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

### From inside the book

Results 1-5 of 18

Page 76

... to in the sequel . In “ Practical Geometry ” the “ Rule ” ( 16 ° ) furnishes the

means of

circle . In Theoretic Constructive Geometry we assume the ability to

these ...

... to in the sequel . In “ Practical Geometry ” the “ Rule ” ( 16 ° ) furnishes the

means of

**constructing**a line , and the “ Compasses ” ( 92 ° ) of**constructing**acircle . In Theoretic Constructive Geometry we assume the ability to

**construct**these ...

Page 77

To

segment . B Construction.— With A and B as centres and with a radius AD

greater than half of Ā ; D AB describe circles . Since AB is < the sum of the radii

and > their ...

To

**construct**the right bisector of a given line segment . Let AB be the givensegment . B Construction.— With A and B as centres and with a radius AD

greater than half of Ā ; D AB describe circles . Since AB is < the sum of the radii

and > their ...

Page 78

... DP is I to L. : . the construction draws a I to L at a given point in L. ( Compare

119 " , Cor . 2 ) Cor . 2. Let L be a given line and C a given point . To draw

through C a line parallel to L. With C as the centre of a circle ,

as given .

... DP is I to L. : . the construction draws a I to L at a given point in L. ( Compare

119 " , Cor . 2 ) Cor . 2. Let L be a given line and C a given point . To draw

through C a line parallel to L. With C as the centre of a circle ,

**construct**a figureas given .

Page 80

Given the sides of a triangle to

triangle in line , as AB , BC , CD . With centre C and radius CD D describe a circle

, and with centre B and radius BA describe a circle . Let E be one point of ...

Given the sides of a triangle to

**construct**it . Constr .-- Place the three sides of thetriangle in line , as AB , BC , CD . With centre C and radius CD D describe a circle

, and with centre B and radius BA describe a circle . Let E be one point of ...

Page 81

To

. Let a and I be two sides and 12 the median to the third side . Suppose ACB is

the required triangle having CD as the given median . By completing the DACBC

...

To

**construct**a triangle when two sides and the median to the third side are given. Let a and I be two sides and 12 the median to the third side . Suppose ACB is

the required triangle having CD as the given median . By completing the DACBC

...

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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.