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

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Page v

Thus a triangle is not the three - cornered portion of the plane inclosed within its

usually termed its vertices and its

Thus a triangle is not the three - cornered portion of the plane inclosed within its

**sides**, but the combination of the three points and three lines forming what areusually termed its vertices and its

**sides**and**sides**produced . This mode of ... Page 3

Ex . Of two

opposite these

greater

Ex . Of two

**sides**of a triangle only one can be the greater , and of the two anglesopposite these

**sides**only one can be the greater . Then , if it is proved that thegreater

**side**is opposite the greater angle it follows that the greater angle is ... Page 23

The points are the vertices of the triangle , and the linesegments which have the

points as end - points are the

lines are usually spoken of as the “

generality ...

The points are the vertices of the triangle , and the linesegments which have the

points as end - points are the

**sides**. The remaining portions of the determinedlines are usually spoken of as the “

**sides**produced . ” But in many casesgenerality ...

Page 24

Hence when the three points , forming the vertices , are given , or when the three

lines or line - segments forming the

given . This is not the case with a rectilinear figure having any number of vertices

...

Hence when the three points , forming the vertices , are given , or when the three

lines or line - segments forming the

**sides**are given , the triangle is completelygiven . This is not the case with a rectilinear figure having any number of vertices

...

Page 25

The angles of the triangle are denoted usually by the capital letters A , B , C , and

the

two figures compared by superposition coincide in all their parts and become ...

The angles of the triangle are denoted usually by the capital letters A , B , C , and

the

**sides**opposite by the corresponding small letters a , b , c . 51 ° . Def . - Whentwo figures compared by superposition coincide in all their parts and become ...

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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.