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

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Page 8

surface . Such is the surface of

the curve , the plane and the curved surface are the elements which go to make ...

**A**surface which is not plane , and which is not composed of planes , is**a**curvedsurface . Such is the surface of

**a**sphere , or cylinder . 19 ° . The**point**, the line ,the curve , the plane and the curved surface are the elements which go to make ...

Page 10

To do this we put C in such

end-

line through

So ...

To do this we put C in such

**a**position that it may be twice as far from one of theend-

**points**of the segment,**A**say, as it is from the other, B. But on the indefiniteline through

**A**and B we may place C" so as to be twice as far from**A**as from B.So ...

Page 11

A straight line is the shortest distance between two

possible to give a reasonable proof of this axiom , no amount of proof could make

its truth more apparent . The following will illustrate the axiom . Assume any two ...

A straight line is the shortest distance between two

**given points**. Although it ispossible to give a reasonable proof of this axiom , no amount of proof could make

its truth more apparent . The following will illustrate the axiom . Assume any two ...

Page 16

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

to, is expressed by

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

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 19

angles or

angle they are com//ementary to one another, and each is the complement of the

...

**A**right angle is denoted by the symbol T. The symbol L also denotes two rightangles or

**a**straight angle. Des. 3.--When two angles together make up**a**rightangle they are com//ementary to one another, and each is the complement of 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.