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

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Page 48

The line through a vertex of a triangle perpendicular to the opposite side is the

perpendicular to that side , and the part of that line intercepted within the triangle

is the

...

The line through a vertex of a triangle perpendicular to the opposite side is the

perpendicular to that side , and the part of that line intercepted within the triangle

is the

**altitude**to that side . Where no reference to length is made the word**altitude**...

Page 49

Where no reference to length is made the word

denote the indefinite line forming the perpendicular Hence a triangle has three

...

Where no reference to length is made the word

**altitude**is often employed todenote the indefinite line forming the perpendicular Hence a triangle has three

**altitudes**, one to each side . 88 ° . Theorem . - The three**altitudes**of a triangle are...

Page 73

The feet of the medians and the feet of the

concyclic points , and the circle bisects that part of each

the orthocentre and the G vertex . D , E , F are the feet of the medians , i.l. , the

middle ...

The feet of the medians and the feet of the

**altitudes**in any triangle are sixconcyclic points , and the circle bisects that part of each

**altitude**lying betweenthe orthocentre and the G vertex . D , E , F are the feet of the medians , i.l. , the

middle ...

Page 90

To construct a triangle when the basal angles and the

construct a right - angled triangle when the hypothenuse and the sum of the sides

are given . 15. To divide a line - segment into any number of equal parts . 16.

To construct a triangle when the basal angles and the

**altitude**are given . 14. Toconstruct a right - angled triangle when the hypothenuse and the sum of the sides

are given . 15. To divide a line - segment into any number of equal parts . 16.

Page 92

The

farthest point of a figure from a side taken as base . The terms base and

are thus correlative . A triangle may have three different bases and as many ...

The

**altitude**of a figure is the line - segment which measures the distance of thefarthest point of a figure from a side taken as base . The terms base and

**altitude**are thus correlative . A triangle may have three different bases and as many ...

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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.