## The First Six Books of the Elements of Euclid: And Propositions I-XXI of Book XI, and an Appendix on the Cylinder, Sphere, Cone, Etc., with Copious Annotations and Numerous Exercises |

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### Common terms and phrases

ABCD altitude angle ACB Axiom base bisector bisects Book called centre chord circle circumference circumscribed common const Construct denote described diagonals diameter difference distance divided draw drawn equal equal angles equiangular equilateral evident Exercises external extremities figure fixed formed four fourth Geometry given circle given line given point greater half Hence inscribed Join less line joining locus magnitudes manner mean meet middle points multiple normal opposite sides pair parallel parallelogram pass perpendicular plane polygon position produced PROP proportional Proposition prove quadrilateral radius ratio rectangle contained regular remaining respectively right angles right line segments sides similar square tangent theorem third touch triangle ABC twice vertex vertical angle whole

### Popular passages

Page 299 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.

Page 186 - When of the equimultiples of four magnitudes (taken as in the fifth definition) the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth...

Page 9 - LET it be granted that a straight line may be drawn from any one point to any other point.

Page 104 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.

Page 124 - The diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...

Page 230 - If from any angle of a triangle, a straight line be drawn perpendicular to the base ; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle.

Page 29 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Page 63 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Page 128 - The diagonals of a quadrilateral intersect at right angles. Prove that the sum of the squares on one pair of opposite sides is equal to the sum of the squares on the other pair.

Page 22 - ACB, DB is equal to AC, and BC common to both ; the two sides DB, BC, are equal to the two AC, CB, each to each, and the angle DBC is equal to the angle ACB : therefore, the base DC is equal to the base AB, and the triangle DBC (Mr. Southey) is equal to the triangle ACB, the less to the greater, which is absurd,