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

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Page vii

In dealing with

Hamilton's word sensor as seeming to me to express most clearly what is meant.

After treating of proportion I have not hesitated to employ those special

In dealing with

**ratio**I have ventured, when comparing two finite lines, to introduceHamilton's word sensor as seeming to me to express most clearly what is meant.

After treating of proportion I have not hesitated to employ those special

**ratios**... Page x

Harmonic

Reciprocals and Reciprocation. SECTION V.—Homography and Involution, 0.

e e e e . . . 252 P A R T I. GENERAL CONSIDERATIONS. I”. A statement Y.

CONTENTS.

Harmonic

**Ratio**. SECTION III.-Anharmonic Properties. SECTION IV.-PolarReciprocals and Reciprocation. SECTION V.—Homography and Involution, 0.

e e e e . . . 252 P A R T I. GENERAL CONSIDERATIONS. I”. A statement Y.

CONTENTS.

Page 147

The fraction * is called in Arithmetic or Algebra the

Geometry it is called the

unity has to the fraction 7% 7? while that of AB becomes o Therefore the

AB to ...

The fraction * is called in Arithmetic or Algebra the

**ratio**7? of m to m, and inGeometry it is called the

**ratio**of AB to CD. Now we has to 77, the same**ratio**asunity has to the fraction 7% 7? while that of AB becomes o Therefore the

**ratio**ofAB to ...

Page 150

eted geometrically by the sensor which brings the denominator so the numerator,

or as the

AMONGST LINE-SEGMENTS. 192°. Des—Four line-segments taken in order ...

eted geometrically by the sensor which brings the denominator so the numerator,

or as the

**ratio**of the numerator to the denominator. SECTION I. PROPORTIONAMONGST LINE-SEGMENTS. 192°. Des—Four line-segments taken in order ...

Page 165

And BC is divided into extreme and mean

construction is readily obtained. A —a Cor. I. The isosceles triangle ADB has

each of its basal angles equal to one-third its vertical angle. Cor. 2. / ABC = 36°, 4

BAC ...

And BC is divided into extreme and mean

**ratio**at D (183°, Ex. 1). Thence theconstruction is readily obtained. A —a Cor. I. The isosceles triangle ADB has

each of its basal angles equal to one-third its vertical angle. Cor. 2. / ABC = 36°, 4

BAC ...

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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.