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

### From inside the book

Results 1-5 of 93

Page 2

The whole is

of its parts. ii. Things,

the ...

The whole is

**equal**to the sum of all its parts, and therefore greater than any oneof its parts. ii. Things,

**equal**to the same thing are**equal**to one another. iii. If**equals**be added to**equals**the sums are**equal**. iv. If**equals**be taken from**equals**the ...

Page 11

Therefore a straight finite line has its end-points further apart than a curved line of

when the line is straight than when it is curved. Des—The distance between two ...

Therefore a straight finite line has its end-points further apart than a curved line of

**equal**length. Or, a less length of line will reach from one given point to anotherwhen the line is straight than when it is curved. Des—The distance between two ...

Page 12

Des—The sum of two segments is that segment which is

placed in line with one end-point in each coincident. Let AB and DE be two

segments, and on the line of which D E. AB is a segment let BC be

Des—The sum of two segments is that segment which is

**equal**to the two whenplaced in line with one end-point in each coincident. Let AB and DE be two

segments, and on the line of which D E. AB is a segment let BC be

**equal**to DE. Page 16

Des—Two angles are

coincide in direction respec. tively with the arms of the other ; or when the angles

are described by the same rotation. Thus, if, when O' is placed upon O, and A e O'

A' is ...

Des—Two angles are

**equal**when the arms of the one O may be made tocoincide in direction respec. tively with the arms of the other ; or when the angles

are described by the same rotation. Thus, if, when O' is placed upon O, and A e O'

A' is ...

Page 18

These four angles consist of two pairs of of fosise or versica/ angles, viz., A., A',

and B, B', A being opposite A', and B being opposite B'. 40°. Theorem.—The

opposite angles of a pair formed by two intersecting lines are

another.

These four angles consist of two pairs of of fosise or versica/ angles, viz., A., A',

and B, B', A being opposite A', and B being opposite B'. 40°. Theorem.—The

opposite angles of a pair formed by two intersecting lines are

**equal**to oneanother.

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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.