# 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 - 279 pages

### Contents

 Section 1 1 Section 2 15 Section 3 16 Section 4 18 Section 5 24 Section 6 29 Section 7 47 Section 8 50
 Section 23 190 Section 24 193 Section 25 194 Section 26 197 Section 27 199 Section 28 199 Section 29 205 Section 30 205

 Section 9 63 Section 10 75 Section 11 83 Section 12 85 Section 13 88 Section 14 89 Section 15 90 Section 16 99 Section 17 103 Section 18 111 Section 19 113 Section 20 115 Section 21 127 Section 22 161
 Section 31 210 Section 32 212 Section 33 221 Section 34 225 Section 35 238 Section 36 239 Section 37 242 Section 38 244 Section 39 247 Section 40 247 Section 41 247 Section 42 247 Section 43 257

### Popular passages

Page 164 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 71 - The radius of a circle is a right line drawn from the centre to the circumference.
Page 69 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 205 - 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 18 - 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 239 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Page 5 - AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal. 5. If equals be taken from unequals, the remainders will be unequal.
Page 133 - If any number of magnitudes be equimultiples of as many others, each of each, what multiple soever any one of the first is of its part, the same multiple is the sum of all the first of the sum of all the rest.
Page 143 - F is greater than E; and if equal, equal; and if less, less. But F is any multiple whatever of C, and D and E are any equimultiples whatever of A and B; [Construction.
Page 155 - Of four proportional quantities, the first and third are called the antecedents, and the second and fourth the consequents ; and the last is said to be a fourth proportional to the other three taken in order.