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

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Page vi

An endeavour is made to connect Geometry with Algebraic forms and

1 ) by an elementary study of the modes of representing geometric ideas in the

An endeavour is made to connect Geometry with Algebraic forms and

**symbols**, (1 ) by an elementary study of the modes of representing geometric ideas in the

**symbols**of Algebra , and ( 2 ) by determining the consequent geometric ... Page 12

Now this is equivalent to saying that AC is longer than AB by the segment DE , or

that AC is equal to the sum of AB and DE . Hence when we have AB = AC - DE

we can write AC = AB + DE . We thus see that in using these algebraic

Now this is equivalent to saying that AC is longer than AB by the segment DE , or

that AC is equal to the sum of AB and DE . Hence when we have AB = AC - DE

we can write AC = AB + DE . We thus see that in using these algebraic

**symbols**... Page 15

The

vertex the angle between them may be denoted by a single letter placed at the

vertex , as the 20 , or by B a letter with or without an arch of dots , as LB ; or by

three ...

The

**symbol**L is used for the word “ angle . " 2. When two segments meet at avertex the angle between them may be denoted by a single letter placed at the

vertex , as the 20 , or by B a letter with or without an arch of dots , as LB ; or by

three ...

Page 18

Def . 2 .-- When two intersecting lines form a right angle at their point of

intersection , they are said to be perpendicular to one another , and each is

perpendicular to the other . Perpendicularity is denoted by the

SYNTHETIC ...

Def . 2 .-- When two intersecting lines form a right angle at their point of

intersection , they are said to be perpendicular to one another , and each is

perpendicular to the other . Perpendicularity is denoted by the

**symbol**I , to be 18SYNTHETIC ...

Page 19

Perpendicularity is denoted by the

perpendicular to . " A right angle is denoted by the

denotes two right angles or a straight angle . Def . 3. - When two angles together

...

Perpendicularity is denoted by the

**symbol**I , to be read " perpendicular to " or " isperpendicular to . " A right angle is denoted by the

**symbol**7 . The**symbol**I alsodenotes two right angles or a straight angle . Def . 3. - When two angles together

...

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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.