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

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Page 1

In the former case it is called a Proposition, that is, something proposed, and

consists of (a) the statement or enunciation of the theorem, and (b) the argument

or

In the former case it is called a Proposition, that is, something proposed, and

consists of (a) the statement or enunciation of the theorem, and (b) the argument

or

**proof**. The purpose of the argument is to show that the truth of the theorem ... Page 3

But on account of the peculiar relation existing between the two, a relation exists

also between the modes of

indirect modes of

But on account of the peculiar relation existing between the two, a relation exists

also between the modes of

**proof**for the two. These are known as the direct andindirect modes of

**proof**. And if any theorem which admits of a converse can be ... Page 11

Although it is possible to give a reasonable

Assume any two points on a thread taken as a physical line. By separating these

as ...

Although it is 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 points on a thread taken as a physical line. By separating these

as ...

Page 17

D

into the successive directions, OB, OC, ..., E F OF, OA describes in succession the

angles AOB, BOC, ..., EO.F, FOA. But in its complete rotation it describes a ...

D

**Proof**–A radius vector which starts O A from coincidence with OA and rotatesinto the successive directions, OB, OC, ..., E F OF, OA describes in succession the

angles AOB, BOC, ..., EO.F, FOA. But in its complete rotation it describes a ...

Page 18

... angles consist of two pairs of of fosise or versica/ angles, viz., A., A', and B, B', A

being opposite A', and B being opposite B'. 40°. Theorem.—The opposite angles

of a pair formed by two intersecting lines are equal to one another.

... angles consist of two pairs of of fosise or versica/ angles, viz., A., A', and B, B', A

being opposite A', and B being opposite B'. 40°. Theorem.—The opposite angles

of a pair formed by two intersecting lines are equal to one another.

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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.