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

### From inside the book

Results 1-5 of 39

Page 7

A P/ame is a surface such that the line

coincides wholly with the surface. The planarity of a surface may be tested by

applying the rule to it. If the rule touches the surface at Some points and not at

others the ...

A P/ame is a surface such that the line

**joining**any two arbitrary points in itcoincides wholly with the surface. The planarity of a surface may be tested by

applying the rule to it. If the rule touches the surface at Some points and not at

others the ...

Page 14

Since the lines EA and EB, which

direction they make an angle with one another at E. I. 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. I. 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 4 DBC and meet AC in E.

CBE, DB = BC, (hyp.) 4 DBE = 4 CBE, (constr.) and BE is common. to o Z\DBE = Z

\CBE, and DE = CE. But AC = AE + EC = AE + ED, which is greater than AD. • '.

Let BE bisect the 4 DBC and meet AC in E.

**Join**D.E. Then, in the Z\s DBE andCBE, DB = BC, (hyp.) 4 DBE = 4 CBE, (constr.) and BE is common. to o Z\DBE = Z

\CBE, and DE = CE. But AC = AE + EC = AE + ED, which is greater than AD. • '.

Page 44

Z)ef-I. A closed figure having four lines as sides is in general called a guadrange

6 or quadrāsaferas. - D Thus ABCD is a quadrang/e. 2. The lime-segments AC

and BD which

Z)ef-I. A closed figure having four lines as sides is in general called a guadrange

6 or quadrāsaferas. - D Thus ABCD is a quadrang/e. 2. The lime-segments AC

and BD which

**join**opposite vertices are the diagonals of the quadrangle. 3. Page 47

Or, the line-segment

trapezoid is equal to one-half the sum of the parallel sides. Cor. 2. When the

transversals meet upon one of the extreme parallels, the figure AEF' becomes a /\

and CD' ...

Or, the line-segment

**joining**the middle points of the nonparallel sides of atrapezoid is equal to one-half the sum of the parallel sides. Cor. 2. When the

transversals meet upon one of the extreme parallels, the figure AEF' becomes a /\

and CD' ...

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### Common terms and phrases

ABCD algebraic altitude base becomes called centre centre-line chord circle coincide common concurrent congruent considered constant construct Converse corresponding denote describe determine diagonals diameter difference direction distance divide draw drawn equal expressed external figure fixed four geometric given line given point gives greater harmonic Hence internal intersect inverse join length lies line-segment mean measure median meet middle point one-half opposite opposite sides pair parallel passes perpendicular placed plane point of contact polar polygon position Proof proved quadrangle radical axis radius range ratio rectangle regular relation respectively right angle right bisector rotation secant segment sense sides similar Similarly 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.