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Library/Paris Manuscript L/95

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Paris Manuscript L — 95

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Bibliothèque de l'Institut de France, Paris

Dico1 adunque la bombardiera, la quale sarà larga di fori e stretta di dentro, in quanto alla potenzia dello offensore essere di più faticosa expugnazione che quella che contrariamente è situata.

Proposizione.

Quella proporzione che hanno in fra loro la grossezza delli angoli traversalmente percossi, tale arà la resistenzia da loro fatta contro al loro percussore.

Adunque l'angolo o p q, per essere molto più grosso che l'angolo n m q, sarà di maggiore resistenzia, con ciò sia che 'l lato p q ha molto più potenzia contro alla potenzia della linia o p, che non ha la linia p m contro alla potenzia della linia n m. Ma vera cosa è che la linia f c per essere situata in obbliquità mezzana, el colpo è minore il doppio in f c che in f a, ultimo grado d'essa obbliquità.

I say, then, that the embrasure which is wide at its opening and narrow within is, as regards the power of the attacker, more laborious to storm than the one situated the contrary way.

Proposition.

Whatever proportion the thickness of the transversally struck angles have among themselves, such will be the resistance they make against their striker.

Therefore the angle o p q, being much thicker than the angle n m q, will be of greater resistance, inasmuch as the side p q has much more power against the power of the line o p than the line p m has against the power of the line n m. But it is true that the line f c, being set at middling obliquity, receives a blow that is smaller by half at f c than at f a, the last degree of that obliquity.

The Splayed Embrasure Hardest to Storm

Why a gun-loop wide at the mouth resists the attacker's shot best

Weapons & Fortification Physics & Mechanics Geometry

Leonardo argues that an embrasure (bombardiera) wide at the mouth and narrow within is, from the attacker's standpoint, harder to storm than one shaped the opposite way. A stated proposition holds that the resistance an angle offers to a striker is proportional to the thickness of the transversally struck angles. He works this through the lettered angles o p q and n m q, showing the thicker angle o p q resists more, and adds that a line f c set at middling obliquity receives a blow only half as strong as the line f a at the extreme degree of slant. A small ball-and-angle sketch sits within the text.

On this page

An embrasure wide at the mouth, narrow within, best resists assault

Leonardo states that a bombardiera wide at its opening and narrow inside is more laborious for an attacker to storm than one built the reverse way. This ties the geometry of the gun-loop directly to its defensive strength against artillery.

Thicker struck angles offer greater resistance to the blow

By the proposition, the resistance an angle makes against its striker is proportional to the thickness of the transversally struck angles. Thus angle o p q, being much thicker than n m q, resists more, since side p q has more power against line o p than line p m has against line n m; and line f c, at middling obliquity, takes a blow half as strong as line f a at the last degree of slant.

Reader's Edition — described with AI from the e-Leo transcription.