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

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Page 13

That point , in a line - segment , which is equidistant from the end - points is the

segment , or , when spoken of alone , simply the point of bisection . EXERCISES .

That point , in a line - segment , which is equidistant from the end - points is the

**middle point**of the segment . It is also called the internal point of bisection of thesegment , or , when spoken of alone , simply the point of bisection . EXERCISES .

Page 15

A line which changes its direction in a plane while passing through a fixed

in the plane is said to rotate about the ... or by three letters of which the extreme

ones denote

A line which changes its direction in a plane while passing through a fixed

**point**in the plane is said to rotate about the ... or by three letters of which the extreme

ones denote

**points**upon the arms of the angle and the**middle**one denotes the ... Page 20

Through a given point in a line only one perpendicular can be drawn to the line .

The line OC is | AB , and ... g.e.d. Def - The perpendicular to a line - segment

through its

...

Through a given point in a line only one perpendicular can be drawn to the line .

The line OC is | AB , and ... g.e.d. Def - The perpendicular to a line - segment

through its

**middle point**is the right bisector of the segment . Since a segment has...

Page 27

54 " Theorem .-- Every

on the right bisector of that segment . ... Def . — The line - segment from a vertex

of a triangle to the

54 " Theorem .-- Every

**point**equidistant from the endpoints of a line - segment ison the right bisector of that segment . ... Def . — The line - segment from a vertex

of a triangle to the

**middle**of the opposite side is a median of the triangle . Cor . 1. Page 32

Since AC is > AB , let D be the point in AC so that AD = AB . Then A is the

LPDB = LPBD , ( 53 ° , Cor 1 ) But LPDB is > LPCB ; LPBD is > LPCB , and PC is

...

Since AC is > AB , let D be the point in AC so that AD = AB . Then A is the

**middle****point**of BD , and PA is the right bisector of BD . ( 42 ° , Def . ) PD - PB ( 539 ) andLPDB = LPBD , ( 53 ° , Cor 1 ) But LPDB is > LPCB ; LPBD is > LPCB , and PC is

...

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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.