## The elements of plane geometry, Volume 1 |

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### Common terms and phrases

ABCD AC is equal acute alternate angle altitude angle ABC angle ACB angle AFG angle BAC angle EDF angles are equal angles equal Apply base bisector bisects called centre coincide common Constr construct a triangle diagonal difference distance divided draw equal to AC exterior angle extremities fall figure formed four Geometry given angle given point given straight line greater half Hence identically equal intersect isosceles triangle join less Let ABC locus meet middle point opposite sides pair parallel parallelogram perpendicular plane point equidistant polygon Post Prob produced projection Prove quadrilateral radius rectangle contained remainder respectively right angles right-angled triangle segments shew side AB side AC square on AC straight line drawn surface THEOR Theorem triangle ABC twice the rectangle unequal vertex vertices whole

### Popular passages

Page 27 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Page 98 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Page 56 - ... is equal to twice as many right angles as the polygon

Page 35 - Any two sides of a triangle are together greater than the third side.

Page 26 - The straight lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal to one another.

Page 37 - Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.

Page 70 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Page 110 - 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 31 - Any two angles of a triangle are together less than two right angles.

Page 115 - In a right.angled triangle, the square on the hypotenuse is equal to the sum of the squares on the sides containing the right angle . . . . 130 Applications of Pythagoras' theorem . . . . 132 THEOREM 6.