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

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Page 4

Ex . From the theorem , “ The product of two odd numbers is an odd number , ” by

making the two numbers equal we obtain as a corollary , “ The

number is an odd number . " EXERCISES . State the contrapositives and the ...

Ex . From the theorem , “ The product of two odd numbers is an odd number , ” by

making the two numbers equal we obtain as a corollary , “ The

**square**of an oddnumber is an odd number . " EXERCISES . State the contrapositives and the ...

Page 5

Some such figures are known to every person under such names as “ triangle , " "

properties and relations of plane geometric figures is Plane Geometry . Such is

the ...

Some such figures are known to every person under such names as “ triangle , " "

**square**, " " circle , " etc. 11 ° . That part of mathematics which treats of theproperties and relations of plane geometric figures is Plane Geometry . Such is

the ...

Page 46

A rectangle with two acljacent sides equal is a

Cor . 5. Since the

of the rectangle , Therefore all the sides of a

A rectangle with two acljacent sides equal is a

**square**, denoted by the symbol O.Cor . 5. Since the

**square**is a particular form of the rhombus and a particular formof the rectangle , Therefore all the sides of a

**square**are equal to one another ... Page 61

What is the axis of symmetry of ( a ) a

triangle , ( d ) an equilateral triangle ? Give all the axes where there are more

than one . 12. When a rectilinear figure has more than one axis of symmetry ,

what ...

What is the axis of symmetry of ( a ) a

**square**, ( 6 ) a rectangle , ( c ) an isoscelestriangle , ( d ) an equilateral triangle ? Give all the axes where there are more

than one . 12. When a rectilinear figure has more than one axis of symmetry ,

what ...

Page 66

A , B , C , D are the vertices of a

inscribed in the same circle . What is the angle between the lines BE and DF ?

between BF and ED ? SPECIAL SECANTS -- TANGENT . 109o . Let P be 66 ...

A , B , C , D are the vertices of a

**square**, and A , E , F of an equilateral triangleinscribed in the same circle . What is the angle between the lines BE and DF ?

between BF and ED ? SPECIAL SECANTS -- TANGENT . 109o . Let P be 66 ...

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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.