[The Ground platt of this Præface in a Table.] I will giue you the +Groundplatt+ of my whole discourse, in a Table annexed: from the first to the last, somewhat Methodically contriued. If Hast, hath caused my poore pen, any where, to stumble: You will, (I am sure) in part of recompence, (for my earnest and sincere good will to pleasure you), Consider the rockish huge mountaines, and the perilous vnbeaten wayes, which (both night and day, for the while) it hath toyled and labored through, to bryng you this good Newes, and Comfortable profe, of Vertues frute. So, I Commit you vnto Gods Mercyfull direction, for the rest: hartely besechyng hym, to prosper your Studyes, and honest Intentes: to his Glory, & the Commodity of our Countrey. _Amen_. _Written at my poore House At Mortlake._ _Anno. 1570. February. 9._ [Decoration] [Transcriber’s Note: The “Groundplat” was printed in the form of a stemma, or tree, on an oversized fold-out page. The layout was impossible to reproduce for this e-text, so the information has been rearranged in nested-list form. Size markings (see note at beginning of e-text) are relative within each paragraph.] _J. DEE_ +‡Here haue you (according to my promisse) the Groundplat of‡+ +my MATHEMATICALL Præface: annexed to _Euclide_ (now first)+ published in our Englishe tounge. An. 1570. Febr. 3. +‡Sciences, and Artes Mathematicall,‡ are, either+ +‡Principall,‡ which are two, onely,+ +Arithmetike.+ +‡Simple‡+, Which dealeth with Numbers onely: and demonstrateth all their properties and appertenances: where, an Vnit, is Indiuisible. +‡Mixt‡+, Which with aide of Geometrie principall, demonstrateth some Arithmeticall Conclusion, or Purpose. +Geometrie.+ +‡Simple‡+, Which dealeth with Magnitudes, onely: and demonstrateth all their properties, passions, and appertenances: whose Point, is Indiuisible. +‡Mixt‡+, Which with aide of Arithmetike principall, demonstrateth some Geometricall purpose, as +EVCLIDES ELEMENTES+. +‡The vse‡ whereof, is either,+ In thinges Supernaturall, æternall, & Diuine: By Application, _Ascending_. In thinges Mathematicall: without farther Application. In thinges Naturall: both Substãtiall, & Accidentall, Visible, & Inuisible. &c. By Application: _Descending_. The like Vses and Applications are, (though in a degree lower) in the +Artes Mathematicall Deriuatiue+. +‡Deriuatiue‡ frõ the Principalls: of which, some haue+ +‡The names of‡ the Principalls: as,+ +_Arithmetike_, vulgar: which considereth+