The elements of geometrie of the most auncient philosopher Euclide of Megara. Faithfully (now first) translated into the Englishe toung, by H. Billingsley, citizen of London. Whereunto are annexed certaine scholies, annotations, and inuentions, of the best mathematiciens, both of time past, and in this our age. With a very fruitfull præface made by M. I. Dee, specifying the chiefe mathematicall scie[n]ces, what they are, and wherunto commodious: where, also, are disclosed certaine new secrets mathematicall and mechanicall, vntill these our daies, greatly missed

Here haue you (according to my promisse) the Groundplat of my MATHEMATICALL Praeface: annexed to Euclide (now first) published in our Englishe tounge. An. 1570. Febr. 3.

••ciences, ••nd Artes Mathe∣••aticall, are, either

• Principall, which are two, onely,
  • ...Arithmetike.
    • ...

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

      The vse whereof, is either,

      • In thinges Supernatu∣rall, ••ternall, & Diuine: By Application, Ascen∣ding. The like Vses and Appli∣cations are, (though in a degree lower) in the Artes Mathema∣ticall Deri∣uatiue.
      • In thinges Mathema∣ticall: without farther Application. The like Vses and Appli∣cations are, (though in a degree lower) in the Artes Mathema∣ticall Deri∣uatiue.
      • In thinges Naturall: both Substātiall, & Ac∣cidentall, Visible, & In∣uisible. &c. By Applica∣tion: Descending. The like Vses and Appli∣cations are, (though in a degree lower) in the Artes Mathema∣ticall Deri∣uatiue.

    • ...

      Mixt, Which with aide of Geometrie principall, demonstrateth some Arithmeticall Con∣clusion, or Purpose.

      The vse whereof, is either,

      • In thinges Supernatu∣rall, ••ternall, & Diuine: By Application, Ascen∣ding. The like Vses and Appli∣cations are, (though in a degree lower) in the Artes Mathema∣ticall Deri∣uatiue.
      • In thinges Mathema∣ticall: without farther Application. The like Vses and Appli∣cations are, (though in a degree lower) in the Artes Mathema∣ticall Deri∣uatiue.
      • In thinges Naturall: both Substātiall, & Ac∣cidentall, Visible, & In∣uisible. &c. By Applica∣tion: Descending. The like Vses and Appli∣cations are, (though in a degree lower) in the Artes Mathema∣ticall Deri∣uatiue.

  • Geometrie.
    • ...

      Simple, Which dealeth with Magnitudes, onely: and demonstrat••th all their properties, passi∣ons, and appertenances: whose Point, is Indiuisible.

      The vse whereof, is either,

      • In thinges Supernatu∣rall, ••ternall, & Diuine: By Application, Ascen∣ding. The like Vses and Appli∣cations are, (though in a degree lower) in the Artes Mathema∣ticall Deri∣uatiue.
      • In thinges Mathema∣ticall: without farther Application. The like Vses and Appli∣cations are, (though in a degree lower) in the Artes Mathema∣ticall Deri∣uatiue.
      • In thinges Naturall: both Substātiall, & Ac∣cidentall, Visible, & In∣uisible. &c. By Applica∣tion: Descending. The like Vses and Appli∣cations are, (though in a degree lower) in the Artes Mathema∣ticall Deri∣uatiue.

    • ...

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

      The vse whereof, is either,

      • In thinges Supernatu∣rall, ••ternall, & Diuine: By Application, Ascen∣ding. The like Vses and Appli∣cations are, (though in a degree lower) in the Artes Mathema∣ticall Deri∣uatiue.
      • In thinges Mathema∣ticall: without farther Application. The like Vses and Appli∣cations are, (though in a degree lower) in the Artes Mathema∣ticall Deri∣uatiue.
      • In thinges Naturall: both Substātiall, & Ac∣cidentall, Visible, & In∣uisible. &c. By Applica∣tion: Descending. The like Vses and Appli∣cations are, (though in a degree lower) in the Artes Mathema∣ticall Deri∣uatiue.

• Deriuatiue frō the Princi∣palls: o•• which, some haue
  • The names of the Principalls: as,
    • Arithmetike, vulgar: which considereth
      • ...Arithmetike of most vsuall whole Numbers: And of Fractions to them appertaining.
      • ...Arithmetike of Proportions.
      • ...Arithmetike Circular.
      • ...Arithmetike of Radicall Nūbers: Simple, Compound, Mixt: And of their Fractions.
      • ...Arithmetike of Cossike Nūbers: with their Fractions: And the great Arte of Algiebar.
    • Geometrie, vulgar: which tea∣cheth Measuring
      • At hand

        All Lengthes.

        Mecometrie.

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

        Embadometrie.

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

        Stereometrie.

      • With distāce from the thing Measured, as,
        • ...

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

          Of which are growen the Feates & Artes of

          • Geodesie: more cunningly to Measure and Suruey Landes, Woods, Waters. &c.
          • ...Geographie.
          • ...Chorographie.
          • ...Hydrographie.
          • ...Stratarithmetrie.

        • ...

          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

          • Geodesie: more cunningly to Measure and Suruey Landes, Woods, Waters. &c.
          • ...Geographie.
          • ...Chorographie.
          • ...Hydrographie.
          • ...Stratarithmetrie.

        • ...

          How broad, a thing is, which is in the Measurers vew: 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.

  • Propre names as,

    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: f••r any time, past, pr••sent, 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, hi•• or l••w.

    Cosmographie,

    Which, wholy and perfectly maketh description of the Heauenly, and also Elementall part of the World: and of these partes, maketh h••m••l••gall application, and mutuall collation necessary.

    Astrologie,

    Which reasonably demonstrateth the operations and effectes of the naturall bea••es of light, and 〈◊〉〈◊〉 In••luence of the Planets, and fixed Starres, 〈◊〉〈◊〉 euery Element and Elementall body: at all times, in any Horiz••n 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 Nūber, Measure, Waight, Figure, Situation, and colour of euery diuers thing contained in the perfect•• body of •••• AN: and geueth certaine knowledge of the Figure, Symmetri••, Waight, Characterization, & due Locall motion of any p••rcell of the sayd body assigned: and of numbers to the said p••rcell appertaining.

    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, Co••••, Sph••re, C••n••id, and Spharo••d: and their pro∣perties.

    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 Continuiti••, and as they are ioyned to the Elementes next them.

    Menadrie,

    Which demonstrateth, how, about Natures Vertue, and power simple: Vertue and force, may be multiplied: and so to directe, to lif••, to pull to, a••d 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 Spharicall Superficie•• of the E••rth, at ••ny depth, to any perpendicular line assigned (whose di∣stance from the perpendicular of the entrance: and the Azi••uth likewise, 〈◊〉〈◊〉 respe••••e of the sayd entrance, is knowen) certaine way, may be prescribed and g••ne, &c.

    Hydragogie,

    Which demonstr••teth the possible leading of water by Natures l••••, and by artificiall helpe, fr•••• 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, ••••y ••e know••n, for any place assigned.

    Zographie,

    Which demonstrateth and teacheth, how, the Intersection of all vsuall 〈…〉〈…〉 assigned (the Center, distanc••, and lightes b••ing determined) may be, by lines, and proper col••urs repre••••••••.

    Architecture,

    Which is a Sci•••••••• gar••ished with many doctrines, and 〈…〉〈…〉, are iudged.

    Nauigation,

    〈1 paragraph〉〈1 paragraph〉

    Thaumaturgike,

    〈1 paragraph〉〈1 paragraph〉

    Archemastrie,

    〈1 paragraph〉〈1 paragraph〉