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

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Page x

SECTION VII .-- Centres and Axes of

SECTION 1 , ---- Anharmonic Division . SECTION II . Harmonic Ratio . SECTION

III . --- Anharmonic Properties . SECTION IV .-- Polar Reciprocals and

Reciprocation .

SECTION VII .-- Centres and Axes of

**Perspective**or Similitude , 178 PART V.SECTION 1 , ---- Anharmonic Division . SECTION II . Harmonic Ratio . SECTION

III . --- Anharmonic Properties . SECTION IV .-- Polar Reciprocals and

Reciprocation .

Page 205

The term

would see A ' coinciding with A and B ' with B , and the segment A'B ' coinciding

with AB . By an extension of this idea O ' is also a centre of

...

The term

**perspective**is introduced from Optics , because an eye placed at Owould see A ' coinciding with A and B ' with B , and the segment A'B ' coinciding

with AB . By an extension of this idea O ' is also a centre of

**perspective**of AB and...

Page 207

EXERCISES 1. The triangle formed by joining the centres of the three excircles of

any triangle is in

excircles of any triangle form a triangle in

tangents ...

EXERCISES 1. The triangle formed by joining the centres of the three excircles of

any triangle is in

**perspective**with it . 2. The three chords of contact of theexcircles of any triangle form a triangle in

**perspective**with the original . 3. Thetangents ...

Page 225

Theorem ... Triangles which are polar reciprocals to one another are in

perpendiculars on A'B ' and A'C ' , BQ and BQ ' be perpenB ' . A diculars on B'C '

and B'A ' , etc.

Theorem ... Triangles which are polar reciprocals to one another are in

**perspective**. Let ABC and A'B'C ' be polar reciprocals . Let AP , AP ' beperpendiculars on A'B ' and A'C ' , BQ and BQ ' be perpenB ' . A diculars on B'C '

and B'A ' , etc.

Page 237

Cor . 5. When 0 = p = , Z cuts S and S ' orthogonally , and OL = 0 , and the centre

of the cutting circle is on the radical axis of the two . SECTION VII . CENTRE AND

AXES OF SIMILITUDE OR

Cor . 5. When 0 = p = , Z cuts S and S ' orthogonally , and OL = 0 , and the centre

of the cutting circle is on the radical axis of the two . SECTION VII . CENTRE AND

AXES OF SIMILITUDE OR

**PERSPECTIVE**OF THE RADICAL AXIS . 237.### 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.