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

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Page 8

A

a point or line lies in a plane does not give it , but a point or line placed in the

plane for future reference is considered as being given . Such a point is usually ...

A

**similar**nomenclature applies to other geometric elements . The statement thata point or line lies in a plane does not give it , but a point or line placed in the

plane for future reference is considered as being given . Such a point is usually ...

Page 10

But on account of the

segment , it is convenient and advantageous to consider both points as dividing

the segment AB . When thus considered , C is said to divide the segment

internally ...

But on account of the

**similar**relations held by C and C ' to the endpoints of thesegment , it is convenient and advantageous to consider both points as dividing

the segment AB . When thus considered , C is said to divide the segment

internally ...

Page 37

... be'a point on the bisector OQ it is shown in a

perpendiculars from Q upon the arms of the angle AOB are equal . g.e.d. 2. If PA

is I to OA and PB is I to OB , and PA = PB , then PO is a bisector of the angle AOB

. Proof .

... be'a point on the bisector OQ it is shown in a

**similar**manner that theperpendiculars from Q upon the arms of the angle AOB are equal . g.e.d. 2. If PA

is I to OA and PB is I to OB , and PA = PB , then PO is a bisector of the angle AOB

. Proof .

Page 43

But such triangles have the same form and are said to be

can have but one obtuse angle ; it is then called an obtuse - angled triangle . A

triangle can have but one right angle , when it is called à right - angled triangle .

But such triangles have the same form and are said to be

**similar**. 5. A trianglecan have but one obtuse angle ; it is then called an obtuse - angled triangle . A

triangle can have but one right angle , when it is called à right - angled triangle .

Page 130

Then AB . CD = BD , BC and AD.CB = BA , BD . 18. ABC is a triangle and OX , OY

, OZ perpendiculars from any point 0 on BC , CA , and AB respectively . Then BX2

+ CY2 + AZ2 = CX2 + AY2 + BZ2 . A

Then AB . CD = BD , BC and AD.CB = BA , BD . 18. ABC is a triangle and OX , OY

, OZ perpendiculars from any point 0 on BC , CA , and AB respectively . Then BX2

+ CY2 + AZ2 = CX2 + AY2 + BZ2 . A

**similar**relation holds for any polygon . 19.### 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.