6th for the peace of men, they will have to do a great deal to appreciate and appreciate the noblest Mili'tarCjComc, So it is not only fipoffana to defend the cities^comc fi diflrc,^but fimilmcntc fi go accrccando rimpregio della Chriftianirˆ,e con Ja pace fi a“anttngal'vnionc de' popolij& il commodo delle Mercantiecon l'abbondanza di tutte cole . Waves are not lacking in writers, who have dealt with this matter of Fortifying, and all of them are good and joyful. Though, in my opinion, they had many reasons, and aucrtimcntijchc could (by writing to them) have (written) the understanding of qx!efi:afcicnza with the foundation of her practice, but /finic for the many, & f dare to diuerfc their opinions lafate irrefolute, which also vna fola dee efier the best, and fi:abilitafoprale reasons. True and, that this Art seems to be in addition to all the other aphlai dillicile to learn, ouero ad ef“crc infegnata per eilequirfi, then that can not fi fi fi with vna, ˜ with more rules give to understand, as the other nafce the other in your nobility, eficendo poficduta by a few. In this regard, the point is to bring us admiration, and then to find other people who, like an amphiot, depend on the ability and height of the genius of the one who wants to do it, who is able to do all that with ingenuity, and with the power to make infinite other men, in order to be able to defend themselves much sooner, that the high school offers it in advance; So that from the righteous judgment of a good Architect Mifitare depends at times, not only the health of the afterlife, but also the confirmation, is the diitruttion of the Kingdoms. And for this reason I have made myself a mofix) d fcriucre of cofi made matter, and with some fpcranza of accoftarmi (as far as fi can) to the clarity of those reasons, & dimoftrationi, that more polphono bring benefit in making understand the easiest, and sure way of Fortify . Proposing this cfi^equire with all those rules, or warnings, that from the experience of forty years I have been able to tell in a few years in Italy, & Flanders, oue I have procured to find myself appreciative of those Princes, and Gentlemen, who have made more rain than the war: I was introduced into this prophet/fiance, and I was encouraged by the gratitude of COSIMO de' Medici, Grand Duke of Tofcana, of glorious memory, and as it is known to all, I was introduced into the royal works, and I was also introduced into the royal works; I have been painted in addition to my natural inclination, I have been looking for all the opportunities to acquilt that intelligence, which is so noble in principle, but then with the thirty years of my life made to the Illustrious Lordship of Venctia, mistress of many war plazas, In the frontiers, against the most powerful enemy of the World, it has always been done to build fortresses, and to retreat in all occurrences, and to confuse the fortification, as well as to reifermi fempre daily certified with the mczo of the eiperience of those diinculties, which could bring doubtful refolutione around the nature of the fi ts. If to the subjects to be conferred their ephc: ...as well as with the ofierfuence of order..; Which he will say in the following Six Books, he will be able with the best reasons to order, and I will reduce to a perfect end all the fabrication of Fortress, so that the clarity of the dimoftraction of your differences, the liquids will be formed with all those proportions, and mifure, as it was done with those who wanted to carry out the work, as well as from the Fifth Book, to be able to guarantee all the comforts, which they can defidcate to facilitate the work with the half of the artifice of Mccanic diuerfi ftroments, so as to raise water, As from leuar with little strength grauifl“mipel“, and to translate the matters with much ease, and to be a paragan of time, and of money, & for vltim in the Septuagint Book fi moftrerˆ the order to keep to defend the Fortresses, which is how much fi can defidcrare in this matter. Et hauendo reduced at the end those my so long labors, with so notable fpefa, and fodisfatto to my defiderio, which was to rejoice to the public feruicio as in the principle di/fi j mi refla folo receive the prize of the aforesaid iatiche, which sign the gratia de benigno Lettore 3 fi as much dcfidcro . T A V O L A FORTIFICATIONS BVONAIVTO LORINI FLORENTINE NOBLEMAN. FIRST BOOK. Where science is shown with easy rules, with the practice of fortifying, and the reasons of all parts of the Fortresses are declared OF THE FIRST PRINCIPLES OF GEOMETRY. CAP.I. BEARING IN MIND that Geometry is not only necessary but also necessary, like the one which is the foundation of all other operations, it