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

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Page x

SECTION VII .-- Centres and Axes of Perspective or

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 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

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. Page 239

When two similar polygons are so placed as to have their homologous sides

parallel , they are in perspective , and the joins of corresponding vertices concur

at a centre of

When two similar polygons are so placed as to have their homologous sides

parallel , they are in perspective , and the joins of corresponding vertices concur

at a centre of

**similitude**. Let ABCD ... , abcd ... be the polygons . Since they are ... Page 241

Then O is the centre of

S S с X H + Z circles S and S ' as being similarly placed Hence X and X ' , as also

Y and Y ' , are homologous points , and ( 283 , Cor . 1 ) the tangents at X and X ...

Then O is the centre of

**similitude**due to considering the L X Х Y X S с с z S Z ' S 'S S с X H + Z circles S and S ' as being similarly placed Hence X and X ' , as also

Y and Y ' , are homologous points , and ( 283 , Cor . 1 ) the tangents at X and X ...

Page 243

When the circles are concentric , the centres of

common centre of the circles , unless the circles are also equal , when one centre

of

...

When the circles are concentric , the centres of

**similitude**coincide with thecommon centre of the circles , unless the circles are also equal , when one centre

of

**similitude**becomes any point whatever . 6. If one of the circles becomes a point...

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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.