+‡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+.
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+
+_Arithmetike_, vulgar: which considereth+
--Arithmetike of most vsuall whole numbers: And of Fractions to them appertaining. --Arithmetike of Proportions. --Arithmetike Circular. --Arithmetike of Radicall Nũbers: Simple, Compound, Mixt: And of their Fractions. --Arithmetike of Cossike Nũbers: with their Fractions: And the great Arte of Algiebar.
+_Geometrie_, vulgar: which teacheth Measuring+
All Lengthes.--+Mecometrie.+ All Plaines: As, Land, Borde, Glasse, &c.--+Embadometrie.+ All Solids: As, Timber, Stone, Vessels, &c.--+Stereometrie.+
+‡With distãce‡+ from the thing Measured, as,
+‡How farre‡+, from the Measurer, any thing is: of him sene, on Land or Water: called +Apomecometrie+. +‡How high or deepe‡+, from the leuell of the Measurers standing, any thing is: Seene of hym, on Land or Water: called +Hypsometrie+. +‡How broad‡+, a thing is, which is in the Measurers view: so it be situated on Land or Water: called +Platometrie+.
+‡Of which‡ are growen the Feates & Artes of+
+Geodesie+: more cunningly to Measure and Suruey Landes, Woods, Waters. &c. +Geographie.+ +Chorographie.+ +Hydrographie.+ +Stratarithmetrie.+
+Perspectiue,+--Which demonstrateth the maners and properties of all Radiations: Directe, Broken, and Reflected.
+Astronomie,+--Which demonstrateth the Distances, Magnitudes, and all Naturall motions, Apparences, and Passions, proper to the Planets and fixed Starres: for any time, past, present, and to come: in respecte of a certaine Horizon, or without respecte of any Horizon.
+Musike,+--Which demonstrateth by reason, and teacheth by sense, perfectly to iudge and order the diuersitie of Soundes, hie or low.