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

### From inside the book

Results 1-5 of 18

Page 74

Trisect a right angle and thence show how to draw a

a circle. . If r, r' be the radii of two circles, and d the distance between them, the

circles touch when d- rit?'. . Give the conditions under which two circles have 4, 3,

...

Trisect a right angle and thence show how to draw a

**regular**12-sided polygon ina circle. . If r, r' be the radii of two circles, and d the distance between them, the

circles touch when d- rit?'. . Give the conditions under which two circles have 4, 3,

...

Page 86

The circles touching the lines and having centres at Op O2, and Os are the

escribed or ea-circ/es of the triangle.

closed rectilinear figure without re-entrant angles (89°, 2) is in general called a

polygon.

The circles touching the lines and having centres at Op O2, and Os are the

escribed or ea-circ/es of the triangle.

**REGULAR**POLYGONS. 132°. Des. I.-Aclosed rectilinear figure without re-entrant angles (89°, 2) is in general called a

polygon.

Page 87

–Let AB, BC be two consecu- > C tive sides of the polygon and O its centre. Then

the triangles AOB, BOC are isosceles and congruent. * 4 OAB = 4 OBA = 4 ...

**regular**polygon, the magnitude of an internal angle is (2 –4) right angles. f? Proof–Let AB, BC be two consecu- > C tive sides of the polygon and O its centre. Then

the triangles AOB, BOC are isosceles and congruent. * 4 OAB = 4 OBA = 4 ...

Page 88

Therefore ABCDEF is a

triangle, AB = AO ; '.. the side of a

circumcircle. 135°. Problem.—To determine which species of

each ...

Therefore ABCDEF is a

**regular**hexagon. Cor. Since AOB is an equilateraltriangle, AB = AO ; '.. the side of a

**regular**hexagon is equal to the radius of itscircumcircle. 135°. Problem.—To determine which species of

**regular**polygons,each ...

Page 90

To inscribe a

circle. A, B, C, D, ... , are consecutive vertices of a

, ..., of a

To inscribe a

**regular**octagon in a circle. To inscribe a**regular**dodecagon in acircle. A, B, C, D, ... , are consecutive vertices of a

**regular**octagon, and A, B, C, D', ..., of a

**regular**dodecagon in the same circle. Find the angles between AC and ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### Common terms and phrases

ABCD algebraic altitude base becomes called centre centre-line chord circle coincide common concurrent congruent considered constant construct Converse corresponding denote describe determine diagonals diameter difference direction distance divide draw drawn equal expressed external figure fixed four geometric given line given point gives greater harmonic Hence internal intersect inverse join length lies line-segment mean measure median meet middle point one-half opposite opposite sides pair parallel passes perpendicular placed plane point of contact polar polygon position Proof proved quadrangle radical axis radius range ratio rectangle regular relation respectively right angle right bisector rotation secant segment sense sides similar Similarly 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.