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

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Page 5

This surface can have no thickness , as in such a case it would include a part of

the board or of the space without or of both , and would not be the

10 ° . A flat surface , as that of a black - board , is a plane surface , or a Plane .

This surface can have no thickness , as in such a case it would include a part of

the board or of the space without or of both , and would not be the

**dividing**limit .10 ° . A flat surface , as that of a black - board , is a plane surface , or a Plane .

Page 10

But on account of the similar relations held by C and C ' to the endpoints of the

segment , it is convenient and advantageous to consider both points as

the segment AB . When thus considered , C is said to divide the segment

internally ...

But on account of the similar relations held by C and C ' to the endpoints of the

segment , it is convenient and advantageous to consider both points as

**dividing**the segment AB . When thus considered , C is said to divide the segment

internally ...

Page 19

For practical purposes the right angle is

degrees ; each degree is

minute into 60 equal parts called seconds . Thus an angle which is one - seventh

of a ...

For practical purposes the right angle is

**divided**into go equal parts calleddegrees ; each degree is

**divided**into 60 equal parts called minutes ; and eachminute into 60 equal parts called seconds . Thus an angle which is one - seventh

of a ...

Page 21

Just as in 23 ° we found two points which are said to divide the segment in the

same manner , so we may find two lines

manner , one

drawn that ...

Just as in 23 ° we found two points which are said to divide the segment in the

same manner , so we may find two lines

**dividing**a given angle in the samemanner , one

**dividing**it internally , and the other externally . Thus , if OE is sodrawn that ...

Page 52

If the middle points of the sides of a Abe joined two and two , the A is

four congruent As . 13. From any point in a side of an equilateral A lines are

drawn parallel to the other sides . The perimeter of the Oso formed is equal to

twice a ...

If the middle points of the sides of a Abe joined two and two , the A is

**divided**intofour congruent As . 13. From any point in a side of an equilateral A lines are

drawn parallel to the other sides . The perimeter of the Oso formed is equal to

twice a ...

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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.