:

TO THE

EADER.

د.

HAT follows is a New Translation, with feveral Alterations, of Eight of the Fifteen Books of EUCLID'S ents of Geometry, wrote long since tin by our famous Dr. Barrow, viz. First Six, Eleventh and Twelfth; are a fufficient Foundation for all ther useful Parts of Mathematicks;

the others being not near so necessary to be known.

But these Elements of Barrow's hither to published, notwithstanding the Brevity and Confpicuity of the Demonstrations, which renders them preferable to any others, are subject to some Deficiencies and Faults. Particularly the Schemes of the Propofitions, mere Copies of those in Peter Herigon's EUCLID, are in general too Small, and indistinct; and many ill adapted to the generality of the Propofitions And others again, almost unintelligible,

as those of Prop. 29, and 30. Lib. II. and Prop. 17. Lib. 12.

Moreover, the second Book wants the Schemes of Prop. 5, 6, 7, 8, which by a bare Contemplation and Attention to the Text, would be almost sufficient to evince their Truth, without reading the DemonStrations.

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These These Inconveniencies I have obviated, in the following Sheets, where the Schemes are made large and distinct, adapted to the generality of the Propositions; the Lines drawn for Construction dotted, to distin guish them from given Lines: others easy to be comprehended put instead of those of Prop. 29, and 30. Lib. 11. and Prop. 17. Lib. 12. and those of Prop. 5, 6, 7, 8. Lib. 2. wanting, are here fupply' d.

I have likewise left out some, and alter'd others of the Algebraick Demonstrations of the Second Book, which appeared to me too Intricate for a Learner not used to that Method, and substituted more easy ones in their room. I have also adapted other Demonftrations to the Schemes of Prop. 29, 30. Lib. 11. and Prop. 17. Lib. 12. and have So distinguished the Schemes representing the Planes and Solids of the Eleventh and Twelfth Books, that a Learner's Imagination will be almost as much assisted as if he had real Material Planes and Solids to

view

Not

t

Not long after the first Publication of these Elements in Latin, a bad English Translation came out by an unknown' hand, who was ignorant of the Subject, as, plainly appears in Def. 1. Lib. I. where he says that a Line is Longitude without Latitude. And in Def. 5. where he again repeats the words Longitude and Latitude for Length and Breadth. And in Prop. 1. Lib. 5, &c.

Tet notwithstanding, this Translation has been reprinted more than once, without any Correction or Alteration, not so much as to make it just and tolerable, English, which obliged me to the Trouble of new doing the following Books, and altering them as above related, not doubting of their acceptance by the English Reader.

2

I have one thing more to say, which is, That it is much better to have the Schemes of the Propositions in the Same Pages with the Propositions (as they are in this Tract) fingly,