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

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Page v

The work differs also from the majority of modern treatises on Geometry in

several

taken as the geometric elements of Plane Geometry , and any one of these or any

...

The work differs also from the majority of modern treatises on Geometry in

several

**respects**. The point , the line , and the curve lying in a common plane aretaken as the geometric elements of Plane Geometry , and any one of these or any

...

Page 7

... most prominent property , and in fact the distinctive property of a straight line ,

is the absolute sameness which characterizes all its parts , so that two portions of

the same straight line can differ from one another in no

... most prominent property , and in fact the distinctive property of a straight line ,

is the absolute sameness which characterizes all its parts , so that two portions of

the same straight line can differ from one another in no

**respect**except in length . Page 11

Two line - segments can be compared with

is called a magnitude of one dimension . Two segments are equal when the end -

points of one can be made to coincide with the end - points of the THE LINE ...

Two line - segments can be compared with

**respect**to length only . Hence a lineis called a magnitude of one dimension . Two segments are equal when the end -

points of one can be made to coincide with the end - points of the THE LINE ...

Page 25

Equality in this

only one kind of comparison is possible , as is the case with line - segments and

angles , the word equal is used . CONGRUENCE AMONGST TRIANGLES . 52 ° .

Equality in this

**respect**is expressed by saying that the figures are equal . Whenonly one kind of comparison is possible , as is the case with line - segments and

angles , the word equal is used . CONGRUENCE AMONGST TRIANGLES . 52 ° .

Page 27

Cor . 3. Since an equilateral triangle is isosceles with

base , all the angles of an equilateral triangle are equal to one another ; or , an

equilateral triangle is equiangular . 54 " Theorem .-- Every point equidistant from

the ...

Cor . 3. Since an equilateral triangle is isosceles with

**respect**to each side asbase , all the angles of an equilateral triangle are equal to one another ; or , an

equilateral triangle is equiangular . 54 " Theorem .-- Every point equidistant from

the ...

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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.