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

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Page vi

... of geometric relations but also conduces to greater generality . In dealing with

proportion the method of

as being equally accurate , easier of comprehension , and more in vi PREFACE .

... of geometric relations but also conduces to greater generality . In dealing with

proportion the method of

**measures**is employed in preference to that of multiplesas being equally accurate , easier of comprehension , and more in vi PREFACE .

Page ix

SECTION V. - The Circle . SECTION VI . - Constructive Geometry , . I PART II .

SECTION 1. - Comparison of Areas . SECTION 11 .-

Areas . SECTION III .-- Geometric Interpretation of Algebraic Forms . SECTION IV

.

SECTION V. - The Circle . SECTION VI . - Constructive Geometry , . I PART II .

SECTION 1. - Comparison of Areas . SECTION 11 .-

**Measurement**of Lengths andAreas . SECTION III .-- Geometric Interpretation of Algebraic Forms . SECTION IV

.

Page 14

... E vanishes . Hence an angle is capable of continuous increase or diminution ,

and is therefore a magnitude . And , being magnitudes , angles are capable of

being compared with one another as to greatness , and hence , of being

... E vanishes . Hence an angle is capable of continuous increase or diminution ,

and is therefore a magnitude . And , being magnitudes , angles are capable of

being compared with one another as to greatness , and hence , of being

**measured**... Page 83

Since SE may be

have their sides passing through the same four points P , Q , R , S , and having P

and Q on opposite sides . Also , since P may be first connected with R or S , two ...

Since SE may be

**measured**in two directions along the line SX , two squares canhave their sides passing through the same four points P , Q , R , S , and having P

and Q on opposite sides . Also , since P may be first connected with R or S , two ...

Page 92

The altitude of a figure is the line - segment which

farthest point of a figure from a side taken as base . The terms base and altitude

are thus correlative . A triangle may have three different bases and as many ...

The altitude of a figure is the line - segment which

**measures**the distance of thefarthest point of a figure from a side taken as base . The terms base and altitude

are thus correlative . A triangle may have three different bases and as many ...

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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.