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

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Page 48

Therefore the three medians of a triangle are

concurrence, O, of the medians of a triangle is the centroid of the triangle. Cor.

Since O is the middle point of BG, and E is the middle point of OG, (81°, 3) . . OE =

}OB ...

Therefore the three medians of a triangle are

**concurrent**. Pes. 2.-The point ofconcurrence, O, of the medians of a triangle is the centroid of the triangle. Cor.

Since O is the middle point of BG, and E is the middle point of OG, (81°, 3) . . OE =

}OB ...

Page 49

The three altitudes of a triangle are

and EF respectively, But the right bisectors of the sides of the /\DEF are

q.e.d. Def-The ...

The three altitudes of a triangle are

**conCurrent**. ... are the right bisectors of DEand EF respectively, But the right bisectors of the sides of the /\DEF are

**concurrent**(86°), therefore the altitudes of the /\ABC are COInCul'rent, F B Dq.e.d. Def-The ...

Page 86

the external bisectors of two angles of a triangle and the internal bisector of the

third angle are

said to be co///near. Cor. 3. The line through any two centres passes through a ...

the external bisectors of two angles of a triangle and the internal bisector of the

third angle are

**concurrent**. /Jes. I.--When three or more points are in line they aresaid to be co///near. Cor. 3. The line through any two centres passes through a ...

Page 98

Any line

parallelogram, . The triangle having one of the non-parallel sides of a trapezoid

as base and the middle point of the opposite side as vertex is one-half the

trapezoid.

Any line

**concurrent**with the diagonals of a parallelogram bisects theparallelogram, . The triangle having one of the non-parallel sides of a trapezoid

as base and the middle point of the opposite side as vertex is one-half the

trapezoid.

Page 187

Then Sin AOP := § Sin BOP = o and putting these values for sin AOP, etc., in the

relation of 234", we have, after multiplying through by OP, C'P. sin AOB + A' P. sin

BO C+ B' P. sin COA = O. Or, let L, M, and N be any three

Then Sin AOP := § Sin BOP = o and putting these values for sin AOP, etc., in the

relation of 234", we have, after multiplying through by OP, C'P. sin AOB + A' P. sin

BO C+ B' P. sin COA = O. Or, let L, M, and N be any three

**concurrent**lines, /, //, /t ...### What people are saying - Write a review

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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.