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

### From inside the book

Results 1-5 of 36

Page 7

A P/ame is a surface such that the line joining any two arbitrary points in it

applying the rule to it. If the rule touches the surface at Some points and not at

others the ...

A P/ame is a surface such that the line joining any two arbitrary points in it

**coincides**wholly with the surface. The planarity of a surface may be tested byapplying the rule to it. If the rule touches the surface at Some points and not at

others the ...

Page 10

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

it virtually but one line. Cor. I. A finite point and a direction determine one line.

Cor.

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 withit virtually but one line. Cor. I. A finite point and a direction determine one line.

Cor.

Page 11

If one figure can be superimposed upon another so as to

in every part, the two figures are necessarily and identically equal, and become

virtually One figure by the superposition. 27°. Two line-segments can be ...

If one figure can be superimposed upon another so as to

**coincide**with the latterin every part, the two figures are necessarily and identically equal, and become

virtually One figure by the superposition. 27°. Two line-segments can be ...

Page 12

made to

The sum of two segments is that segment which is equal to the two when placed

in line with one end-point in each coincident. Let AB and DE be two segments,

and ...

made to

**coincide**with the end-points of the other by superposition. 28°. Des—The sum of two segments is that segment which is equal to the two when placed

in line with one end-point in each coincident. Let AB and DE be two segments,

and ...

Page 16

Des—Two angles are equal when the arms of the one O may be made to

are described by the same rotation. Thus, if, when O' is placed upon O, and A e O'

A' is ...

Des—Two angles are equal when the arms of the one O may be made to

**coincide**in direction respec. tively with the arms of the other ; or when the anglesare described by the same rotation. Thus, if, when O' is placed upon O, and A e O'

A' is ...

### 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.