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

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Page 2

... put into the form— - If C is not D then A is not B, which is called the

contrapositive of the former. The truth of a theorem establishes the truth of its

contrapositive, and vice versa, and

GTEOMETRY.

... put into the form— - If C is not D then A is not B, which is called the

contrapositive of the former. The truth of a theorem establishes the truth of its

contrapositive, and vice versa, and

**hence**if either is proved the 2 SYNTHETICGTEOMETRY.

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positive, and vice versa, and

Two theorems are converse to one another when the hypothesis and conclusion

of the one are respectively the conclusion and hypothesis of the other. Ex. If an ...

positive, and vice versa, and

**hence**if either is proved the other is proved also. 6°.Two theorems are converse to one another when the hypothesis and conclusion

of the one are respectively the conclusion and hypothesis of the other. Ex. If an ...

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And

arguments in regard to physical lines, if from such arguments we exclude

everything that would involve the idea of breadth. The diagrams employed to

direct and assist us ...

And

**hence**arguments in regard to geometric lines may be replaced byarguments in regard to physical lines, if from such arguments we exclude

everything that would involve the idea of breadth. The diagrams employed to

direct and assist us ...

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(3) A line is not necessarily limited in length, and

follow a line as far as we please without coming to any necessary termination.

This property is conveniently expressed by saying that a line extends to infinity. 3.

(3) A line is not necessarily limited in length, and

**hence**, in imagination, we mayfollow a line as far as we please without coming to any necessary termination.

This property is conveniently expressed by saying that a line extends to infinity. 3.

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For, if A and P be the points, the direction AP is given, and

A and having the direction AP is given. Cor. 3. Two lines by their intersection

determine one finite point. For, if they determined two, they would each pass ...

For, if A and P be the points, the direction AP is given, and

**hence**the line throughA and having the direction AP is given. Cor. 3. Two lines by their intersection

determine one finite point. For, if they determined two, they would each pass ...

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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.