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, Whichdealeth with Numbers onely: and demonstrateth all their propertiesand appertenances: where, an Vnit, isIndiuisible. | In thinges Supernaturall, æternall, &Diuine: By Application, Ascending. | |||||||||
Arithmetike. | Mixt, Whichwith aide of Geometrie principall, demonstrateth someArithmeticall Conclusion, or Purpose. | The vse | The like Vses and Applications are,(though in a degree lower) in the Artes MathematicallDeriuatiue. | |||||||
Principall, which are two,onely, | | In thinges Mathematicall: without fartherApplication. | ||||||||
Sciences, and ArtesMathematicall, are, either | | Simple, Whichdealeth with Magnitudes, onely: and demonstrateth all theirproperties, passions, and appertenances: whose Point, isIndiuisible. | ||||||||
| Geometrie. | In thinges Naturall: both Substãtiall, &Accidentall, Visible, & Inuisible. &c. By Application:Descending. | ||||||||
Mixt, Whichwith aide of Arithmetike principall, demonstrateth someGeometricall purpose, as EVCLIDES ELEMENTES. | ||||||||||
Arithmetike, vulgar: which considereth | Arithmetike of most vsuall whole numbers: And of Fractions tothem appertaining. Arithmetike of Proportions. Arithmetike Circular. Arithmetike of Radicall Nũbers: Simple, Compound, Mixt: And oftheir Fractions. Arithmetike of Cossike Nũbers: with their Fractions: And thegreat 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: morecunningly 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: Seeneof 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 besituated on Land or Water: called Platometrie. | Stratarithmetrie. | |||||||||
| Perspectiue, | Which demonstrateth the maners and propertiesof 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 ofany Horizon. | |||||||||
Musike, | Which demonstrateth by reason, and teachethby sense, perfectly to iudge and order the diuersitie of Soundes,hie or low. | |||||||||
Cosmographie, | Which, wholy and perfectly maketh description ofthe Heauenlym and also Elementall part of the World: and of thesepartes, maketh homologall application, and mutuall collationnecessary. | |||||||||
Astrologie, | Which reasonably demonstrateth theoperations and effectes of the naturall beames of light, andsecrete Influence of the Planets, and fixed Starres, in euery Elementand Elementall body: at all times, in any Horizon assigned. | |||||||||
Statike, | Which demonstrateth the causes of heauinesand lightnes of all thinges: and of the motions and properties toheauines and lightnes belonging. | |||||||||
Anthropographie, | Which describeth the Nũber, Measure, Waight,Figure, Situation, and colour of euery diuers thing contained in theperfecte body of MAN: and geueth certaine knowledge of the Figure,Symmetrie, Waight, Characterization, & due Locall motion of anypercell of the said body assigned: and of numbers to the said percellappertaining. | |||||||||
Propre names | Trochilike, | Which demonstrateth the properties of allCircular motions: Simple and Compound. | ||||||||
Helicosophie, | Which demonstrateth the designing of allSpirall lines: in Plaine, on Cylinder, Cone, Sphære, Conoïd, andSphæroid: and their properties. | |||||||||
Pneumatithmie, | Which demonstrateth by close hollowGeometricall figures (Regular and Irregular) the straunge properties (inmotion or stay) of the Water, Ayre, Smoke, and Fire, in theirContinuitie, and as they are ioyned to the Elementes nextthem. | |||||||||
Menadrie, | Which demonstrateth, how, aboue NaturesVertue, and power simple: Vertue and force, may be multiplied: andso to directe, to lift, to pull to, and to put or cast fro, anymultiplied, or simple determined Vertue, Waight, or Force:naturally, not, so, directible, or moueable. | |||||||||
Hypogeiodie, | Which demonstrateth, how, vnder theSphæricall Superficies of the Earth, at any depth, to anyperpendicular line assigned (whose distance from theperpendicular of the entrance: and the Azimuth likewise, inrespecte of the sayd entrance, is knowen) certaine way, may beprescribed and gone, &c. | |||||||||
Hydragogie, | Which demonstrateth the possible leading ofwater by Natures law, and by artificiall helpe, from any head (beingSpring, standing, or running water) to any other place assigned. | |||||||||
Horometrie, | Which demonstrateth, how, at all timesappointed, the precise, vsuall denomination of time, may be knowen,for any place assigned. | |||||||||
Zographie, | Which demonstrateth and teacheth, how, theIntersection of all visuall Pyramids, made by any plaine assigned(the Center, distance, and lightes being determined) may be, bylines, and proper colours represented. | |||||||||
Architecture, | Which is a Science garnished with many doctrines,and diuers Instructions: by whose iudgement, all workes by other workmenfinished, are iudged. | |||||||||
Nauigation, | Which demonstrateth, how, by the Shortestgood way, by the aptest direction, and in the shortest time:a sufficient Shippe, betwene any two places (in passagenauigable) assigned, may be conducted: and in all stormes and naturalldisturbances chauncing, how to vse the best possible meanes, torecouer the place first assigned. | |||||||||
Thaumaturgike, | Which geueth certaine order to make straungeworkes, of the sense to be perceiued: and of men greatly to be wondredat. | |||||||||
Archemastrie, | Which teacheth to bring to actuall experiencesensible, all worthy conclusions, by all the ArtesMathematicall purposed: and by true Naturall philosophie,concluded: And both addeth to them a farder Scope, in the termes of thesame Artes: and also, by his proper Method, and in peculiar termes,procedeth, with helpe of the forsayd Artes, to the performance ofcomplete Experiences: which, of no particular Arte, are hable(Formally) to be challenged. | |||||||||
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