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

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Page 70

The angle at which two circles intersect is the angle between their tangents at the

point of intersection . Def . 2. When two circles intersect at right angles they are

said to cut each other

...

The angle at which two circles intersect is the angle between their tangents at the

point of intersection . Def . 2. When two circles intersect at right angles they are

said to cut each other

**orthogonally**, The same term is conveniently applied to the...

Page 71

If , in the Fig . to 114 ° , PA be made the radius of a circle and P its centre , the

circle will cut the circle S

perpendicular to the radii . Hence a circle S is cut

having its ...

If , in the Fig . to 114 ° , PA be made the radius of a circle and P its centre , the

circle will cut the circle S

**orthogonally**. For the tangents at A are respectivelyperpendicular to the radii . Hence a circle S is cut

**orthogonally**by any circlehaving its ...

Page 119

... and where no reference is made to length the join of two points may be taken

to mean the line determined by the points . 2. The foot of the perpendicular from a

given point to a given line is the

... and where no reference is made to length the join of two points may be taken

to mean the line determined by the points . 2. The foot of the perpendicular from a

given point to a given line is the

**orthogonal**projection , or simply the projection ... Page 210

( 1789 ) a O which cuts two Os '

Cor . 4. A 0 having its centre on the radical axis of two given Os , and cutting one

of them

( 1789 ) a O which cuts two Os '

**orthogonally**has its centre on their radical axis .Cor . 4. A 0 having its centre on the radical axis of two given Os , and cutting one

of them

**orthogonally**, cuts the other**orthogonally**also . S 259o . Let P , Q be ... Page 211

Το raw a circle so as to pass through a given point and cut a given circle

common centre - line of two circles to find a pair of points which are inverse to

both circles ...

Το raw a circle so as to pass through a given point and cut a given circle

**orthogonally**. 3. To draw a circle to cut two given circles**orthogonally**. 4. On thecommon centre - line of two circles to find a pair of points which are inverse to

both circles ...

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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.