The elements of Euclid, explained and demonstrated in a new and most easie method with the uses of each proposition in all the parts of the mathematicks / by Claude Francois Milliet D'Chales, a Jesuit ; done out of French, corrected and augmented, and illustrated with nine copper plates, and the effigies of Euclid, by Reeve Williams ...

DEFINITIONS.

1. * 1.1 Those Circles are equal, whose Diameters, or Semidiameters, are equal.

2. * 1.2 A Line toucheth a Circle when meeting with the Circumference there∣of it cutteth not the same: as the Line AB.

3. * 1.3 Circles touch each other, when Meeting they cut not each other; as the Circles AB and C.

4. * 1.4 Right Lines in a Circle are equal∣ly distant from the Center, when Per∣pendiculars drawn from the Center to those Lines are equal. As if the Lines EF, EG, being Perpendiculars to the Lines AB, CD, are equal, AB, CD, shall be equally distant from the Center; because the Distance ought always to be taken (or measured) by Perpendicular Lines.

5. * 1.5 A Segment of a Circle is a Figure terminated on the one side by a streight Line, and on the other by the Cir∣cumference of a Circle; as LON, LMN.

6. The Angle of a Segment is an Angle which the Circumference ma∣keth

with a streight Line; as the An∣gle OLN, LMN.

7. * 1.6 An Angle is said to be in a Seg∣ment of a Circle, when the Lines which form the same are therein; as the An∣gle FGH, is in the Segment FGH.

8. * 1.7 An Angle is upon that Arch to which it is opposite, or to which it serveth for a Base; as the Angle FGH, is up∣on the Arch FIH, which may be said to be its Base

9. * 1.8 A Sector is a Figure comprehend∣ed under two Semidiameters, and un∣der the Arch which serveth to them for a Base; as the Figure FIGH.

Notes

• * 1.1

  Def. of the 3 Book.
• * 1.2

  Fig. 1.
• * 1.3

  Fig. 2.
• * 1.4

  Fig. 3.
• * 1.5

  Fig. 4.
• * 1.6

  Fig. 5.
• * 1.7

  Fig 6.
• * 1.8

  Fig. 6.