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

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Page 16

The angle between two lines , when the vertex is not , where I and M denote the

lines in the one - letter notation ( 22 ° ) ; or ( ( AB , CD ) , where AB and CD

denote the ...

GEOMETRY .

The angle between two lines , when the vertex is not , where I and M denote the

lines in the one - letter notation ( 22 ° ) ; or ( ( AB , CD ) , where AB and CD

denote the ...

**One**-**half**of a circumangle is a straight angle 16 SYNTHETICGEOMETRY .

Page 17

a right angle . B 37o . Theorem .-- If any number of lines meet in a point , the sum

of all the adjacent angles formed is a circumangle . OA , OB , OC , ... , OF are ...

**One**-**half**of a circumangle is a straight angle , and onefourth of a circumangle isa right angle . B 37o . Theorem .-- If any number of lines meet in a point , the sum

of all the adjacent angles formed is a circumangle . OA , OB , OC , ... , OF are ...

Page 47

Or , the line - segment joining the middle points of the nonparallel sides of a

trapezoid is equal to

transversals meet upon one of the extreme parallels , the figure AEF ' becomes a

A and ...

Or , the line - segment joining the middle points of the nonparallel sides of a

trapezoid is equal to

**one**-**half**the sum of the parallel sides . Cor . 2. When thetransversals meet upon one of the extreme parallels , the figure AEF ' becomes a

A and ...

Page 52

The internal bisector of one angle of a A and the external bisector of another

angle meet at an angle which is equal to

is the orthocentre of the AABC . Express the angles AOB , BOC , and COA in

terms of ...

The internal bisector of one angle of a A and the external bisector of another

angle meet at an angle which is equal to

**one**-**half**the third angle of the A. 16. Ois the orthocentre of the AABC . Express the angles AOB , BOC , and COA in

terms of ...

Page 64

An angle at the circle is

corresponding to major and minor to minor . LAOB minor is 2LAPB . Р A B с Q

Proof . - Since AAPO is isosceles , B ' LOAP LOPA , ( 53 , Cor . 1 ) and LOAP +

LOPA ...

An angle at the circle is

**one**-**half**the corresponding angle at the centre , majorcorresponding to major and minor to minor . LAOB minor is 2LAPB . Р A B с Q

Proof . - Since AAPO is isosceles , B ' LOAP LOPA , ( 53 , Cor . 1 ) and LOAP +

LOPA ...

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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.