Batman vppon Bartholome his booke De proprietatibus rerum, newly corrected, enlarged and amended: with such additions as are requisite, vnto euery seuerall booke: taken foorth of the most approued authors, the like heretofore not translated in English. Profitable for all estates, as well for the benefite of the mind as the bodie. 1582.

De Triangulo. cap. 128.

A Triangle is a figure with the cor∣ners that bee euen as much as two euen corners. That is an euē corner, it is determined in another place: the soule

of lyfe y^t hath three vertues in it selfe, of gendering, of nourishing, and of waxing is likened to y^e Triangle, y^t is the first of figures of Geometrie. For y^e soule of life is the first of all soules, & hath in it selfe three maner vertues. Among cornered fi∣gures, the triangle is the first for hee is Solidus, long, & broad. Therefore each fi∣gure with corners, as the Quadrangle, & y^e fiue cornered figure, conteineth as ma∣ny Triangles, as there be lines drawen frō corner to corner, as it fareth in y^e qua∣drangle, y^t conteineth two Triangles, if one line be drawen from one corner to the contrary corner in this wise

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And conteineth 4 triangles: if another line be drawen from another corner to y^e contra∣ry corner in this wise

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. And so in all other figures, for he conteineth as many triagles, as they haue corners, as the quadrangle conteyneth foure Triangles, if two lines bee drawne, & stretcheth from two corners to the contrary corners. And by lines drawen, y^e fiue cornered figure conteineth the triangles, and the sixt cor∣nered figure are, & the seuen cornered fi∣gure seuen, & so of other as Boetius saith li. 1. Arsmetrice. cap. 6. But the triangle may not be so dealed in other figures thē Triangles in this wise, this figure is so printed

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of breadth, y^t other figures be resolued & deled in triangles: and for this figure is bosid to no principles, nor taketh thereof figures beginning of breadth: therfore this figure to dealed in it selfe, as he sayth there. And none other figure may be thought, that hath not beginning and principall of the Triangle: For the Triangle is the beginning and Ele∣ment of other figures and shapes, & that is knowen in numbers. For the number of foure is compowned of three, y^t is a tri∣angle in numbers, & of one, that maketh foure & out to three: For one hath this dig∣nitie. That he conteineth in it selfe all the vertue of numbers, y^t 〈…〉〈…〉 thereof not in deede but in might & vertue, as Boetius sayth, libro. ••. cap. 14. And so the num∣ber of fiue is compowned of foure and one in sted of a Triangle: And so it may be shewed of all other Numeral figures. For alway each number is meresed of a triangle figure, as Boetius determineth then in termes openly, & leiteth ensāples in figures of foure, of fiue, of sixe, & of se∣uen, & of many other. Also y^e triangle fi∣gure hath another singular property: for of such other figure 〈…〉〈…〉 may be the chiefe side of a triangle: and so vpon each other figure may be re••red a triangle: for each other figure Piramidale, y^t hath in it selfe y^e shape of a triangle, ••btaineth in it selfe as many triangles, as y^e chiefe side containeth corners. And if a quadrangle is set for the chiefe ground & flo••, there may arise a figure Piramidales, y^t contei∣neth in it selfe as many triangles, as the quadrangle hath corners in it selfe in this wise. Also if y^e chiefe side of 〈…〉〈…〉 be fiue cornered, the Triangle Piramis, y^t 〈…〉〈…〉 may present fiue triangles vpon that Ba∣sis, as it fareth in a Piramidale figure y^t may be Basis of the figure Piramis, as he saith. And in the Piramidale tri∣angle, 3. manner triangles may be found, as y^e corners therof be three, in this wise. And so the disposition of God seemeth wonderfull in all things, and namely in numbers & in figures: Of other figures, both of numbers & of Geometry, it is re∣quisite now to cease for difficultye & di∣uersitie of endlesse many figures, though y^e consideration of al be full profitable to y^e lore of diuinity, as in the quadrangle, that is much solide and stedfast among figures & numbers, and is square, and presenteth the lore of the Gospell, that hath stedfastnesse in y^e foure parts of the worlde, as Beda sayeth super Genesis. A corner is called in Augulus, as touch∣ing of two lines y^t toucheth either other, and is the common subiect of many fi∣gures. For all the foresaid figures be de∣termined vnder diuersitie of angles. And of diuers touching of lines cōmeth diuers angles. For some angle is called Rectus angulus & sōe Obl. quus or Re∣flexus, & some Acutus, and some Ob••u∣sus. And most vertue is in the Angle that is called Rectus, for therein all the vertue is strengthned, y^t is in the lynes that come from the Bests to the angle and y^e vertue is strengthned by concourse and meeting and touching of lines, as it fareth in the eie that conteyneth all thing vnder an angle: For the highnesse

that commeth from the thing, y^t is seene straight to the eye maketh Pirame:* 1.1 of the which the point is in the blacke of the eye, and the broad ende in the thing that is séene: and those beames be angled in the middle of the black of the eie, and by the angle of that Pirame, the sight is shapen, as the Author of Perspectiue sayth. Looke before li. 3. de natura Visus. lib. 5. de materio oculorum. The partes contrarye set and diuided among them∣selues, come togethers in angles, and bee ioyned there.

Of the kinde of angles and of figures little is héere said, because of ensample, that we may know that the reason ther∣of is needfull to know diuers priuities of holy writ, that bee diuerslye lapped in likenesse of numbers and of figures: For as the circle betokeneth the soule Ratio∣nall, so the triangle betokeneth the soule of féeling. For as the Quadrangle con∣teineth two triangles, if a line be drawn from y^e one angle thereof to the contrary angle, so the soule of feeling conteyneth in itselfe two triangles of might and of vertue. For y^e soule of feelling hath three vertues of the soule of life, and there o∣uer the vertue of conceiuing, and concu∣piscible and irassible. For the soule of fee∣ling is soule of life, and not again ward. And so of other figures be diuers priuye reasons, & spiritually taken, and spiritual things with corporal be accorded. Under these figures be comprehended reasons of measures and of weights.

Notes

• * 1.1

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