will be evident.

[12] Concerning the meaning of total predication, see page 45 of the Dissertation, Vol. I. of this work.

[13] Mr. Simson in his note to this proposition observes, that he thought proper to change its enunciation, so as to preserve the same meaning; “because (says he) the literal translation from the Greek, is extremely harsh, and difficult to be understood by beginners.” Whatever difficulty learners may find in conceiving this proposition abstractedly, is easily removed by its exposition in the figure; and therefore, I conceive, that Mr. Simson acted very injudiciously in altering its enunciation. Besides, the following comment of Proclus shews, that there is great beauty in Euclid’s statement of this proposition; the greatest part of which is lost in Mr. Simson’s indiscreet alteration. It would appear strange that such liberties should be taken by one, who professes in his preface, _to remove blemishes, and restore the principal books of the Elements to their original accuracy_, if Mr. Simson had not informed us in his note, that the present Commentary of Proclus unfolding the beauty and _accuracy_ of this proposition, is too _trifling_ to merit a relation! See more concerning this proposition in the note to Prop. 5.

[14] See the Comment of Clavius on this proposition.

[15] And from hence, also appears the emptiness and arrogance of Mr. Simson’s note to this proposition, which we have already exploded.

[16]

This too may be easily effected by means of the first problem, and the present. Thus let _a b c_ be a right angle, which it is required to trisect; then, upon the side _a b_, describe an equilateral triangle _c d b_, and bisect the angle _d b c_, and the angles _a b d_, _d b e_, _e b c_, shall be equal. For the angle _d b c_, is one third of two right angles, or two thirds of one right, and consequently the angle _d b a_, is one third of a right angle; and this is equal to _d b e_, the half of _d b c_. Therefore they are all equal.

[17]

The method of dividing an angle in any given ratio, by means of a right line and circle only, seems to have been entirely unknown to the ancients, as well as to the moderns. However, the author of this translation presumes he has discovered the means of solving this arduous problem; and that such as admit the truth of his demonstration respecting the quadrature of the circle in page 56 of his Dissertation,