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A00429 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; Elements. English Euclid.; Dee, John, 1527-1608.; Candale, François de Foix, comte de, 1502-1594.; Billingsley, Henry, Sir, d. 1606. 1570 (1570) STC 10560; ESTC S106699 1,020,889 884

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Diuine By Application Ascending The like Vses and Applications are though in a degree lower in the Artes Mathematicall Deriuatiue In thinges Mathematicall without farther Application The like Vses and Applications are though in a degree lower in the Artes Mathematicall Deriuatiue In thinges Naturall both Substātiall Accidentall Visible Inuisible c. By Application Descending The like Vses and Applications are though in a degree lower in the Artes Mathematicall Deriuatiue Mixt Which with aide of Geometrie principall demonstrateth some Arithmeticall Conclusion or Purpose The vse whereof is either In thinges Supernaturall ●ternall Diuine By Application Ascending The like Vses and Applications are though in a degree lower in the Artes Mathematicall Deriuatiue In thinges Mathematicall without farther Application The like Vses and Applications are though in a degree lower in the Artes Mathematicall Deriuatiue In thinges Naturall both Substātiall Accidentall Visible Inuisible c. By Application Descending The like Vses and Applications are though in a degree lower in the Artes Mathematicall Deriuatiue Geometrie Simple Which dealeth with Magnitudes onely and demonstrat●th all their properties passions and appertenances whose Point is Indiuisible The vse whereof is either In thinges Supernaturall ●ternall Diuine By Application Ascending The like Vses and Applications are though in a degree lower in the Artes Mathematicall Deriuatiue In thinges Mathematicall without farther Application The like Vses and Applications are though in a degree lower in the Artes Mathematicall Deriuatiue In thinges Naturall both Substātiall Accidentall Visible Inuisible c. By Application Descending The like Vses and Applications are though in a degree lower in the Artes Mathematicall Deriuatiue Mixt Which with aide of Arithmetike principall demonstrateth some Geometricall purpose as EVCLIDES ELEMENTES The vse whereof is either In thinges Supernaturall ●ternall Diuine By Application Ascending The like Vses and Applications are though in a degree lower in the Artes Mathematicall Deriuatiue In thinges Mathematicall without farther Application The like Vses and Applications are though in a degree lower in the Artes Mathematicall Deriuatiue In thinges Naturall both Substātiall Accidentall Visible Inuisible c. By Application Descending The like Vses and Applications are though in a degree lower in the Artes Mathematicall Deriuatiue Deriuatiue frō the Principalls 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 teacheth 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 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 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 distance 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 Thaumaturgike Archemastrie ¶ The first booke of Euclides Elementes IN THIS FIRST BOOKE is intreated of the most simple easie and first matters and groundes of Geometry as namely of Lynes Angles Triangles Parallels Squares and Parallelogrammes First of theyr definitions showyng what they are After that it teach●th how to draw Parallel lynes and how to forme diuersly figures of three sides foure sides according to the varietie of their sides and Angles