The compleat gentleman fashioning him absolute in the most necessary & commendable qualities concerning minde or bodie that may be required in a noble gentleman. By Henry Peacham, Mr. of Arts sometime of Trinity Coll: in Cambridge.

CHAP. 9. (Book 9)

Of Geometrie. (Book 9)

SInce Plato would not suffer any to enter his Schoole, which was 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, or not entred into Geometrie; and Xenocrates turned away his auditors, if vnfurni∣shed with Geometrie,* 1.1 Musicke and Astronomie, affir∣ming they were the helpes of Philosophie: I am also bound by the Loue I beare to the best arts and your stu∣dies, to giue it you also in charge. Philo the Iew calleth it the Princesse and mother of all Sciences, and excellent∣ly was it said of Plato, that God did alwaies 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉; but more diuinely of Salomon:* 1.2 That God did dispose all his creatures according to measure, number and weight; that is, by giuing the Heauens their constant and perpetuall motion, the elements their places and praedominance ac∣cording to lightnesse or grauitie, and euery creature its number and weight, without which, it were neither able to stand vpright or mooue. To the cōsideration of which depth of wisedome let vs vse the helpe of this most inge∣nious and vsefull Art, worthy the contemplation, and pra∣ctise of the greatest Princes, a Science of such importance,* 1.3 that without it, we can hardly care our bread, lie drie in our beds, buy, sell, or vse any commerce else whatsoeuer.

The subiect of Geometrie is the length, breadth, and height of all things,* 1.4 comprised vnder the figures of Tri∣angles, Squares, Circles, and Magnitudes of all sorts, with their termes or bounds.

It hath properly the name from measuring the earth, being first found out in Aegypt; for when Nilus with his ouer-flowing drowned and confounded the limits of their fields, certaine of the inhabitants more ingenious

then the rest, necessitie compelling, found out the rules of Geometry, by the benefit whereof, after the fall of the water, euery man had his owne portion of ground lot∣ted and laide out to him: so that from a few poore and weake principles at the first,* 1.5 it grew to that height that from earth it reached vp to the heauens, where it found out their Quantities, as also of the Elements and the whole world beside.

Out of Aegypt, Thales, brought it into Greece, where it receiued that perfection we see it now hath.

For by meanes hereof are found out the formes and draughts of all figures, greatnesse of all bodies, all man∣ner of measures and weights, the cunning working of all tooles, with all artificiall instruments whatsoeuer.

All engines of warre, for many whereof (being anti∣quated) we haue no proper names; as Exosters, Sam∣bukes, Catapultes, Testudo's, Scorpions, &c. Petardes Grenades, great Ordnance of all sorts.

By the benefit likewise of Geometrie,* 1.6 we haue our goodly Shippes, Galleies, Bridges, Milles, Charriots and Coaches (which were inuented in Hungarie and there called Cotzki) some with two wheeles, some with more, Pulleies and Cranes of all sorts.* 1.7

Shee also with her ingenious hand reares all curious roofes, and Arches, stately Theaters, the Columnes sim∣ple and compound, pendant Galleries, stately Win∣dowes, Turrets, &c. and first brought to light our clockes and curious Watches (vnknowne to the ancients:) lastly our kitchin Iackes, euen to the wheele-barrow. Beside whatsoeuer hath artificiall motion either by Ayre, wa∣ter, winde, sinewes or chords, as all manner of Musicall instruments, water workes and the like.

Yea, moreouer such is the infinite subtiltie, and im∣mense depth of this admirable Art, that it dares contend euen with natures selfe, in infusing life as it were, into the sencelesse bodies of wood, stone, or mettall: witnesse the

wooden doue of Archytas, so famoused not onely by A∣gellim, but many other authors beyond exception, which by reason of weights equally peized within the bodie,* 1.8 and a certaine proportion of ayre (as the Spirit of life en∣closed) flew cheerefully forth as if it had beene a liuing Doue.

