# Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of Euclid. With Notes, Critical and Explanatory

Johnson, 1803 - Euclid's Elements - 279 pages

### Contents

 Section 1 1 Section 2 7 Section 3 7 Section 4 17 Section 5 xii Section 6 xii Section 7 18 Section 8 24
 Section 20 63 Section 21 83 Section 22 90 Section 23 95 Section 24 111 Section 25 125 Section 26 189 Section 27 190

 Section 9 33 Section 10 35 Section 11 23 Section 12 24 Section 13 29 Section 14 33 Section 15 21 Section 16 25 Section 17 37 Section 18 45 Section 19 47
 Section 28 193 Section 29 194 Section 30 195 Section 31 199 Section 32 199 Section 33 199 Section 34 212 Section 35 221 Section 36 234 Section 37 242

### Popular passages

Page 63 - AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so as at length to become greater than AB.
Page 31 - THE Angle formed by a Tangent to a Circle, and a Chord drawn from the Point of Contact, is Equal to the Angle in the Alternate Segment.
Page xii - To find the centre of a given circle. Let ABC be the given circle ; it is required to find its centre. Draw within it any straight line AB, and bisect (I.
Page xxiii - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. LET ab be the given straight line, which may be produced to any length both ways, and let c be a point without it. It is required to draw a straight line perpendicular to ab from the point c.
Page 63 - Lemma, if from the greater of two unequal magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes.
Page 24 - IN a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF. Draw* the straight line GAH touching the circle in the a 17. 3. point A, and at the point A, in the straight line AH, makeb b 23.
Page i - ELEMENTS of GEOMETRY, containing the principal Propositions in the first Six and the Eleventh and Twelfth Books of Euclid, with Critical Notes ; and an Appendix, containing various particulars relating to the higher part* of the Sciences.
Page xii - The radius of a circle is a right line drawn from the centre to the circumference.
Page 30 - To bisect a given arc, that is, to divide it into two equal parts. Let ADB be the given arc : it is required to bisect it.
Page 7 - Beciprocally, when these properties exist for 'two right lines and a common secant, the two lines are parallel.* — Through a given point, to draw a right line parallel to a given right line, or cutting it at a given angle, — Equality of angles having their sides parallel and their openings placed in the same direction.