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

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Page vii

... division , etc. , as applied to the line and circle ; and it is believed that a student

who

form will be greatly assisted in the wider discussion of them in analytical conics .

... division , etc. , as applied to the line and circle ; and it is believed that a student

who

**becomes**acquainted with these geometric extensions in this their simplerform will be greatly assisted in the wider discussion of them in analytical conics .

Page 6

In the practical applications of Geometry the diagrams frequently

material or represent material objects . ... A pulley or wheel

arms

cords ...

In the practical applications of Geometry the diagrams frequently

**become**material or represent material objects . ... A pulley or wheel

**becomes**a circle , itsarms

**become**radii of the circle , and its centre the centre of the circle ; stretchedcords ...

Page 11

If one figure can be superimposed upon another so as to coincide with the latter

in every part , the two figures are necessarily and identically equal , and

virtually one figure by the superposition . 27 ° . Two line - segments can be ...

If one figure can be superimposed upon another so as to coincide with the latter

in every part , the two figures are necessarily and identically equal , and

**become**virtually one figure by the superposition . 27 ° . Two line - segments can be ...

Page 13

In Art . 23 ° , if C

30 ° the internal point of bisection is spoken of . What meaning can you give to

the “ external point of bisection ” ? SECTION II . RELATIONS OF TWO LINES.

In Art . 23 ° , if C

**becomes**the middle point of AB , what**becomes**of C ' ? 5. In Art .30 ° the internal point of bisection is spoken of . What meaning can you give to

the “ external point of bisection ” ? SECTION II . RELATIONS OF TWO LINES.

Page 14

If the stars appear to recede from one another , the angle at E

Thus , if B moves into the position of C , the angle between EA and EC is greater

than the angle between EA and EB . Similarly , if the stars appear to approach ...

If the stars appear to recede from one another , the angle at E

**becomes**greater .Thus , if B moves into the position of C , the angle between EA and EC is greater

than the angle between EA and EB . Similarly , if the stars appear to approach ...

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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.