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

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Page 23

The points are the vertices of the

points as end-points are the sides. The remaining portions of the determined

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 thepoints as end-points are the sides. The remaining portions of the determined

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

...

Page 24

The

of lines determines the same number of points ... are given, or when the three

lines or line-segments forming the \ sides are given, the

given.

The

**triangle**is distinctive in being the rectilinear figure for which a given numberof lines determines the same number of points ... are given, or when the three

lines or line-segments forming the \ sides are given, the

**triangle**is completelygiven.

Page 25

The angles of the

the sides opposite by the corresponding Small letters a, b, c. 51°. ZJes.—When

two figures compared by superposition coincide in all their parts and become ...

The angles of the

**triangle**are denoted usually by the capital letters A, B, C, andthe sides opposite by the corresponding Small letters a, b, c. 51°. ZJes.—When

two figures compared by superposition coincide in all their parts and become ...

Page 26

Since two congruent

— When two

respectively equal to two sides and the included angle in the other, all the parts in

the ...

Since two congruent

**triangles**can be made to coincide in all their parts, therefore— When two

**triangles**have two sides and the included angle in the onerespectively equal to two sides and the included angle in the other, all the parts in

the ...

Page 27

Des. 2.-A

side as base, all the angles of an equilateral

, ...

Des. 2.-A

**triangle**in which all the sides are equal to one another is an equi/aferas**triangle**. Cor. 3. Since an equilateral**triangle**is isosceles with respect to eachside as base, all the angles of an equilateral

**triangle**are equal to one another ; or, ...

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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.