The English Euclide, being the first six elements of geometry, translated out of the Greek, with annotations and useful supplements / by Edmund Scarburgh.

  • Euclid
Date:
1705
Catalogue details

Licence: Public Domain Mark

Credit: The English Euclide, being the first six elements of geometry, translated out of the Greek, with annotations and useful supplements / by Edmund Scarburgh. Source: Wellcome Collection.

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    ference en, the angle bgl is alfo greater than the angle ehn: and if lefs, ’tis lefs. There being then four magnitudes, the two circumferences b c, ef, and the two angles bgc, ehf: and of the circumference bc, and of the angle bgc are taken equimultiples, the circumference bl, and the angle bgl. Alfb of the circumference ef, and of the angle ehf, are taken equimultiples, the circumference EN,and the angle ehn. And it is prov’d, that if the circumference bl ex¬ ceeds the circumference en, the angle bgl does alfo exceed the angle ehn; and if equal, ’tis equal; and if lefs ’tis lefs: therefore as the circumference bc is to the circumference ef, fo the angle bgc is to the angle ehf [Def 5-. El. V.]. But as the angle bgc is to the angle ehf, fo the angleb ac is to the angle edf [Prop, x5*. El. V.]: for each is the double of each [Prop. 20. El. III.]. And therefore as the circumference bc is to the circumference ef, fo the angle bgc is to the angle ehf, and the angle bag to the angle edf. Therefore in equal Circles, the angles have the fame proportion with the circumferences on which they infift, whether the inlifting angles be at the Centers, or at the circumferences.. Which was to be demonftrated. Here Euclide ends the laft Propofition of his Sixth Element of Geometry,
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