## Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry |

### From inside the book

Page 56

All the interior

All the interior

**angles**of any rectilineal figure are**together equal to twice as many right**angies as the figure has sides , wanting**four right angles**. D E D F E B B A A Let ABCDE be any rectilineal figure ; all its interior**angles**A ... Page 57

All the interior

All the interior

**angles**of any quadrilateral figure are**together equal**to**four right angles**. Scholium . Let n denote the number of the sides of a polygon , s the sum of all the interior**angles**, and r a**right angle**; then the ... Page 58

are

are

**equal to twice as many right angles as**there are sides of the figure ( Prop . L ) . Therefore all the interior and all the exterior**angles**are**together equal**to all the interior**angles together with four right angles**. Page 60

The sum of all the internal

The sum of all the internal

**angles**of any rectilinear figure is**equal to twice as many right angles**, except**four**, as the figure has sides . If all the sides of any rectilinear figure be produced outward , the sum ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### Common terms and phrases

ABC is equal ABCD angle ABC angle BAC arch base base ABC bisect BOOK called centre chord circle circumference coincide common cone Consequently cylinder demonstrations described diagonals diameter difference distance divided draw drawn equal angles equal bases equiangular exterior angle extremities figure follows fore geometry given straight line gles greater half Hence interior intersect join less Let ABC magnitude manner mean meet opposite angles opposite side paral parallel parallel lines parallelogram pass perp perpendicular plane polygon prism produced Prop proportional PROPOSITION proved pyramid Q. E. D. Cor quantities radius ratio rectangle contained remaining respects right angles segments side AC sides similar solid square stand straight line surface tangent THEOREM third triangle ABC wherefore

### Popular passages

Page 36 - Any two sides of a triangle are together greater than the third side.

Page 80 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.

Page 42 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line...

Page 30 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.

Page 20 - LET it be granted that a straight line may be drawn from any one point to any other point.

Page 38 - Problem. At a given point in a given straight line to make a rectilineal angle equal to a given rectilineal angle.

Page 113 - Wherefore also the angle BAD is equal to the angle CAD : Therefore the angle BAC is cut into two equal angles by the straight line AD.

Page 24 - DE ; the point B shall coincide with the point E, because AB is equal to DE; and AB coinciding with DE, AC shall coincide...

Page 36 - The greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.