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

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Page x

SECTION II,_

Concurrence, SECTION IV.-Inversion and Inverse Figures. SECTION V.—Pole

and Polar. SECTION VI.-The Radical Axis. SECTION VII.-

Perspective or ...

SECTION II,_

**Centre**of Mean Position, SECTION III.-Collinearity andConcurrence, SECTION IV.-Inversion and Inverse Figures. SECTION V.—Pole

and Polar. SECTION VI.-The Radical Axis. SECTION VII.-

**Centres**and Axes ofPerspective or ...

Page 6

Thus in Mechanics we consider such things as levers, wedges, wheels, cords, etc

., and our diagrams become representations of these things. A pulley or wheel

becomes a circle, its arms become radii of the circle, and its

Thus in Mechanics we consider such things as levers, wedges, wheels, cords, etc

., and our diagrams become representations of these things. A pulley or wheel

becomes a circle, its arms become radii of the circle, and its

**centre**the**centre**of ... Page 54

The fixed point is the

moveable points is the radius of the circle. The curve itself, and especially where

its length is under consideration, is commonly called the circumference of the ...

The fixed point is the

**centre**of the circle, and the distance between the fixed andmoveable points is the radius of the circle. The curve itself, and especially where

its length is under consideration, is commonly called the circumference of the ...

Page 55

Again, since all radii of the same G) are equal, if a line could cut a G) three times,

three equal segments could be drawn from a given point, the

given line. And this is impossible (63°, 3). Therefore a line can cut a G) only ...

Again, since all radii of the same G) are equal, if a line could cut a G) three times,

three equal segments could be drawn from a given point, the

**centre**of the G), to agiven line. And this is impossible (63°, 3). Therefore a line can cut a G) only ...

Page 56

and O is equidistant from A, B, and C. (86°) '.. the G) with

equal to OA, passes through B and C. 7.e.d. 2. Any G) through A, B, and C must

have its

and O is equidistant from A, B, and C. (86°) '.. the G) with

**centre**at O, and radiusequal to OA, passes through B and C. 7.e.d. 2. Any G) through A, B, and C must

have its

**centre**equally distant from these three points. But O is the only point in ...### 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.