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

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Page 18

These four angles consist of two pairs of opposite or vertical angles , viz . , A , A ' ,

and B , B ' , A being opposite A ' , and B being opposite B ' . .. 40 ° . Theorem .--—

The opposite angles of a pair formed by two

These four angles consist of two pairs of opposite or vertical angles , viz . , A , A ' ,

and B , B ' , A being opposite A ' , and B being opposite B ' . .. 40 ° . Theorem .--—

The opposite angles of a pair formed by two

**intersecting**lines are equal to one ... Page 22

The lines L , M

to L and M. The angle between L ' and M ' is equal to that between L and M.

SECTION III . THREE OR MORE POINTS AND LINES . THE TRIANGLE . N 46 ° .

The lines L , M

**intersect**at 0 , and through O , L ' and M ' are drawn I respectivelyto L and M. The angle between L ' and M ' is equal to that between L and M.

SECTION III . THREE OR MORE POINTS AND LINES . THE TRIANGLE . N 46 ° .

Page 39

Two lines , in the same plane , which do not

parallel . Next to perpendicularity , parallelism is the most important directional

relation . It is denoted by the symbol ll , which is to be read “ parallel to ” or “ is

parallel to ...

Two lines , in the same plane , which do not

**intersect**at any finite point areparallel . Next to perpendicularity , parallelism is the most important directional

relation . It is denoted by the symbol ll , which is to be read “ parallel to ” or “ is

parallel to ...

Page 44

Two lines , which are respectively perpendicular to two

sides is in general called a quadrangle cor quadrilateral . Thus ABCD is a

quadrangle .

Two lines , which are respectively perpendicular to two

**intersecting**lines ,**intersect**at some finite point . B 80 ° . Def.-I. A closed figure having four lines assides is in general called a quadrangle cor quadrilateral . Thus ABCD is a

quadrangle .

Page 45

The quadrangle formed when two parallel lines

is a parallelogram , and is usually denoted by the symbol p . 81 ° . Theorem .-- In

any parallelogram1. The opposite sides are equal to one another . 2.

The quadrangle formed when two parallel lines

**intersect**two other parallel linesis a parallelogram , and is usually denoted by the symbol p . 81 ° . Theorem .-- In

any parallelogram1. The opposite sides are equal to one another . 2.

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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.