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

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Page 9

A point is

indefinite line is also

letter |- g o has no reference to any point. A B A segment is

...

A point is

**denoted**by a single letter whereever practicable, as “the point A.” Anindefinite line is also

**denoted**by a single letter as “the line L,” but in this case theletter |- g o has no reference to any point. A B A segment is

**denoted**by naming its...

Page 12

... where =

AB and DE in line so as to have one common point as an end-point for each. The

interpretation of the whole is, that AC is equal in Zemg// to AB and DE together.

... where =

**denotes**equality in length, and +**denotes**the placing of the segmentsAB and DE in line so as to have one common point as an end-point for each. The

interpretation of the whole is, that AC is equal in Zemg// to AB and DE together.

Page 15

When two segments meet at a vertex the angle between them may be

a single letter B placed at the vertex, as the 4-O , or by a letter with or without an

arch of dots, as 4.8 ; or by three letters of which the extreme ones

When two segments meet at a vertex the angle between them may be

**denoted**bya single letter B placed at the vertex, as the 4-O , or by a letter with or without an

arch of dots, as 4.8 ; or by three letters of which the extreme ones

**denote**points ... Page 16

The angle between two lines, when the vertex is not o /N pictured, or not referred

to, is expressed by A (L. M.), or LM, where L and M

letter notation (22°); or 4 (AB, CD), where AB and CD

The angle between two lines, when the vertex is not o /N pictured, or not referred

to, is expressed by A (L. M.), or LM, where L and M

**denote**the lines in the one-letter notation (22°); or 4 (AB, CD), where AB and CD

**denote**the lines in the ... Page 18

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

intersection, they are said to be ser/endicular to one another, and each is ser/

esidicular to the other. Perpendicularity is

SYNTH ETIC ...

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

intersection, they are said to be ser/endicular to one another, and each is ser/

esidicular to the other. Perpendicularity is

**denoted**by the symbol L, to be read I 8SYNTH ETIC ...

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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.