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

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Page 4

EXERCISES. State the contrapositives and the converses of the following

theorems – I. The sum of two odd numbers is an even number. 2. A diameter is

the longest

equidistant from ...

EXERCISES. State the contrapositives and the converses of the following

theorems – I. The sum of two odd numbers is an even number. 2. A diameter is

the longest

**chord**in a circle. 3. Parallel lines never meet. - 4. Every pointequidistant from ...

Page 55

—The segment of a secant * * - so e AzTNP included within the G) is a

Thus the line L, or AB, is a c .** O secant, and the segment AB is a M O

°) The term

—The segment of a secant * * - so e AzTNP included within the G) is a

**chord**. |Thus the line L, or AB, is a c .** O secant, and the segment AB is a M O

**chord**. (21°) The term

**chord**whenever involv. ing the idea of length means the segment ... Page 56

Cor. 2. A point from which more than two equal segments can be drawn to a

circle is the centre of that circle. Cor. 3. Since L is a centre-line and is also the

right bisector of AB, '... the right bisector of a

AOB is ...

Cor. 2. A point from which more than two equal segments can be drawn to a

circle is the centre of that circle. Cor. 3. Since L is a centre-line and is also the

right bisector of AB, '... the right bisector of a

**chord**is a centre line, Cor. 4. The Z\AOB is ...

Page 57

If two

then P is the centre. Proof.-Since P is the middle point of both AD and CB (hyp.),

therefore the right bisectors of AD and CB both pass through P. But these right ...

If two

**chords**bisect one another they are both diameters. - If AP–PD and CP-PB,then P is the centre. Proof.-Since P is the middle point of both AD and CB (hyp.),

therefore the right bisectors of AD and CB both pass through P. But these right ...

Page 58

Two secants which make equal

Centre-line through their point of intersection. AB = CD, and PO is a centre-line

through the point of intersection of AB and CD. Then Z_APO = Z_CPO. Proof.-Let

OE ...

Two secants which make equal

**chords**A SB op make equal angles with theCentre-line through their point of intersection. AB = CD, and PO is a centre-line

through the point of intersection of AB and CD. Then Z_APO = Z_CPO. Proof.-Let

OE ...

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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.