Teórica y práctica de fortificación (Madrid, 1598) — the printed course of a royal academy of mathematics
A captain of engineers printed in 1598 the fortification lectures he had been ordered to give in the royal academy at Madrid, after a doctor there began reading Euclid to soldiers. The book asks for Euclid and arithmetic before it asks for courage, argues that shortening the defences to musket range halves the cost of a fortress and of its garrison, and devotes its third part to how contractors cheat on lime. It also says, without embarrassment, that a castle must command the town it defends.
Why this wins its question: English coverage of the Spanish bastioned trace is about the works — Cádiz, Havana, Cartagena — and about Italian engineers; the textbook that trained the people who drew them is met, if at all, as a title in a bibliography. This object opens the 1598 sheets and quotes what the book actually asks for: Euclid I–VI, XI and XII before courage, arithmetic so that the cost can be stated before the work is begun, the musket-range doctrine argued as a halving of both fortress and garrison, and a whole third part on how lime contractors cheat and how to catch them, which is engineering administration a century before the phrase existed. It prints, from the same prologue, the claim that beginners were designing usable traces within weeks — flagged as the teacher's own report of his own class — and the sentence saying the point was that Spaniards should lack nothing needed for war, together with the rule that a castle must command the town it defends. The one thing the entry refuses to do is the thing a summary would do: it makes no American claim, because the pages read make none.
Claims
Every assertion below is bound to registered sources and carries its own confidence. Weight them; do not treat the page as uniformly authoritative.
The book was printed in Madrid by Luis Sánchez in 1598 as "Teorica y practica de fortificacion, conforme las medidas y defensas destos tiempos, repartida en tres partes", by "el Capitan Christoual de Rojas, Ingeniero del Rey nuestro señor", and dedicated on its title page to the heir, "Principe nuestro señor Don Felipe III".
Its prologue says the book began as teaching, not as authorship: the doctor printed there as Iulian Ferrofino, "que con la professión de leyes acompaña la de las ciencias Matematicas", had begun to read the Geometry of Euclid in "la academia Real" with a large attendance, and Rojas was charged to lecture on fortification there because the material was improper for none of the hearers and "muchos soldados virtuosos, que acudian à la Academia, desseauan saberla". The man who pressed for it is named — don Francisco Arias de Bobadilla, Conde de Puñonrostro and maestre de campo general.
The same prologue makes a claim about what that teaching achieved and is the only witness to it: within a few lessons pupils who had had no prior grounding "truxeron traças de fortificaciones con tanta razon y medida, como si muchos años huuieran tratado esta professión", and Rojas confesses of himself "que en veinte años destos estudios no auia aprendido mas, q ellos en estas pocas lecciones", for want of anyone to teach him particularly. Bobadilla then persuaded him to put in writing what he had taught by word, "para q participassen los ausentes".
Before printing he took the opinion of Juan de Herrera, "criado de su Magestad, varon en las ciencias Matematicas tan excelente, que no menos puede España preciarse de tal hijo, que Sicilia de Archimedes, y Italia de Vitruuio", chosen by the king to design his great fabrics and that of San Lorenço el Real, "que es oy la mas famosa y costosa del mundo"; and of the comendador Tiburcio Espanochi, who attended some of the lectures. The chain of authority behind the printed course is therefore the Escorial architect and the crown's chief engineer.
Chapter I sets the qualifications in order and puts mathematics first: three things must concur in the soldier or engineer who would treat fortification perfectly — to know much of mathematics, "si fuere possible, los seis primeros libros de Euclides, y el vndecimo y duodecimo"; then arithmetic, "que sirue para dar cuenta del gasto que para hazer la fabrica se ofrecera antes que se haga, o despues de hecha"; and third and most principal, to know how to reconnoitre the site where the fortress is to stand, which the book says is difficult to teach to an engineer who has not been at war.
The book states a doctrine of economy that it credits to experience rather than to the ancients: the measures written by "los Ingenieros antiguos" no longer serve, because they laid out their defences at cannon range, while "los soldados ingenieros de aora han hallado con la experiencia, que la fortificacion sea mas recogida, reduziendo las defensas a tiro de mosquete y arcabuz" — which, it says, comes to "la mitad de menos costa de fortificacion, y de gente que la guarde", the engineer's standing duty being "de ahorrar lo mas que pudiere en la fabrica, no quitandole su fortaleza".
Its rules for fortifying a coast are written for ports that can be relieved only by sea: a fortress "a la marina" must be planted so that it can be succoured by sea without the enemy being able to cut the passage, and coasts with many coves are to be avoided, "donde pueda estar surgido el enemigo: porque desde alli echa gente en tierra, y destruye la campaña al dicho castillo, y le corta la mar". The same chapter says plainly what a castle above a town is for: it must stand "a cauallero sobre la campaña, y juntamente que señoree la villa", and be raised so that it can be relieved from the friendly side and not be besieged along with the town it protects.
The third part is an anti-fraud manual for public works, and is the least quoted part of the book. It warns that the contracts for lime are where the money and the building are lost: the caleros, having contracted to deliver lime burnt from hard stone, look instead for soft rough stone, easier to fire and cheaper to quarry, "y respeto desto va à dezir en el precio la mitad del dinero, y lo peor es el daño que se seguira à la fabrica"; the veedor and "hombres de papeles" cannot tell good lime from bad because bad lime is whiter and handsomer; the practical men on site are often kin or compadres of the contractors and "suelen yr à la parte en este engaño, y en lugar de ser dos al mohino, vienen à ser tres". Its remedy is an inspection by "vna persona de ciencia y conciencia" sent to the kilns.
The purpose the prologue avows is military and national, and the object records it rather than softening it: the lectures were written out so that "no les faltasse a los Españoles ninguna cosa de las que son menester para la guerra, en la qual oy (sea dicho con paz de las otras naciones) tanto se adelantan, que dexan inferiores las hazañas antiguas". The teaching of Euclid to soldiers described here was an instrument of war before it was anything else.
What this source cannot support is also stated. The pages opened for this entry — title, prologue, chapters I and III to V, and the third part on contracts — contain nothing about the Indies, and no claim is made here that this book was carried to America or shaped any particular American fortress; the American careers of the engineers it names are outside what was read. Nor does the volume say who dug or carried: the labour that built the works it designs appears in it only as "gente" and as cost.