Return to John Dee’s Preface.

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.

     

Simple, Which dealeth with Numbers onely: and demon­strateth all their properties and apper­tenances: where, an Vnit, is Indiui­sible.

   

In thinges Super­naturall, æternall, & Diuine: By Appli­cation, Ascending.

 

Arithmetike.

Mixt, Which with aide of Geometrie principall, demon­strateth some Arith­meticall Conclusion, or Purpose.

 

The vse
whereof, is either,

The like Vses and Appli­cations are, (though in a degree lower) in the Artes Mathe­maticall Deriuatiue.

Principall, which are two, onely,

 
 

In thinges Mathe­maticall: without farther Appli­cation.

Sciences, and Artes Mathe­maticall, are, either

 
 

Simple, Which dealeth with Magni­tudes, onely: and demon­strateth all their properties, passions, and apper­tenances: whose Point, is Indiui­sible.

 
 

Geometrie.

In thinges Naturall: both Substã­tiall, & Accidentall, Visible, & Inuisible. &c. By Appli­cation: Descending.

   

Mixt, Which with aide of Arith­metike principall, demon­strateth some Geometricall purpose, as EVCLIDES ELEMENTES.

     
   

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.

The names of the Princi­palls: as,

 

At hand

All Lengthes.—

All Plaines: As, Land, Borde, Glasse, &c.

All Solids: As, Timber, Stone, Vessels, &c.

Mecometrie.

Embadometrie.

Stereometrie.

Deriuatiue frõ the Princi­palls: of which, some haue

 

Geometrie, vulgar: which teacheth Measuring

 

How farre, from the Measurer, any thing is: of him sene, on Land or Water: called Apomecometrie.

   

Geodesie: more cunningly to Measure and Suruey Landes, Woods, Waters. &c.

     

With distãce from the thing Measured, as,

How high or deepe, from the leuell of the Measurers standing, any thing is: Seene of hym, on Land or Water: called Hypso­metrie.

 

Of which are growen the Feates & Artes of

Geographie.

 

Choro­graphie.

 

Hydro­graphie.

   

How broad, a thing is, which is in the Measurers view: so it be situated on Land or Water: called Plato­metrie.

   

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.

Cosmo­graphie,

Which, wholy and perfectly maketh description of the Heauenlym and also Elementall part of the World: and of these partes, maketh homologall appli­cation, and mutuall collation necessary.

Astro­logie,

Which reasonably demon­strateth the opera­tions and effectes of the naturall beames of light, and secrete Influence of the Planets, and fixed Starres, in euery Element and Elementall body: at all times, in any Horizon assigned.

Statike,

Which demon­strateth the causes of heauines and lightnes of all thinges: and of the motions and properties to heauines and lightnes belonging.

Anthropographie,

Which describeth the Nũber, Measure, Waight, Figure, Situation, and colour of euery diuers thing contained in the perfecte body of MAN: and geueth certaine knowledge of the Figure, Symmetrie, Waight, Charac­terization, & due Locall motion of any percell of the said body assigned: and of numbers to the said percell apper­taining.

Propre names
as,

Trochilike,

Which demon­strateth the properties of all Circular motions: Simple and Compound.

 

Helico­sophie,

Which demon­strateth the designing of all Spirall lines: in Plaine, on Cylinder, Cone, Sphære, Conoïd, and Sphæroid: and their properties.

Pneuma­tithmie,

Which demon­strateth by close hollow Geometricall figures (Regular and Irregular) the straunge properties (in motion or stay) of the Water, Ayre, Smoke, and Fire, in their Conti­nuitie, and as they are ioyned to the Elementes next them.

   

Menadrie,

Which demon­strateth, how, aboue Natures Vertue, and power simple: Vertue and force, may be multi­plied: and so to directe, to lift, to pull to, and to put or cast fro, any multi­plied, or simple deter­mined Vertue, Waight, or Force: naturally, not, so, direc­tible, or moueable.

Hypogeiodie,

Which demon­strateth, how, vnder the Sphæricall Super­ficies of the Earth, at any depth, to any perpen­dicular line assigned (whose distance from the perpen­dicular of the entrance: and the Azimuth likewise, in respecte of the sayd entrance, is knowen) certaine way, may be prescribed and gone, &c.

Hydra­gogie,

Which demon­strateth the possible leading of water by Natures law, and by artificiall helpe, from any head (being Spring, standing, or running water) to any other place assigned.

Horometrie,

Which demon­strateth, how, at all times appointed, the precise, vsuall denomi­nation of time, may be knowen, for any place assigned.

Zographie,

Which demon­strateth and teacheth, how, the Inter­section of all visuall Pyramids, made by any plaine assigned (the Center, distance, and lightes being deter­mined) may be, by lines, and proper colours repre­sented.

Archi­tecture,

Which is a Science garnished with many doctrines, and diuers Instructions: by whose iudgement, all workes by other workmen finished, are iudged.

Nauigation,

Which demon­strateth, how, by the Shortest good way, by the aptest direction, and in the shortest time: a suffi­cient Shippe, betwene any two places (in passage nauigable) assigned, may be conducted: and in all stormes and naturall distur­bances chauncing, how to vse the best possible meanes, to recouer the place first assigned.

Thaumaturgike,

Which geueth certaine order to make straunge workes, of the sense to be perceiued: and of men greatly to be wondred at.

 

Arche­mastrie,

Which teacheth to bring to actuall experience sensible, all worthy conclu­sions, by all the Artes Mathe­maticall purposed: and by true Naturall philo­sophie, concluded: And both addeth to them a farder Scope, in the termes of the same Artes: and also, by his proper Method, and in peculiar termes, procedeth, with helpe of the forsayd Artes, to the perfor­mance of complete Experi­ences: which, of no parti­cular Arte, are hable (Formally) to be challenged.

Return to John Dee’s Preface.