Albeit Iul. Cals. Scaliger* 1.9 accounteth this Doue no great peece of workemanship, when he saith, he is able to make of his owne inuention with no great labour, a ship which shall swimme, and steere it selfe, and by the same reason that Architas his Doue was made, that is, by ta∣king the pith of rushes couered ouer with bladders, or those thinne skinnes, wherein gold-beaters beate their leaues, and wrapped about with little strings of sinewes, where when a Semicircle shal set one wheele on going; it mooning others, the wings shall stirre and mooue for∣ward. This Archytas was a most skilfull Mathematician, as it may be gathered out of Horact,* 1.10 who calleth him Mensorem, a Measurer

Et marie & terra, numero{que} carentis arena, Of sea and land, and number-wanting sand.

And not inferiour to the aforesaid Doue of Archytas was that woodden Eagle,* 1.11 which mounted vp into the aire, and flew before the Emperour to the gates of No∣rimberg of which, as also of that yron flie, that flew about a table, Salust lord of Bartas maketh mention. Ramus attributeth the inuention of either of these, in the pre∣face of his 2. booke of his Mathematicall obseruations, to Ioannes Regiom••ntanus.

Callicrates, if we may credite Plinie,* 1.12 made Antes and other such like small creatures of Iuorie, that their parts and ioynts of their legges could not be discerned.

Myrmecides Milesius also among other monuments of his skill, made a Coach or Waggon with foure

wheeles, which together with the driuer thereof, a flie could easily hide and couer with her wings: Besides a Ship with her sailes, which a little Bee could ouerspread. Varr••* 1.13 teacheth how small peeces of this nature and sub∣tilest workmanship, may be discerned, that is, saith he, by laying close about them, blacke horse haires. Of later times, Hadrian Iunius* 1.14 tels vs that he saw with great de∣light and admiration, at Mechlin in Brabans, a cherrie stone cut in the forme of a basket, wherein were fifteene paire of dice, distinct each with their spots and number, very easily of a good eye to be discerned.

And that the Ilias of Homer written,* 1.15 was enclosed within a nut, Cicere tels vs he saw it with his eyes, though Alexander thought it worthy of a farre better case, the rich Cabinet of Darius. By the statue of Homer the an∣cients vsually set a nightingale (as by Orpheus a Swanne) for the manifold varietie and sweetnesse of his voice, or the continuance or holding out to the last the same sweetnesse: for some are of opinion, that the perfection of Musicall sounds are to be discerned in the Nightingales notes. Plinie* 1.16 reckoneth vp sixteene seuerall tunes shee hath, and fitteth them to Latine words very properly as vnto Ditties, which the translator of Plinie hath nothing neere so well fitted in the English which might surely haue beene as wel done, as I haue obserued in their notes. But to returne,* 1.17 Scaliger (whether in iest or earnest I know not) tels Cardanus of a flea he saw with a long chaine of gold about his necke, kept very daintily in a boxe, and being taken forth, could skip with his chaine, and some∣time sucke his mistresses white hand, and his belly being ful, get him to his lodging againe, but this same 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 Alexander wittily scoffed, when he gaue a fellow onely a bushell of pease, for his paines of throwing euery time a pease vpon a needles point standing a pretty way off.

Archimedes to the wonder of all the world, framed a brasen heauen, wherein were the seauen planets with

their motions. Hereof Claudian wrote a wittle Epigram.

Sap••r King of Persia (as Du Bartas in the sixt day of his diuine weeke mentioneth) had an heauen of glasse, which, proudly sitting in his estate, he trod vpon with his feete, contemplating ouer the same, as if he had beene Iupiter, and vpon this occasion calling himselfe brother to the Sunne and Moone, and partner with the Starres; for in his letter to the Emperour Constantius he begin∣neth thus: Rex regum Sap••r,* 1.18 particeps Syderum, frater Soli•• & Luna, &c.

Nor must I forget that heauen of siluer sent by Ferdi∣nand the Emperour,* 1.19 to Solyman the great Turke, wherein the motions kept their true courses with those of the heauens,* 1.20 the starres arising and setting, the Planets kee∣ping their oblique motion, the Sunne Eclipsed at his iust time, and the Moone duely changing euery Moneth with the same in the Heauen. By these see the effects of this di∣uine knowledge, able to worke wonders beyond all be∣leefe, in so much as Archimedes affirmed, hee would moue the whole Earth, might a place bee giuen him whereon to stand. But I rather beleeue him, who saith, The Founda∣tion thereof shall neuer be mooued.* 1.21 Much was it, that with his left hand only, he could by his skil draw after him the weight of fiue thousand bushels of graine, and deuise (at the cost of Hier••) those rare engines, which shot small stones at hand, but great ones a farre of; by benefit of which deuice onely, while the stones fell as thicke as haile from heauen among the enemies, Syracusa was preferred from the furie of Marcellus ready to enter with a reso∣lute and most powerfull Armie. The Oracle of Apollo being demanded when the warre and miserie of Greece should haue an end, replyed: If they would double the Altar in Delos, which was of a cubique forme; which they tryed by adding another cube vnto it, but that auailed nothing. Plato then taking vpon him to expound this riddle, affirmed the Greekes, were reproued by Apollo

