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.

    296/306 page 280
    THE ADDITAMENT Of T H E 0 N, And moreover alfo the Sectors, That is, they have the fame proportion with the Circumfe¬ rences, on which they injift. I fay alfo, that as the circumference bc is to the circumference ef, fo the Senior bgc is to the Sector ehf. For let be joyned bc, ck, and in the circumferences bc, ck, the points x, o, being taken^ let b x, x c, c o, o k, be alfo joyned. Now forafmuch as the two lines bg, gc, are equal to the two lines cg;gk, and they contain equal angles; therefore theWeBc is equal to the bafe ck, and the Triangle gbc to the Trianglegck [Prop. 4. El. I.]. /■ 6 And becaufe the circumference bc is equal to the circumference ck; therefore the remaining circumference bac compleating the whole Circle abc, is equal to the remaining circumference kac, compleating the fame Circle: fo that alfo the angle b x c is equal to the angle cok [Prop. x7. EL III]; therefore the Segment bxc is like to the Segment cok [Def 10. El. III.], and they are upon equal ftrait lines bc, ck: but like Segments of Circles upon equal ftrait lines are equal to one another [Prop. 14. El. III.]; therefore the Segment bxc is equal to the Segment cok: and alfo the Tri¬ angle bgc is equal to the Triangle cgk ; therefore the whole Se&or bgc is equal to the whole Sector cgk. 5* By
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