is therefore very important to consider, as it is necessary to give principle to what is proposed to treat Ciiiaintut in the following Books, aphrodite that fenza tal mezo faria impo/fibiic power eflequire , ne less well 'to understand any cofa^poi that even the Shoemakers^ the cficcutori de plus mustache efiercitij fono neceffitati to form, & d'intendere the features, co what fi must be done with those faperfaces^e forms j that they want to do ^ and all the more so to those who will defer dcdicarfi to rcalije works much more dcgnej As are the Fortifications, where fi is the confirmation of the Stars, But on that science depends the clearest, easiest and most easily dwelt, and it will be necessary to do, pruning ourselves with them, not to be able to really do so; all the coffers created by the naiura, but also those that yourenio with the value, ^ with the artifice of the ingenuity we would find again& d those add, ˜ decrease, and judge them their pcrfectations, ˜ imperfectations, fi as offences have been committed, that such a lance is so imposible that it is impossible for us to infect, or moult any part of it in the future {your,fi as you will say,fi as you will say,fiwhen we deal with the dignity, that goes with the ftelfa fcience^ and we have to think about the principle, it will define the bodies formed by femplic lines, conforming however to what we will judge to be able to search for intelligence to the one, which will be dealt with in the prefect Operajper el“er qiicio principle dclk Mathematical fcientie, the main reason to reach all the major, & most occult intelligences of nature. And yet here we will deal with the three coffers of the pointedly line3& of the surface. D I F F I N I T I O N I. It is the principle of the point noted with A. I say, that it is good that there is g^U and the principle, & the term of all the lines, not for that fi includesin elf any part of g;oHczza,Iarghe2za,˜ deepen, - ina as an indiuifiable cofa fcrapre fi deuc fcrapre with trust, because not ferue to anything else, than to vn ^ femplice term for diuifions, oucro for body compartments. D I F F I N I T “ O N E II. The line is vna continuous eftenfione — a vn'aitroje point to vn'aitroje as Ci tell her fena width, grof- fezza,ne depth , with which fi i.irconfcriuono all the figurc, which from the idea are stopped: nefideueineila trust any part of matter/) body^ but fempreimaginarlajCñmc ieniphcelungiicz^a B C, which does not wait for anything else, which rapprcfcncncntato those forms, which fi \will do. D I F F I N I T “ O N E III. The parallel lines, two lines, are two, but more, as fi sees from these two letters FD, Gé, pull equally lonlane the vna from the otherj'altrajfi that will go in infinity '^er lengthj don't ever reach the end of the line. DIFFINITION lV The AngoIo.s'appeUa that part, doue two lines fi come to join together, that is the IH, HK, which fi join in H, douc form in the last part the angle. DIFFINITION V. t h e dluerfity of the angles, it will be possible to refere in three ways, that is, Taciitoper L, romifoper M, &iIreftoper N, doue the perpŽdicular line fal'vno, and the other right angle N^ & the acute L/will be the minor of the rectum, the octulo M, the major , DIFFINITION VI If the right angle is the right angle, it is formed by two lines that are flat, and the other one is perpendicular, and this angle is determined, and perfect in all the fabrications. If you make it in this way, that is to say, in A B, the line in pious, which will be divided into two parts BDA, noting the point D, where it will want to form the corner, and then stop the tip of the line in A, and with the other one, widening up to B, will pull the semicircle BH, and similarly from the part B, the other semicircle AF, and douse quite two lines fi will come to intercept each other (i.e. in C) he will make the principle of the straight line, which will be perpendicular to the point, D, fi that the part, CB, will make to the CA; And so the right angle BDC, to the ADC, which we will prefix to demonstrate". DIFFINITION VII The circle is a flat figure, contained by a line, called a circumference, in the middle of which is the point C 5 from which all the straight lines, which go to the circumference AB, I am equal to each other, & that point is called the center of the circle. DIFFINITION VII, The equilateral triangle is formed with three equal lines, which are joined to their tefte N M 0,ferrando the fuperl“cie P, THE ifochclcj triangle is formed and two lines isgua . lij that is for Je R S, SQ^ & your R Q^ unequal. The triangle of three unequal kti , called fcaIeno> is made with unequal tics lynx, which phono TV, Vi" ST. D I F F I N I T T O N E IX. The