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.

There is a sea coast hauing sundry harboroughes, townes, villages, castels and suche like situate thereon, whose platte in due proportion I require, with the exact distances of euery place from other, hauing therefore elected a loftie seate, from whence I may beholde all these places, (mine instrument situate as is declared) remouing the index to the fardest being a Castell standing in the mouthe of an Hauen, hauing receiued it throughe my sightes, the line fiduciall of mine Index, cutteth 30 Grades, thence remouing it to the next, being a village or fisher towne, the Index cutteth 50 degrees, againe at the next being a Citie, it cutteth 75 grades at the fourth being a great Baye I note bothe the entrances, at the Esterne side of the Baye it cutteth 75 Degrees, at the Westerne 100 Degrees, finally at the far∣dest place Westward, being a fort within the land, the Index doth cut 130 grades. Thus haue I the Table of my first station, as foloweth.

The Table of my first Station.

The Castle

30 Degrées

The Uillage,

50 Degrées

The Citye,

75 Degrées

The Esterne head of the Baye,

95 Grades

The Westerne head of the Baye,

97 ½ Grades

The Fort within the lande.

130 Grades

This done, I beholde an other highe Hill, from whence I may in like manner view all these places, & turning my Index therunto, I find the line Fiduciall lying vpon 180 degrées. Then carying my instrument thither, &

placing it in all pointes there, as it was at the first station, I turn my index againe to the first marke or castle, finding it to cut 15 grades, at the second 25 degrées, at the third 40 grades, and so to the rest as appéereth in this Ta∣ble folowing. And as I haue done of these few, so might I how many nota∣ble markes so euer there were, wryting their names seuerally with their Degrées noted, as ensueth.

The Table of my second Station.

The Castle

15 Degrées

The Uillage,

25 Degrées

The Citye,

40 Degrées

The Esterne head of the Baye,

50 Grades

The Westerne head of the Baye,

55 Grades

The Fort within the lande.

80 Grades

[illustration]

With these Tables repaire to a plaine smoothe Superficies, drawing therin a faire Circle as you sée deuided in 360 partes, and from his Centre A, I pul out right lines to euery Grade noted in my first table▪ AC the line 〈2+ pages missing〉〈2+ pages missing〉

••e castle, AD of the village, AE of the citie, and so foorth of the rest, ending 〈◊〉〈◊〉 the line AB, cutting 180 degrees in my circle, then making B a centre I 〈◊〉〈◊〉 a circle diuided as the other at A, and from his centre pull out streight 〈◊〉〈◊〉 to all those grades that were noted in my seconde table: nowe marking the ••••••course of semblable lines, that is to say, where the line of the castle issuing frō A 〈◊〉〈◊〉 with the line of the Castle proceeding from B, I note it with a starre as 〈◊〉〈◊〉 may beholde at the letter C, and thus prosecuting the like in the rest, always 〈◊〉〈◊〉 a starre or like marke vpon the concourse of correspondent right lines (all 〈◊〉〈◊〉 intersections not regarded) I haue finally situated al these places in due pro∣••••••tion, noting them with these letters CDEFGH: as in the figure you may see. Now to lerne the distance betweene euery of them, I diuide the space betweene B into 5 parts, for so many miles by mensuration I finde betwene my two 〈◊〉〈◊〉, then drawing right lines from C to D, from D to E, and so from euery one 〈◊〉〈◊〉, opening my compasse to one of these partes, I measure how many times it ••onteyned in euery of these right lines: wherby I conclude the number of miles betweene euery of them, as appeareth in the table folowing.

The Table.

The distance of euery marke from the stations.

• C 5 myles, 1 furlong.
• D 5 myles, ½ furlongs.
• F 5 myles, 3 furlongs.
• G 6 myles, 1 furlong.
• H 6 myles, 3 furlongs.
• C 9 myles, 6 furlongs.
• D 9 myles, 1 furlong.
• E 8 myles, 3 furlongs.
• F 7 myles.
• G 7 myles, 2 furlongs.
• H 5 myles.

The distance of euery marke from other.

• CD 1 myle 6 furlongs.
• CE 4 myles ½ furlongs.
• CF 5 myles 5 furlongs.
• CG 6 myles 1 ½ furlongs.
• CH 9 myles.
• DE 2 myles 3 furlongs.
• DF 4 myles 1 furlongs.
• DG 4 myles 4 furlongs.
• DH 7 myles 4 furlongs.
• EF 1 myle 7 ½ furlongs.
• EG 2 myles 2 ½ furlongs.
• EH 5 myles 5 furlongs.
• FG 5 furlongs.
• FH 3 myles 6 furlongs.
• GH 3 myles 4 furlongs.

Thus passing or chaunging your stations, you may make seueral plattes, conteyning the true proportion and distances of townes, villa∣ges, portes, rodes, hilles, riuers, and all other notable places through •••• whole Realme, but then how to reduce them all into one fayre carde or mappe you shall be taught hereafter.