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

### From inside the book

Results 1-5 of 74

Page 4

... The sum of two odd numbers is an even number. 2. A diameter is the longest

chord in a circle. 3. Parallel lines never meet. - 4. Every point equidistant from the

end-points of a

... The sum of two odd numbers is an even number. 2. A diameter is the longest

chord in a circle. 3. Parallel lines never meet. - 4. Every point equidistant from the

end-points of a

**linesegment**is on the right bisector of that segment, - SECTION I. Page 8

The point, the line, the curve, the plane and the curved surface are the elements

which go to make up geometric figures. ... A limited portion of a line, especially

when any reference is had to its length, is a sinise line, or a

simply ...

The point, the line, the curve, the plane and the curved surface are the elements

which go to make up geometric figures. ... A limited portion of a line, especially

when any reference is had to its length, is a sinise line, or a

**line**-**segment**, orsimply ...

Page 9

That absolute sameness (14°) which characterizes every part of a

directly to the following conclusions:— (1) No distinction can be made between

any two

That absolute sameness (14°) which characterizes every part of a

**line**leadsdirectly to the following conclusions:— (1) No distinction can be made between

any two

**segments**of the same**line**equal in length, except that of position in the**line**. Page 10

To do this we put C in such a position that it may be twice as far from one of the

end-points of the

So ...

To do this we put C in such a position that it may be twice as far from one of the

end-points of the

**segment**, A say, as it is from the other, B. But on the indefinite**line**through A and B we may place C" so as to be twice as far from A as from B.So ...

Page 11

Des—The distance between two points is the length of the

connects them or has them as end-points. ... Hence a

of one dimension, Two

made to ...

Des—The distance between two points is the length of the

**segment**whichconnects them or has them as end-points. ... Hence a

**line**is called a magnitudeof one dimension, Two

**segments**are equal when the end-points of one can bemade to ...

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### 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.