orthogonal triangle is formed with the right angle B^, for the part B A, B C, with the diagonal A C, which is the destination of the perfect picture. Seque Tambligonio j which can clTcr of three unequal sides, & with the right angle E, for the parts ED, DF, Fƒ, check half of a wide square. The form G; vicn called rhombus , formed with two angoliottufi s & with two acute of equal sides . D I F F I N I T I O N E X. II qu;,dro perfect E, is formed with four equal lines, with right angles from ciafchcduna dclk lue parts . II long square FG, is formed with two paralel lines, &le fue tcfte joined with two other perpenclicular lynxes at right angles. DIFFERENT COMPARTMENTS OF CIRCLES. Jrcolo H I, oucro !a circoIarc line, which perfectly forms the rot—dita of the spheiic bodies/over your centre A, will fi compartmentalize Tempre per mcrˆ^ by pulling the line C B, which palfi fopra and helium fuo centrojche - both the fupert“cic A Hj and A I. It will be the most perfect form of cipherh of tiittcIeaItrc,attefo cheviŽ ' formed with vna fola line fopra Ilio centrojche,doue neceffectively comes of each frame to elTer pulled with equal proportion, fenza allonranarle^o auuicinarfcgli more in vna part than in the other. And yet, "all those who will be partworked from the aforesaid centre to your circumference, will be equal to each other; feruŽdonc such form by foundation, & by certainty guide in all operations, in the forSea, those bodies, or surfaces, which can be necessary, and badly needed, to cleanse the corners, which in the fcguŽti Fortresses there will moftrate. And before we will first propose the will from the prefent circle AB, we will cauare the perfect picture, from which the fc will be able to hauerela right to compartmentalize all the other forms of angles diuerf“; that is compartifcafila said circumference in four equal parts AC, & B C, pulling the lines from vn point al“'akw/i hauera foramato the aforesaid picture. Et wanting to form the figures of five ^ and of fei angles, & the others, which follow, fi fi will always divide the circumference in that number of parts, or else angles, which fi will want ^ pulling then the lines in the way, you said. And that's what they call a practice compartire. There are also other ways, & other rules to make such compartments, for theorica , liquors we will moftrate , not because it is necessary to make the faperl i, but they will fi noterannOj As we like Geometric j attefo, and that the true , & jufto compartment is that , which fi ago with the opening of the compfibper practical. And first to defray the pcntangle, which is figure of five angles, fi will form the circus. I of that greatness ^ that will make them efler your diameter, that we place the C D, perpendicular diameter, & the EF, horizontal, so that it comes to compare in four equal parts your circumference j, comparing then vna of the two parts of the mezo .diameter, jn mezo j that will make in F, doue fi will stop vna tip the compafio, widening the other until the circumference of mezo in D, & by pulling the femicircle E D, fi will notice the sign E, from which fi will pull a straight line, until the D, which will make E D^ laquale will come to elTere vna of the five parts of the quintangle, opentango lo> that we doueueueurare . The compartment of the corners will make the most facikjattefo that of all the citcoli refer to you with the compass, your circumference contains as many times as your opening will make, from which then, that the compass will be appealed to you. The slice of the angle, which will follow the line B C, in your circumference7a; then the half that, which will do in D, will draw the line perpendicular to your center, which will make AD, & replicated slices times in the circumference, will form the propofect figure of the sliced corners. It will also be possible to divide the circle in as many parts as we would like, i.e. in as many parts as we would like the five angles^comparting the circle in as many parts as we would like the five angles^comparting the circle in as many parts. compartifca the circumference of the four parts, which we will say fia B C,iii five jdelle quali parti fŽ ne deono deono pigliar quattro, che farˆ in E, & tirarla straight line E B, che farˆ vna delle £Jnque parti di tuttoala circonferenza . And to conclude it, the vor- If you have the fei, or the fettcjouero the eight corners, and as many as you want to do, the four parts of the circle will always start in that number of corners, with whomever you want to cover them. & then taking four of the four parts of the circle, fi will pull the diametrical line, which will always make the predctcc partijcon partijcon which will give the whole