de neuer
perceaue what a demonstration was, no not so muche, as whether
there were any or none, tyll he had by geometrie gotten abilitee
to vnderstande it, although he heard the beste teachers that
were in his tyme. It shuld be to longe and nedelesse also to
declare what helpe all other artes Mathematicall haue by
geometrie, sith it is the grounde of all theyr certeintie, and
no man studious in them is so doubtful therof, that he shall
nede any persuasion to procure credite thereto. For he can not
reade .ij. lines almoste in any mathematicall science, but he
shall espie the nedefulnes of geometrie. But to auoyde
tediousnesse I will make an ende hereof with that famous
sentence of auncient Pythagoras, That who so will trauayle by
learnyng to attayne wysedome, shall neuer approche to any
excellencie without the artes mathematicall, and especially
Arithmetike and Geometrie.

And yf I shall somewhat speake of noble men, and gouernours of
realmes, howe needefull Geometrye maye bee vnto them, then must
I repete all that I haue sayde before, sithe in them ought all
knowledge to abounde, namely that maye appertaine either to good
gouernaunce in time of peace, eyther wittye pollicies in time of
warre. For ministration of good lawes in time of peace Lycurgus
example with the testimonies of Plato and Aristotle may suffise.
And as for warres, I might thinke it sufficient that Vegetius
hath written, and after him Valturius in commendation of
Geometry, for vse of warres, but all their woordes seeme to saye
nothinge, in comparison to the example of Archimedes worthy
woorkes make by geometrie, for the defence of his countrey, to
reade the wonderfull praise of his wittie deuises, set foorthe
by the most famous hystories of Liuius, Plutarche, and Plinie,
and all other hystoriographiers, whyche wryte of the stronge
siege of _Syracusae_ made by that valiant capitayne, and noble
warriour _Marcellus_, whose power was so great, that all men
meruayled how that one citee coulde withstande his wonderfull
force so longe. But much more woulde they meruaile, if they
vnderstode that one man onely dyd withstand all Marcellus
strength, and with counter engines destroied his engines to the
vtter astonyshment of _Marcellus_, and all that were with hym.
He had inuented suche balastelas that dyd shoote out a hundred
dartes at one shotte, to the great destruction of _Marcellus_
souldiours, wherby a fonde tale was spredde abrode, how that in
Syracusae