because they were ignorance of Geometry. Nor heerein can I blame them, since the doubling of the Cube in So∣lides, and Quadrature of the Circle in plaine, hath euer since so troubled our greatest Geometricians, that I feare except Apollo himselfe ascend from Hell to resolue his owne probleme, we shall not see it among our ordina∣rie Stone-cutters effected.

But in briefe, the vse you shall haue of Geometry, will be in suruaying your lands, affoording your opinion in building anew, or translating; making your milles aswell for grinding of corne as throwing foorth water from your lower grounds, bringing water farre off for sundry vses. Seeing the measure of Timber, stone and the like (wherein Gentlemen many times are egregiously abu∣sed and cheated by such as they trust) to contriue much with small charge and in lesse roome. Againe, should you follow the warres (as who knowes the bent of his Fate) you cannot without Geometry fortifie your selfe, take the aduantage of hill or leuell, fight, order your Battaglia in square, triangle, crosse (which forme the Prince of Orange hath now alate taken vp) cres••entwise (and many other formes Iovius sheweth) leuell and plant your Ordinance, vndermine, raise your halfe Moones, Bulwarkes, Casamates, Rampires, Rauesins, with many other meanes as of offence and defence, by fortification. So that I cannot see how a Gentleman, especially a Soul∣dier and Commander may be accomplished without Ge∣ometrie, though not to the heighth of perfection, yet at the least to be grounded and furnished with the princi∣ples and priuie rules heereof. The Authors I would commend vnto you for entrance hereinto are in English. Cookes Principles, and the Elements of Geometry, writ∣ten in Latin by P. Ramus, and translated by M. Doctor Hood, sometime Mathematicall Lecturer in London. M. Blundeuile, Euclide translated into English. In Latine you may haue the learned Iesuite Clauius, Melancthon,

Frisius, Valearius his Geometry Military. Albert Du∣rer hath excellently written heereof in high Dutch, and in French Fercadell vpon Euclide, with sundry others.

Notes

• * 1.1

  Lacrius lib. 4.
• * 1.2

  Wisedome chap. 11.
• * 1.3

  Petrach de reg∣no lib. 2. ••. 14.
• * 1.4

  Protiu in Eu∣cl••d. lib. 2. c. 14.
• * 1.5

  Martianus Ca∣pellain Geem. Precleses in Eu∣clid. lib. 2. c. 4.
• * 1.6

  See the Hun∣garian Histo∣ry.
• * 1.7

  Whence Couch had the name
• * 1.8

  Agellius l. 10 cap. 12.
• * 1.9

  Scaliger ••uer∣cis. 326. ad Cardanum.
• * 1.10

  Horat. lib. 1. C••rm. Ode ••8.
• * 1.11

  Bartas le 6 〈◊〉〈◊〉 du 1. Semain.
• * 1.12

  Plin. l. 7. c. 21. & lib. 36. c. 5.
• * 1.13

  Varr•• de ling•• a Latin. lib. 6.
• * 1.14

  Iunius lib. ani∣mad cap. 6.
• * 1.15

  Plin. lib. 7. cap. 21.
• * 1.16

  Pliny lib. 10. cap. 29.
• * 1.17

  Ex••rcitat. 326
• * 1.18

  Carl. Rhodigin. lib. 8. cap. 3.
• * 1.19

  P. ••onius & Sabellicus is Suppleme••: Hist. lib. 24.
• * 1.20

  This Heauen was carried by 12. men before Soly∣man, and ta∣ken to peeces and set vp a∣gaine by the maker.
• * 1.21

  Plutarch in Marcello. 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 Psalm. 24.