circle is there as fi sees in the ED part, for the DF, which feiuc per k figure of fei angles. Et fc there was/will be propofto want to want to give a given circumference to another squared one equally propose donated half less, i.e. by the club A jBjC.,1 ), over the centre R, to ensure another one, which contains half of the surface of the circle, and the diametric lines A, B, C, D, & the sides of the painting, from point to point to the top or, as I see it, then defacing the fertile circle I will give to eflb the painting E G, H F, which will make the first half dd, which will moftre i & fŽ inside that fertile circle r^J. The four lines will be drawn in circumference, the four lines will form the fruitful picture, which will still make up half of the first, and likewise the third circle, which will make up the fourth part of the first. From the circular body there is, as has been said, the right angle, which is truly the soul of all the operations that make up the vfo of the Gcomctrici flowers to be built, as well as in architecture, in the construction of public buildings, & deprived, with that greater beauty^ & comfort, which fi dcfidera j & however all the forms (although of unequal sides, doucl“ poflfa by vna part form helium right angle)fi poflbno co'l half of that proportion, <5 ^ mifurare . Yes as for eflempio fi will see for the three different angles, that is the triangle of equal sides A: B, C, fi reduces in a long square with the pulling of the perpendicular hnea CH, over the bafe R B^ fi that in H, comes to form the right angle, & pulling with the fiefib ango lo the part A D, & D C, equal to the part of the bafe H B, fi will form the propofto square along A D, C H, to make equal the afe DC, to the H B, & the triangle G, to the triangle Y. Then follows the fertile triangle of unequal sides, that is A,B,C, which diuifa the height C, over the bafe A B, in two equal parts, which will make it in F, & transfportandola part, ouero the height of F C, to the tefte of ella bafe, that is in B D, & A E, at right angles, co'l pull the line D E, fi will form the long square AB, DE, equal to the triangle called A,BX, for cfier equal to triangle N And for the holding, & vit“mo TS C with the right angle S, ef“endo CT, the diagonal of the painting.fi will compartmentalize the S C, in two parts, that is in D, & translating the D Q in T V, at right angles over the bay S T, co'l pull the D V, fi will come to forriiarc the long painting D V, T Sj equal to triangle T 5 C, for cfitr fimilnicnte egua The two triangles A R . CI refines for last to moflrarc,comc fi fi stop in four ways the ouati, i.e. with*^ triangles , & with quadrangles , & circles, the first tbnnifi lt opra la bafe AB, the two triangles of equal sides, i.e. A B D^ & A B C, doucndoll do the C, center to pull the part of the circle E G, pull the F H, & B A, for the tede H E, & G E. Then follow the two squares R S , to form the propofto ouato , that is for the part of the circle P Q^ fi will do the center L, & fimilmcnte for the N OM , & for the tcfle P O , And then the third with the three circles for the circumference FI, the center will make C, & pearl HLDjlciefte LI, “ H, are made by the ItelTi circles. It will be possible to form the propofto ouato fcmplicemcntc , with a double rope , with no rope at all. dcIJc said olkruanoni of the circles, or of the angolijcio c—partifcafi fopra vn pianola mon- The length, which will be given to him, for cficisipio will make D C, in eight parts, of which she will take her, who will make the AB, l.ifciandone from each of the ine tits, vna, that is AC, BD, douc fi fi will stick the duecauicchi, or nails, A B, to which fi auolgcrˆ doubly vna rope fotnlc, oucro fpago well tied to the tcftc, which is so double, along the fpatio A D, i.e. of sliced parts, taking then another caiicchio, ochiodo, &conia fua tip nicffo in the tefta between the two ropes, fi andari holding them so pulled, defcriuendo the line D E, C D, co'i fai e fcorrer feu“pre the said rope as follows double among the Duecauicchi AB, with which fi will come to form, fi as others like it, ouato circle. As the hip of the whole body^he can read us J lecondo, & iJ fifth Book of Colmo Bartoli on the subject dd mifurare , doue f rouerˆ Ja clarity of all fue pardj with moki other details very vtili j si for the science as for the practice of the fcgue. REGOLA PER FORMARELE PIANTE DELLE FORTEZZE. CON LE LOR MISVRE C A P. I, SOGLIONO ef^crc le regole di non poco g“ouamcnto a tutti, per Io molto benefici, con liquali prtfuppongo ad prefente ragionare j perche da quelle fi viene a poflederc il vero fondamento della fcienza , & infieme ˆ tener memoria delle parti pi notabili, che fi ricercano