9 Euery whole is greater then his part.
As the whole is equal to all his partes taken together, so is it grea∣ter
* 1.1THe principles thus placed & ended, now follow the propositions, which are sentences set forth to be proued by reasoning and demonstrations, and therfore they are agayne repeated in the end of the demonstration•• For the proposition is euer the conclusion, and that which ought to be p••oued.
* 1.2Propositions are of two sortes, the one is called a Probleme, the other a Theoreme.
* 1.3A Probleme, is a proposit••on which requireth some action, or doing: as the makyng of some ••igure, or to deuide a figure or line, to apply figure to ••igure, to adde figures to∣gether, or to subtrah one from an other, to describe, to inscribe, to circumscribe one fi∣gure within or without another, and suche like. As of the first proposition of the first booke is a probleme, which is thus•• Vpon a right line geuen not being infinite, to describe an ••∣quilater triangle, or a triangle of three equall sides. For in it, besides the demonstration and contemplation of the mynde, is required somewhat to be done: namely•• to make an equilater triangle vpon a line geuen. And in the ende of euery probleme, after the de∣monstration, is concluded a••ter this man••er, Which is the thing, which was required to be done.
* 1.4A Theoreme, is a proposition, which requireth the searching ou•• and demonstration of some propertie or passion of some figure: Wherin is onely speculation and contem∣plation of minde, without doing or working of any thing•• As the fifth proposition of the first booke, which is thus, An Isosceles or triangle of two equall sides, hath his angles at th•• base, equall the one to the other, &c. is a Theoreme. For in it is required only to be pro∣ued and made plaine by reason and demonstratiō, that these two angles be equall, without further working or doing. And in the end•• of ••u••ry Theoreme, after the demonstration is concluded after this ma∣ner, Which thyng was required to be demonstrated or proued.