## ELEMENTARY SYNTHETIC GEOMETRY OF THE POINT, LINE AND CIRCLE IN THE PLANE |

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Page 13

It is also called the

alone, simply the Žoint of Óisection, EXERCISES. I , If two segments be in line

and have one common endpoint, by what name will you call the distance

between ...

It is also called the

**internal**Zoint of bisection of the segment, or, when spoken ofalone, simply the Žoint of Óisection, EXERCISES. I , If two segments be in line

and have one common endpoint, by what name will you call the distance

between ...

Page 20

The one which lies within the angle is the

without is the easterna/ C bisector. G Let AOC be a given angle ; and \ £ let EOF

be so drawn that Z_AOE = Z E O C. E F is the

Also ...

The one which lies within the angle is the

**internal**bisector, and the one lyingwithout is the easterna/ C bisector. G Let AOC be a given angle ; and \ £ let EOF

be so drawn that Z_AOE = Z E O C. E F is the

**internal**bisector of the angle AOC.Also ...

Page 21

and the external bisector of AOC is the

angle, COB, and vice versa. The reason for calling GH a bisector of the angle

AOC is given in the definition, viz., GH makes equal angles with the arms. Also,

OA and ...

and the external bisector of AOC is the

**internal**bisector of its supplementaryangle, COB, and vice versa. The reason for calling GH a bisector of the angle

AOC is given in the definition, viz., GH makes equal angles with the arms. Also,

OA and ...

Page 26

4 APC = 4 BPC ; - Therefore the right bisector of the base of an isosceles triangle

is the

and the same line the converse is true, Des. 2.-A triangle in which all the sides ...

4 APC = 4 BPC ; - Therefore the right bisector of the base of an isosceles triangle

is the

**internal**bisector of the vertical angle. And since these two bisectors are oneand the same line the converse is true, Des. 2.-A triangle in which all the sides ...

Page 27

... of the opposite side is a median of the triangle. Cor. I. Every triangle has three

medians. Cor. 2. The median to the base of an isosceles triangle is the right

bisector of the base, and the

LINES.

... of the opposite side is a median of the triangle. Cor. I. Every triangle has three

medians. Cor. 2. The median to the base of an isosceles triangle is the right

bisector of the base, and the

**internal**bisector THREE OR MORE POINTS ANDLINES.

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### Common terms and phrases

ABCD algebraic altitude base becomes called centre centre-line chord circle coincide collinear common concurrent congruent considered constant construct Converse corresponding cuts denote describe determine diagonals diameter difference direction distance divided draw drawn equal expressed external figure fixed point four geometric given given line given point gives greater harmonic Hence internal intersect inverse joins length lies line-segment mean measure median meet middle point opposite opposite sides orthogonally pair parallel passes pencil perpendicular perspective placed plane polar polygon position Proof proved quadrangle radical axis radius range ratio reciprocal rectangle regular relation remaining respect right angle right bisector rotation segment sides similar Similarly similitude square straight symbol taken tangent theorem touch triangle vertex vertices

### Popular passages

Page 176 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.

Page 183 - The sides of a triangle are proportional to the sines of the opposite angles.

Page 260 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...

Page 19 - Every circumference of a. circle, whether the circle be large or small, is supposed to be divided into 360 equal parts called degrees. Each degree is divided into 60 equal parts called minutes, and each minute into 60 equal parts called seconds.

Page 77 - J_ to the given line. .'. the construction gives the perpendicular to a given line at a given point in the line.

Page 122 - And conversely, if the square on one side of a triangle is equal to the Bum of the squares on the other two sides, the angle contained by these two sides is a right angle.

Page 124 - The difference of the squares of two sides of a triangle is equal to the difference of the squares of the segments made by the altitude upon the third side.