neli'operarei Et concorrendoci la diletta tione , fi verrˆ ad apprendere e/la icicnza , con quella maggior facilitˆ , che li pofla defiderare , e particolarmente nel comporre, e defcriuere le feguenti piante j attefo che dipendendo qiiefte da' lineamenti, e da compartimenti di circoli^ fempre , che fi lapri Ja proportione di vna fola di ef“e piante di Fortezza, ouer corpo di baluardo, fi potranno fapere tutte le alrrcche occorreranno farfii accrefcendole, ˜ fminuendole, conforme a fiti, come al fuo luogo ii dirˆ . Et prima proporremo voler formare vna pianta d'vna Forrezza di lati eguali , fi come anco iaranno le altre chefeguono, cio che i baluardi vengano egualmente dittanti l'vno dall'altro , douc iarˆ neceflario di defcriuere vn circolo fopra la carta, ouero altra materia , in cui fi vorrˆ formare efja piantaj & quello egualmente compartire in tante parti ,quanti faranno i baluardi , che fi vorranno c“rcohre fabricare j & per˜ diremo d'hauer delcritto con la punta mobile dei compaflo il circolo , che per lo cellario p diametro A B, fi vede,con la hnea morta , fatta di punti ; ilqual circolo , per elTempio , s'intenda di p¡ªe^',fi volercou“partireinottopartijper formare otto baluardi, che faranno notati per LRS, con glia!È la Forteztri, che fceuono ; e tirate che fi haucranno le linee rette , da vn punto all'altro , fi faranno formati gli E^. etto angoli, fopra li quali fi debbono defcriuere i liioi baluardi,con quelle mifure, & prorortioni, che n^a j, ocVo pi li pollano appoi tal e difefaj elTcndo per˜ necefiaiio prima deliberare la iorte della mifura, con baluardi . thcfi vorrˆ formare, e mifurare tutto il corpo della Fortezzaiondeperpigliar lapi familiare,ci feruiremodel braccio Fiorentino,oueio del paflo Vinitiano,ilqual pafio contiene tre di elle braccia, & le loi- mijlpaflo cinque piedi, fi come ne' due feguenti du'cgni fi vedcjper AB, milura d'vn piede Vinitia- Iurej“o, compartito in dodeci oncicje per C D. il mtzo braccio Fiorentino i con lequali mifure faranno formati tutti i diftgni della preicntc opera . Et hauendo fiabilito (Ci^n.c s\ detto) la mifura, della quale ci vorremo leruirc , fi douerˆ poi ftabilire la lunghezza delle difefe, che fi vorranno dare a efla Fortezzajcio quanto douerˆ effere la diftantia dal fianco (luogo ddk artiglierie) alia punta dell'angolo intcriore dell'altro Laluaido, che gli firˆ incontro ; ilquale dcue ei:er guai dato, e difefo da clTe .!rtiglierie,dipendendo da quefta mifura, onero diftantia tutta la perk'ttir.ne,& ia imperfetiione del' Ja Fortezzaiperche ef“endo fatta coli troppa lunga difefa,le artiglierie de' fianchi non vi potrebbono ^f^rnfˆce iare quella gran pallata , che bifr gnc ria nelle difcfc di terra, ˜ d'altra materia , che il ni.iiico faceffe co propor per trauerlare , & impadronirfi dei follo , ne meno arriuarcbbono le palle di piombo da mofchetto , tionac^ mi jnefie nelli facchctti,pcr tirare con le artiglierie,a otfefa di elio nimico,come an;o all'incontro, elTen me\'íro*flo fatta la difefa troppo corta ( dopo che fi doueria fabricare pi numero di baluardi) i fuoi fianchi fefa.nedierrebbono cfpolti ali 'ellere imboLcati,e per con fcguenza ammazzati i Bombardieri da gii archibunimici,che Ifanno di fuori afcofi ^e coperti intorno la contralcarpa ,& ancora le piazze de' ba- jeHa porTuardi verrebbono piccole,e con affai deboli difefe,e tanto pi facendo a proportione piccolo il fian tcTza . cojeffetti tutti da fuggire,volendo bene,e con ragione fortificaie,e mafl“me in pian0j& in fito efpHo ˆ potente nimico,come del tutto a fuo luogo fŽ n'alfegneranno le ragionijC folo al prefente dire- fettioni . mo , che la detta difefa dal fianco alla punta del baluardo , fia di paffi i8o. che farˆ delle pi lunghe, che fi debbcn fare , quali fono braccia intorno a 540. & per˜ volendo per elTempio formare gli otto .e non angoli delti di fopra, fi farˆ che ciafcuna delle otto parti fieno i detti paffi cento ottan ta,cio,fi ccm- vuok eiparrirˆ per effempio la R S, in none parti \guali,che ciafcuna di quelle farˆ di palla venti,con lequa Jj'',li fi noterˆ la fcala AB. di pafIacento,c—par'tcndola poi in quelle pi minute parti,che fi potrˆ ,e per /;, neVa“ lo meno in dieci,come fi vedci& quefta farˆ la giufta,c real mifura di detta pianta con la propoila di cento ottanta pai!!, pei cf“ciele dette parti R S, cgiu“i ci'ogn 'intorno alla fua circonfcrcn. i, &. la diftanza , che dee efiere dal fianco d'vn baluardo aJja punta dell'altro H V, che la lunoI“C7Z i della detta difefa , & douendofi con la propofta fcala miAirare, & proportionare li membri con iiitro the body of the Fortress, we will give principle to the bulwark , as head of cfib body j ilqualc va tormato over the corners in four different