A geometrical practise, named Pantometria diuided into three bookes, longimetra, planimetra, and stereometria, containing rules manifolde for mensuration of all lines, superficies and solides: with sundry straunge conclusions both by instrument and without, and also by perspectiue glasses, to set forth the true description or exact plat of an whole region: framed by Leonard Digges gentleman, lately finished by Thomas Digges his sonne. Who hathe also thereunto adioyned a mathematicall treatise of the fiue regulare Platonicall bodies, and their Metamorphosis or transformation into fiue other equilater vniforme solides Geometricall, of his owne inuention, hitherto not mentioned of by any geometricians.

Example.

SVppose a shippe on the sea C, whose distaunce I desire to knowe standing on the cliffe GFE, your glasse A equidistantly eleuate, AB the perpendicu∣lare lyne 72 inches, E your viewing station, DE the altitude of your eye 69 in∣ches, BE the distance betweene your two perpendiculare lines 20 foote, FG the heigth of the cliffe from the sea 96 pase. Now by deductings 69 inches the alti∣tude of your eye from 72 the lengthe of AB, the plumbe line from the glasse, there remayneth 3 your Diuisor; yf the grounde be leuell, otherwise ye muste adde or detracte the difference or vnequalitie according to the rules to fore gi∣uen, but here supposing your grounde leuell your diuisor remayneth 3. then re∣solue 20 foote into inches, and multiplye the same in the altitude of the cliffe vp to the glasse 98, so haue ye 23520, whiche diuided by 3 yeldeth in the quotient 7840, whiche is the exacte distaunce of that parte of the shippe whiche ye did es∣pye from the centre of your glasse.

YOu may on this manner from an highe hill or mountayne, hauing any playne or leuell grounde on the toppe, not onely measure the distance of any marke that ye can sée, but also set foorth the true platte and proportion of an whole Countrey, with all the Townes, Coastes, Harboronghes. &c.

For yf you mene circularely about your glasse, alway when you espy any marke, setting vp a staffe, writing thervppon the name of the place ye sée, whether it be village, porte, roade, or such lyke, ye shall in the end situate as it were the whole countrey in due proportion vpon your plat¦fourme, so that measuring the distaunce of euery staffe set vp from the middle lyne perpendiculare falling from the glasse, and the distaunce likewise of euery staffe from other, ye may (working by the golden rule) finde out the exacte distaunce of euery towne, village, porte, roade or suche lyke from your platfourme, and also how farre euery one is di∣stante off from other. Thus muche I thought good to open concerning the effects of a playne Glasse, very pleasant to practise, yea most exactlye seruing for the description of a playne champion countrey. But maruey∣louse are the conclusions that may be perfourmed by glasses concaue and conuex of circulare and parabolicall fourmes, vsing for multiplication of beames sometime the ayde of glasses transparent, whiche by fraction should vnite or dissipate the images or figures presented by the reflection

of other. By these kinde of glasses or rather frames of them, placed in due angles, ye may not onely set out the proportion of an whole region, yea represent before your eye the liuely ymage of euery towne, vil∣lage, &c. and that in as little or great space or place as ye will prescribe, but also augment and dilate any parcell thereof, so that whereas at the firste apparance an whole towne shall present it selfe so small and com∣pacte together that ye shall not discerne any difference of streates, ye may by applycation of glasses in due proportion cause any peculiare house, or roume thereof dilate and shew it selfe in as ample fourme as the whole towne firste appeared, so that ye shall discerne any trifle, or reade any letter lying there open, especially if the sonne beames may come vnto it, as playnly as if you wer corporally present, although it be distante from you as farre as eye can discrye: But ef these conclusions I minde not here more to intreate, hauing at large in a volume by it selfe opened the miraculous effectes of perspectiue glasses. And that not onely in matters of discouerie, but also by the sunne beames to fire, pou∣der, or any other combustible matter, whiche Archimedes is recorded to haue done at Syracusa in Sicilie, when the Romane Nauy approched that Towne. Some haue fondly surmised he did it with a portion of a section Parabolical artificially made to reflect and vnite the sonne beames a great distance of, and for the construction of this glasse take great pay∣nes with highe curiositie to write large and many intricate demonstra∣tions, but it is a méere fansie and vtterly impossible, with any one glasse whatsoeuer it be to fire any thing, onely one thousand pase off, no though it were a 100 foote ouer, marry true it is, the Parabola for his small di∣stance, most perfectly doth vnite beames, and most vehemently burneth of all other reflecting glasses. But how by applycation of mo glasses to extende this vnitie or concourse of beames in his full force, yea to aug∣ment and multiply the same, that the farder it is caried the more violent∣ly it shall pearse and burne. Hoc opus hic labor est, wherein God sparing lyfe, and the tyme with oportunitie seruing, I minde to imparte with my countrey men some suche secretes, as hath I suppose in this our age ben reuealed to very fewe, no lesse seruing for the securitie and defence of our naturall countrey, than surely to be meruailed at of straungers.