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

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Page 86

the external bisectors of two angles of a triangle and the internal bisector of the

third angle are concurrent . Def . 1. - When three or more points are in line they

are said to be

a ...

the external bisectors of two angles of a triangle and the internal bisector of the

third angle are concurrent . Def . 1. - When three or more points are in line they

are said to be

**collinear**. Cor . 3. The line through any two centres passes througha ...

Page 197

Three or more points in line are

point are concurrent . Def . 2. - A tetrågram or general quadrangle is the figure

formed by four lines no three of which are concurrent , and no two of which are ...

Three or more points in line are

**collinear**, and three or more lines meeting in apoint are concurrent . Def . 2. - A tetrågram or general quadrangle is the figure

formed by four lines no three of which are concurrent , and no two of which are ...

Page 201

( BX ) ( sin BAX ) respectively . will be denoted by the symbols BX sin BAX and (

CX sin CAX It is readily seen that three points on the sides of a triangle can be

( BX ) ( sin BAX ) respectively . will be denoted by the symbols BX sin BAX and (

CX sin CAX It is readily seen that three points on the sides of a triangle can be

**collinear**only when an even number of sides or angles ( 2 or o ) are divided ... Page 204

ABC , A'B'C ' are two As having their vertices connecting concurrently at 0 , and

their corresponding sides intersecting in X , Y , Z. To prove that X , Y , Z are

perpendiculars AP ...

ABC , A'B'C ' are two As having their vertices connecting concurrently at 0 , and

their corresponding sides intersecting in X , Y , Z. To prove that X , Y , Z are

**collinear**. B s A IR A P R C Proof .-- To the sides of Y AA'B'C ' drawperpendiculars AP ...

Page 205

Also , since AA ' , BB ' , CC ' are concurrent at 0 , they divide the angles A ' B ' , C '

so that sin AA'B ' , sin BB'C ' . sin CCA - 1 , sin AA'C ' . sin BB'A ' . sin CC'B ' BX = 1

, and X , Y , Z are

Also , since AA ' , BB ' , CC ' are concurrent at 0 , they divide the angles A ' B ' , C '

so that sin AA'B ' , sin BB'C ' . sin CCA - 1 , sin AA'C ' . sin BB'A ' . sin CC'B ' BX = 1

, and X , Y , Z are

**collinear**. CX The converse of this theorem is readily ...### What people are saying - Write a review

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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.