ways, that is. Piglili from the fcala the length ofpaffi thirty joueio arms nouantaj& stop the tip of the compafio fopra the corner Lj& with the other one on each side fi note i points G K, which will make the width of the bulwark throat , ouero your corner intc“ ioie L H G, & The childish blusher fbprays all the other corners of the bulwarks: taking then vnafquadict'.a , will pull Ja line HI, purlunga paia thirty at least ^ that falls in said point H, & face right angle over the line, oucr cortina H N, & the imile fi will do to the other side GM, & fopra turci the other bjl'Ja'rJ. ^ The intcriori angles of the bulwarks, pulling always the first few lines with pencils, so that we can make a mistake in pulling them, but / so that they do not reltar dcfcritte with the nail, a task that will sign the dilegno, fi fi as for the dotted lines fi will see. And in order to form the said bastions, it is necessary to take the difefa of its farthest fronts Difefa de dalfianco, which will be able to do so, cjoc in the length of the curtain, & quefto fi will do so in order to make the ef- l^aluardo, fa difefa , because by making a preface to the half of the curtain (as it can still do there in the proposed Je pagliare' cttangoJo 5 & so much more so than the others, which are running) such part of the curtain, (that is your square inside) will come to rare the office, which makes the side; & mafl“me with your caualierc in the fcoprije, & in defending the phofiT , with the front of the bulwark. Nevertheless, in order to move how much Ila Ja diiferenza in taking elfa difefa from the third, or from the half of said curtain, we will form to the prefect your bastions, sung by the third j that is fi fi will divide each curtain in three parts, as fi sees, pearl NH, in P O, doue pofla the line fopra the pimto O, & at the end of the line of the pronre dd £anco I, fŽ will pull another one, which goes in infinity, & fimilmente on the other side pulling the baluanio ZM, and doue fi interfecherˆ fopra the first Qj^iuj fopra the inferior angle, ouero the tip of the bulwark MQJ. And to form the balls, orero mumps, which come to cover that part of the flank, doue deuono flar the artillery, fi will compartmentalize the line MG, (which we said effer thirty pale) in three parts; two of which will give it for the groifness of the ball, which cut M Y, & vna to the width of the flank YG, & in vltimo fi will form (to iron the bulwark) fr—fedd ba the half circle X &. But taking the difefa from the half of the curtain, as for V T, fi sees ef- luardo, cofer formed the angle K, although rather more acute than the other first one, fi potila therefore compose- "ormaretare , venendosi la contrafcarpa fcouata dal fianco , che nella difefa cauata dal terzo non fi pu˜, fi as i^ sees for t"= (f, ilqual folfo fi dee form in this way, that is, the wide face, I meet the angle Q^ of the bulwark j paifi thirty, which will make YES, and being able to make, that the contrafcar- P'fef" sweatshirt, will be fpazzled from the side, fi will pull to such straightness; but not being able to do so, it will make us paralell the Q&& front, until the MrC side: ...is no quicker than the Q.J.P., than the trusting. make it at least more imperfect, that it does not eviler such part fcoperta, making it looked at from the other squares, & caualieri di fopra . PLAN OF SEVEN CORNERS. CAP. II. If we want to form the fctrangoIo,oucro vna fortress with slices ba!uardi,fi could fenza any alteratone (false that of fc takes Ja of fc ago to the half of the curtain)v{arlc previous mifureaffcgna The garden with the aitinoli garden, to make this form involves angles, which can be called mc iaranno all from the firm jn up,aptly that in the ftfl:o,& in the fifth.that they run at a whisker their ramparts of vcrrebbono too sharp,& very long forehead,which would bring not a little imperfection to the Fortczzai& for this cjfiequire fi defcriua fopra the center divided into sliced parts as fi as fi sees. But to vary difefa, & to make it more vtiJe we will propose to make 1 60. onde fi fcompartifcainS.partcIaJinea E Q^ &dafcunafarˆ2o. pafl“jConliquaJififormerˆlafcaJa TS, dipafi“ 100. and wanting to form! bastions, fi will notice on two sides the intcriorous needle of pail“ thirty, as we have said, and fi sees for E F I , forming with the IkfTa mifura the lynxes, which make the right angle of the goi—. side F H , If IR, fopra h cortina Pia fcgucendo the reflex with the already said mifure ^ and proportioni . SIX-CORNER PLAN, CAP. III. If the Fortress is to be built with bulwarks, and if the length of the fortress is to be five hundred and fifty arms, then it is to be divided into two parts, which for the Temple, it is to be eleven, and each arm is to be fifty, fi that with four of effective parts fi will be able to make the fcaja of arms ducente i and to form the ramparts we will propose to take Ja difcia from the fourth h {>o,ne ^^"^ curtain,which will make F O, dcfcriuendo the front G, although fi pofla also take called djfefa from the from the third one forming Ja fronte H, "Scfiacquifterebbe lofpatio PF, doucporriaftare more va of the cor. piece of art iglieria^for such a difefa, nevertheless the angle H, will come rather of too much acuity.