The elements of plane geometry, Volume 1 |
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Common terms and phrases
AB is equal ABCD AC is equal adjacent angles adjoining sides alternate angle angle ABC angle ACB angle AFG angle BAC angle CAB angle DEF angle EDF angle FGD angles are equal angles equal BA and AC base BC bisector bisects centre circle cutting Constr construct a triangle contrapositive diagonal distance draw a circle equal angles equal to AC equal to CD exterior angle find the locus Geometry given angle given point given straight line greater Hence hypotenuse identically equal interior opposite angle isosceles triangle less Let ABC meet middle point obtuse angle opposite sides parallel straight lines parallelogram perpendicular point equidistant Prob produced quadrilateral rectangle contained rectangle whose base right angles right-angled triangle shew side AB side AC sides equal square on AC squares on AB straight line drawn Theorem trapezium triangle ABC triangles are identically twice the rectangle vertex
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.