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

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Page 14

Since the lines EA and EB , which

direction they make an angle with one another at E. 1. If the stars appear to

recede from one another , the angle at E becomes greater . Thus , if B moves into

the ...

Since the lines EA and EB , which

**join**the eye and the stars , have not the samedirection they make an angle with one another at E. 1. If the stars appear to

recede from one another , the angle at E becomes greater . Thus , if B moves into

the ...

Page 37

Let BE bisect the LDBC and meet AC in E.

CBE , DB = BC , ( hyp . ) LDBE = LCBE , ( constr . ) and BE is common . ADBE =

ACBE , and DE = CE . But AC = AE + EC = AE + ED , which is greater than AD .

Let BE bisect the LDBC and meet AC in E.

**Join**DE . Then , in the As DBE andCBE , DB = BC , ( hyp . ) LDBE = LCBE , ( constr . ) and BE is common . ADBE =

ACBE , and DE = CE . But AC = AE + EC = AE + ED , which is greater than AD .

Page 44

I. A closed figure having four lines as sides is in general called a quadrangle cor

quadrilateral . Thus ABCD is a quadrangle . 2. The line - segments AC and BD

which

I. A closed figure having four lines as sides is in general called a quadrangle cor

quadrilateral . Thus ABCD is a quadrangle . 2. The line - segments AC and BD

which

**join**opposite vertices are the diagonals of the quadrangle . qe.cl. B A D 3. Page 47

... and let AG || to FC meet BO in G.

through the middle of AB and is ll to AG , ... O is the middle of BG . ( 84 ° , Cor 2 )

Again , DO passes through the middle points of two sides of the ACBG , CG is | to

...

... and let AG || to FC meet BO in G.

**Join**CG . F Then , BAG is a A and FO passesthrough the middle of AB and is ll to AG , ... O is the middle of BG . ( 84 ° , Cor 2 )

Again , DO passes through the middle points of two sides of the ACBG , CG is | to

...

Page 52

The

another . 19. The median to the hypothenuse of a right - angled triangle is equal

to one - half the hypothenuse . 20. If one diagonal of a O be equal to a side of the

...

The

**joins**of the middle points of the opposite sides of any quadrangle bisect oneanother . 19. The median to the hypothenuse of a right - angled triangle is equal

to one - half the hypothenuse . 20. If one diagonal of a O be equal to a side of the

...

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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.