Ëu douendofi f abricare that part, which is fcopcrta by the enemy, with the femplicc earth, & somewhat circular for greater safety, fi can involve such fua acutezzaj& all the more coming ia ia)xx wall from bailo^copcrta from the height of the contrafcarpa^comc to your place will tell them. VLTIMA PLANT OF CINQVE A N G O L L C A P. I I I I. THIS plan fi can call the last of those j that fi dcuono fortify, I believe that the shape quadraraj and maflime the triangular, for the last body formed, folo with three lines, not Ci pofibno, nor fi dcuono fortify, so that it is already not necessary to build campal forts, made with the femplicc earth, to prevent thepaflo of the f“rade, and of* rivers, in the will to aficdiarc vna Fortress, oucro foitificarc vn fito montuofo, not efporto fc not to batteries from hand, ficomealfine of the fertile Book fi moftrerˆ . And in order to form a fifth angle, we will propose to make the fue difcfe long arms five hundred twenty, although the more effective they will make long in the acute angles, the more they will be able to make the squares wide, and the fronts of the bulwarks octufi i ftantc Ja length of cfledifefejma bring.ino then the oppofitioni already said . But form the fcala, for which fi deue fi deue to divide into threedjcci parts on either side of the said angle, which will be the fegnato A B , & each of the headlights forty arms, forming your fcala , As then to form the ramparts , & to escape those angles, cjie per natupA brings the shape foprafcritta , fi will be able to pull the first line of the flank C F j of arms fcttˆntacinque, which are pawed 2 5 . & to escape even the sharpness of bulwarks will be able to refrain your throat, & make it of palfi 40. at least, & make the flanks conna {ol square, taking the difefa from the fifth, which will make B R, Q^, & fi will form the forehead F S D , Jbpra the inner corner A CE . Auertendochelemifure already affixed to the Fortress, not iideuouo ffŽ fŽ not for nece/fitˆ dd fito j & for the sharpness of the angle intcriore , doue you have to plant the bulwark, so that it does not come with too long fronts, & even for the sharpness of the angle infeTíore, for the reasons said, & that will tell . Of the two bishops held for the sake of the victory: The ratiiie of the features in defacing the fudette four plants, or rather as a neccfiary foundation, to identify it well, in order to understand the effects of the fingers that can give to the fronts of the ramparts of the hilarious bulwarks the diuerfity of the corners, & for the prcualci fi Icmpre of the miles^ & more comfortable for the claws of the hips, & as it has been said to flee the corners^ that for the too much accuEezzapotefTcro e“lere Difcfi. OF THE COMPARTMENT OF CIRCLES AND PROPORTIONI, WHICH FIND THEMSELVES IN THE DIVERSITY OF THE CORNERS. C A P, V . From the pronortlone, which will find a hefiere in the compartments of spherical bodies formed with a femplicc vna line, dcfcritra around your center, ficaucˆfempre fenza any errorc the proportion of any other body, or surface, depending entirely on compartments jcauati by efla fua circumference; because cf“! cndo equal, or unequal between them, will be proportioned to similar fcmpre fcmpre all those, which will depend on and / or will depend on: although greater, or lesser size, cerne more will like, but in accordance with the measures of the fcala, that fi f blush in forming the defenses, ouero cficquirc the work, which should be made real. And because it is necessary for the prefect to deal with the diuerfity of the corners, which can be necessary in the Fortifications, in the phytophile over the ramparts, he will make us cognizant of the diuerfity, which he finds among them j and conofcere for theorica hperfejtioni, 6th imperfections, which he can bring in practice; and for ellequir, form the said circle over the centre A , until your circumference over the CD , half of the circle will be divided into one hundred and eighty degrees , which will be that part of the Zodiac ^ D G C , which (over the Orizonte stone , and by dividing this circumference into three parts, and drawing the line at your centre, you will have