Volume 2

The elements of Euclid explain'd. In a new, but most easie method, together with the use of every proposition through all parts of the mathematicks / Written in French, by that exccellent [sic] mathematician F. Claud. Francis Milliet de Chales ... And now carefully done into English. And purg'd from a multitude of errors, which had escap'd in the original.

Euclid

Date:: 1685

Credit: The elements of Euclid explain'd. In a new, but most easie method, together with the use of every proposition through all parts of the mathematicks / Written in French, by that exccellent [sic] mathematician F. Claud. Francis Milliet de Chales ... And now carefully done into English. And purg'd from a multitude of errors, which had escap'd in the original. Source: Wellcome Collection.

168/392 page 158

$PROPOSITION XXL |} A THEOREM. The angles, that are in the fame fegment of a θε) cle, or that have the fame arch for their baal’ are ‘equal, ι Α ορ j' the angles BAC and BI] har are in the fame fegmenty) 3 a circle, which 15 greater thi a femicircle, they will be: bide 7¢ qual. Draw the lines BI aap CL. | Demonfiration. i * The angles A and D are each of them) (ii: half of the angle BIC, (by the preceding ,) rhea)’ fore they are ‘equal. Tr hey have likewife {νι fame arch BC for their bafe. a = Secondly, let the angles A anc à be inthe fame feoment BAD, whill aN is lefs chan a femicircle ; they We neverthelefs be equal. ; AR | D emonftration. 2 All che angles of che triangle ABE are ecq}” to all che angles of the triangle DEG, (47 1. \ bot, roll. of the 33.1.) but che aneles AEB and Di are equal, (61 rhe 1 50 1.) Alfo the angles Ε' FA | by$

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