THat•• which in thes•• 9. Problemes, is said of circles•• is much more sayd of squares, by whose meanes, circles, are thus handled. And therefore seing to all Polygonon right lined figures, equall squares [ 1] may be made, by the falt of the second: and contrariwise, to any square, a right lined figure may be made [ 2] equall, and withall, like to any right lined figure geuen, by the 25 of the sixt. And fourthly, seing vpon [ 3] the said plaine figures•• as vpō base•• may Pri••mes, Parallelipipedons, Pyramids, sided Columnes, Cones, [ 4] and Cylinders, be reared: which being * 1.1 all of one height, shall haue that proportion, one to the o∣ther, that their bases haue, one to the other. And fiftly, seing Spheres, Cones, and Cylinders are one to other in 〈◊〉〈◊〉 knowen proportions: and so may be made, one to the other in any proportion as∣signed. [ 5] And 〈◊〉〈◊〉, seing vnder euery one of the kindes of figures, both plaine, and solide, infinite cases may chaunce, by the ayde of these Problemes, to be soluted and executed: How infinite (then) vpon [ 6] infinite, is the number of practises, either Mathematicall, o•• Mechanicall, to be performed, of compa∣risons betwene diuers kindes, of plaines to plaines, and solides to solides••
Fa••••h••••••ore, to speake of playne superficiall figures, in respect of the con••••r, or Area of the circle, [ 7] sundry mixt line figures, Anular and Lunular figures: and also of circles to be geuen equall to the sayd ••••••sed figures•• and in all proportions els: and euermore thinking of solides, (like high) set vpon a∣ny of those vnused figures, (O Lord) in cōsideration of al the premisses, how infinite, how straunge and [ 8] ••••credible ••••••••••••ation•• and practise••, may (by the ayde and direction of these few problemes) 〈◊〉〈◊〉 redi∣ly into the imagination•• and handes of them, that will bring their minde and intent wholy and fixedly to such mathematicall discourses? In these Elementes, I entend but to geue to young beginners some 〈◊〉〈◊〉, and courage to exercise ••heir owne witts, and talent, in this most pleasant and profitable sci∣••nc••. All ••hinge•• 〈◊〉〈◊〉 not, neither y•••• ••an, in euery place be sayd. Opportunitie, and S••ff••ci••••ty, best are to be allowed.