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

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Page 15

A line which changes its direction in a plane while passing through a

in the plane is said to rotate about the point . The point about which the rotation

takes place is the pole , and any segment of the rotating line , having the pole as

...

A line which changes its direction in a plane while passing through a

**fixed point**in the plane is said to rotate about the point . The point about which the rotation

takes place is the pole , and any segment of the rotating line , having the pole as

...

Page 53

The compasses , whatever be their form , furnish us with two

which , from the rigidity of H the instrument , are supposed to preserve an

unvarying distance from one another . Then , if one of the

the other ...

The compasses , whatever be their form , furnish us with two

**points**, A and B ,which , from the rigidity of H the instrument , are supposed to preserve an

unvarying distance from one another . Then , if one of the

**points**A is**fixed**, whilethe other ...

Page 54

surface , the moving point describes a physical circle . The limit of this physical

circle , when the curved line has its thickness diminished endlessly , is the

geometric circle . Def . 2 .-- The

distance ...

surface , the moving point describes a physical circle . The limit of this physical

circle , when the curved line has its thickness diminished endlessly , is the

geometric circle . Def . 2 .-- The

**fixed point**is the centre of the circle , and thedistance ...

Page 67

Let P be a

the secant L , cutting the circle in P and Q , depends upon the position of Q. As Q

moves along the the secant rotates about P as pole . While 2 makes one

complete ...

Let P be a

**fixed point**on the OS and Q a variable one , S T Р T ' The position ofthe secant L , cutting the circle in P and Q , depends upon the position of Q. As Q

moves along the the secant rotates about P as pole . While 2 makes one

complete ...

Page 71

Hence a circle S is cut orthogonally by any circle having its centre at a

without S and its radius the tangent from the ... If the tangents at A and C are

, and the tangent at B is variable , we have the following theorem : The segment

of a ...

Hence a circle S is cut orthogonally by any circle having its centre at a

**point**without S and its radius the tangent from the ... If the tangents at A and C are

**fixed**, and the tangent at B is variable , we have the following theorem : The segment

of a ...

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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.