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

### From inside the book

Results 1-5 of 86

Page 8

The study of spatial figures constitutes Solid Geometry , or the Geometry of Space

, as distinguished from Plane Geometry . 20 ° .

line is said to be

The study of spatial figures constitutes Solid Geometry , or the Geometry of Space

, as distinguished from Plane Geometry . 20 ° .

**Given**Point and Line . A point orline is said to be

**given**when we are made to know enough about it to enable us ... Page 10

Let A be the

of all the lines that can pass through the point A , only one can have the direction

AP , and this one must lie along and coincide with AP so as to form with it ...

Let A be the

**given**point , and let the segment AP mark the**given**direction . Then ,of all the lines that can pass through the point A , only one can have the direction

AP , and this one must lie along and coincide with AP so as to form with it ...

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 19

From ( 36 ° ) we have I circumangle = 2 straight angles = 4 right angles . In

estimating an angle numerically it may be expressed in any one of the

. If a right angle be taken as the unit , a circumangle is expressed by 4 , i.e. four

right ...

From ( 36 ° ) we have I circumangle = 2 straight angles = 4 right angles . In

estimating an angle numerically it may be expressed in any one of the

**given**units. If a right angle be taken as the unit , a circumangle is expressed by 4 , i.e. four

right ...

Page 20

seconds and six - sevenths of a second . This is denoted as follows : 51 ° 25 ' 42 "

A B 42 ° . Theorem .-- Through a

be drawn to the line . The line OC is | AB , and OD is any other line through 0 .

seconds and six - sevenths of a second . This is denoted as follows : 51 ° 25 ' 42 "

A B 42 ° . Theorem .-- Through a

**given**point in a line only one perpendicular canbe drawn to the line . The line OC is | AB , and OD is any other line through 0 .

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### 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.