formed the triangle of equal sides, noted for 5, which will be A F C, that is, of degrees feflanta fopra eJTo Orizonte CD, and by dividing it into two fi will form the picture with the right angle marked for 4. which will make AGCj, of degrees nouanta , & the fifth angle fati, A C H 5 of grndi one hundred octants; the fefto angle vˆ , A C I ^ of degrees one hundred twenty; the fettimo A C L , of degrees one hundred twenty eight, and the octane, ACM, of degrees one hundred thirty-fivec; and how much then to the ninth^decimo , & to others, which feguono,! With the order of the compartments, and numbers, he may, by taking order of compartments and numbers, open the form and nature of all the others, which may be necessary; there that they may come in the last minute, so much octulij that they will be in a straight line, and equal to the said Juo Orizonte^ which he will do to the line of degrees cCto ctcanta . If you can still see in the other part of the other part, when the elf Orizonte C D is blasted, the angles of the circle elf will be the circumference of the Turkish elf, and noted with their number, that is, from the fifth to the fourth to the fourth ten'Uo equal in their first sayings of fopra; with the half of which, and of which of these degrees, it will always be possible to determine the difefc of the Fortress, not only in the difpute, but in the operations it will not make any error. THE STRATAGEM TO BE TAKEN BY THE ANGOLA ET TO BE TRANSPORTED IN SEVERAL SIZES. C A P. V I . QU A N D O that with the intelligence of lineamcnti, which by Th corica we must mean, fi will add practical chicken of the former; to eidequirequire as much, that he will make books out of them, and that operations will not be easy, but amateurish, and this he will do with the half of the mathematical instruments, and among the easy ones, he will make the team up to form not only the books, But the ilfelfe is a real work, and this instrument is made of metal with a circular shape, which gives the perieption of all the other instruments, because it is divided into two parts in a circumference, so that the diameter, oucro TOrizonte, that ball above the centre from which all the lines, which will be drawn from helium centre to circumference, will be equal, & will clearly form their angles, and though in small form, they will always be equal to each other in every greatness, & propose of mifura, which fquadra fi sees in the feguent difcgno for A B C 5 Squadrazoc and deue cfier fabricata, and with much diligence involves, that is, tin with two lines in the way of compafio c—giiitc inficine in the tefte,ouero in cŽtro A; & rather far away from two jointfier efier the femicircolio DE,c—partito in cento ottanta gradi,che farˆ pari al foprafcritto,doue fi potranno vedere tutti li angoli^ come s' detto. Aucf tcndo^cke the tefta of the femicircle E, fia incafiata, and still motionless in the part outside the arm AB, as fi sees in E, & the fimile in the other CAj in Gj doue A will make the center of the World . Et il feniicircolo E G Dj fopraalnoftro orizonte D E , doue fcinpre we find ourselves, so that alarming the arm AC, comes to Scroll through the said femicircle until the end of the fuatcfta D, &ef]cndo A, center, & AD, half of the diameter DE, which will have the angle AG E, when opening, & ironing the arm AC, will femprc the ifleifa of the A B C j clTendoui make difference the size of the flroment , that mof“ra the angle in magoiorc, or in lesser form, although for the proposition of the fue mifure f“a fempre fno fteflo , & in the occaf“oni will bring the way to translate the dikgni of great in small, orero of small in gran di , conforming to cfle mifure , not needing fapcr 'other, that the number of degrees of fuabafe E G , that fenza akun'erroic, it will moflrrerˆ the shape of the angle contained over the said center A, so that the cloth trafffa trafportar from vn defegno to the other, or pull the strings of vn bastion, orero the whole body of the Fortress, in defcgnare your fundamentals j and for example we will say want the prefect to form the anoolo right, but fi afiargheid the mobile part C, for infino al fegno I, until it is over the line Al, that is to say, for the purpose of nouanta degrees, & fi will have formed the said right angle ABI,ficomc still opening it perinfino R, at degrees cent'otto . But if we begin the tenth, not on the D side, but on the E side, & this was done by mistake, though not by mistake, by numbering it by tens, & this made the fifth angle, &in S, ilfeflo; and with this order will all "^! the others, who will need to be able, because of the numbers, to open the form a and the nature of said angles, to be able to fortify them.