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

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Page 16

When two angles , as AOP and POP ' , have one arm in common lying between

the

which starts from any given direction and inakes a complete rotation so as to ...

When two angles , as AOP and POP ' , have one arm in common lying between

the

**remaining**arms , the angles are adjacent angles . 36 ° . Def .-- A radius vectorwhich starts from any given direction and inakes a complete rotation so as to ...

Page 23

The points are the vertices of the triangle , and the linesegments which have the

points as end - points are the sides . The

lines are usually spoken of as the “ sides produced . ” But in many cases

generality ...

The points are the vertices of the triangle , and the linesegments which have the

points as end - points are the sides . The

**remaining**portions of the determinedlines are usually spoken of as the “ sides produced . ” But in many cases

generality ...

Page 35

... of the

consequence . Thus it is sufficient that two sides and the included angle in one

triangle shall be respectively equal to two sides and the included angle in

another .

... of the

**remaining**parts and hence the congruence of the triangles follow as aconsequence . Thus it is sufficient that two sides and the included angle in one

triangle shall be respectively equal to two sides and the included angle in

another .

Page 41

... draw PQ a common I to AB and CD . Then AOPE = AOQF ; LAEF = LEFD .

Similarly the

LCFE , etc. Proof - LAEG = supplement of LAEF , and LCFE = supplement of LEFI

) .

... draw PQ a common I to AB and CD . Then AOPE = AOQF ; LAEF = LEFD .

Similarly the

**remaining**alternate angles are equal . ( 72 ) ( 64 ° ) q.e.d. 2. LAEG =LCFE , etc. Proof - LAEG = supplement of LAEF , and LCFE = supplement of LEFI

) .

Page 74

If a hexagon circumscribe a circle the sum of three alternate sides is equal to that

of the

which is tangent to the inner is bisected by the point of contact ; and the parts ...

If a hexagon circumscribe a circle the sum of three alternate sides is equal to that

of the

**remaining**three . 15. If two circles are concentric , any chord of the outerwhich is tangent to the inner is bisected by the point of contact ; and the parts ...

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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.