## The first six books of the Elements of Euclid, with annotations and exercises by J. Casey, Book 11 |

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### Common terms and phrases

ABCD AC is equal adjacent angles altitude angle ABC angle ACB angle BAC angular points Axiom bisector centre chord circles touch circumference circumscribed circle collinear common concurrent lines const coplanar cyclic quadrilateral Dem.—If Dem.—Let Dem.—Since diagonals diameter divided draw equal angles equal to AC equiangular equilateral triangle escribed circles Euclid Exercises exterior angle external Geometry given circle given line given point greater Hence the angle hypotenuse inscribed less line joining locus manner meet middle points multiple nine-points circle opposite sides parallel parallelogram parallelopiped PEOP perpendicular plane points of intersection prism produced PROP Proposition prove radii radius rectangle contained rectilineal figure regular polygon respectively equal right angles right line segments semicircle sides AC similar tangent theorem triangle ABC vertex vertical angle

### Popular passages

Page 295 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.

Page 182 - 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 102 - 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 122 - 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 226 - 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 126 - 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 194 - If there be any number of proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.