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

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Page 1

... such as space,

be defined. 2°. Des—A 7%eorem is the formal statement of some mathematical

relation. A theorem may be stated for the purpose of being subsequently proved,

...

... such as space,

**straight**, direction, etc., which express elementary ideas cannotbe defined. 2°. Des—A 7%eorem is the formal statement of some mathematical

relation. A theorem may be stated for the purpose of being subsequently proved,

...

Page 6

of which every part has the same direction. For every part of a line must have

some direction, and when this direction is common to all the parts of the line, the

...

**Straight**Zine. For want of a better definition we may say that a**straight**line is oneof which every part has the same direction. For every part of a line must have

some direction, and when this direction is common to all the parts of the line, the

...

Page 7

The most prominent property, and in fact the distinctive property of a s/ragg// line,

is the absolute sameness which characterizes all its parts, so that two portions of

the same

The most prominent property, and in fact the distinctive property of a s/ragg// line,

is the absolute sameness which characterizes all its parts, so that two portions of

the same

**straight**line can differ from one another in no respect except in length. Page 10

2, is impossible. Cor. 4. Another statement of Cor. 2 is—Two lines which have two

points in common coincide and form virtually but one line. 25°. Arjoma.-A

line is the shortest distance between two IO SYNTHETIC GEOMETRY.

2, is impossible. Cor. 4. Another statement of Cor. 2 is—Two lines which have two

points in common coincide and form virtually but one line. 25°. Arjoma.-A

**straight**line is the shortest distance between two IO SYNTHETIC GEOMETRY.

Page 11

A

possible to give a reasonable proof of this axiom, no amount of proof could make

its truth more apparent. - The following will illustrate the axiom. Assume any two ...

A

**straight**line is the shortest distance between two given points. - Although it ispossible to give a reasonable proof of this axiom, no amount of proof could make

its truth more apparent. - The following will illustrate the axiom. Assume any two ...

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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.