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

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Page vii

Parts IV . and V. contain a synthetic treatment of the theories of the mean centre ,

of

line and circle ; and it is believed that a student who becomes acquainted with ...

Parts IV . and V. contain a synthetic treatment of the theories of the mean centre ,

of

**inverse**figures , of pole and polar , of harmonic division , etc. , as applied to theline and circle ; and it is believed that a student who becomes acquainted with ...

Page x

SECTION IV . - Inversion and

SECTION VI . - The Radical Axis . SECTION VII .-- Centres and Axes of

Perspective or Similitude , 178 PART V. SECTION 1 , ---- Anharmonic Division .

SECTION II .

SECTION IV . - Inversion and

**Inverse**Figures . SECTION V .-- Pole and Polar .SECTION VI . - The Radical Axis . SECTION VII .-- Centres and Axes of

Perspective or Similitude , 178 PART V. SECTION 1 , ---- Anharmonic Division .

SECTION II .

Page 137

OP = OT2 ( 169 ) .. the radius is a geometric mean between the join of any point

with the centre and the perpendicular from the centre upon the chord of contact of

the point . Def . - P and Q are called

OP = OT2 ( 169 ) .. the radius is a geometric mean between the join of any point

with the centre and the perpendicular from the centre upon the chord of contact of

the point . Def . - P and Q are called

**inverse**points with respect to the circle ... Page 207

OF INVERSION AND

upon a centre - line of a circle that the radius is a geometric mean ( 169 " , Def . )

between their distances from the centre are called

OF INVERSION AND

**INVERSE**FIGURES . S 256o . Def . - Two points so situatedupon a centre - line of a circle that the radius is a geometric mean ( 169 " , Def . )

between their distances from the centre are called

**inverse**points with respect to ... Page 208

P and Q come together at B ; so that any point on the circle of inversion is its own

inversion is any point at infinity . р U T S 257o . Problem .-- To find the circle to ...

P and Q come together at B ; so that any point on the circle of inversion is its own

**inverse**. 6. When P comes to C , 2 goes to co ; so that the**inverse**of the centre ofinversion is any point at infinity . р U T S 257o . Problem .-- To find the circle to ...

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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.