## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical Trigonometry |

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Resultat 1-5 av 31

Side 6

Of three sided figures , an

19. An isosceles triangle is that which has only two sides equal . AAA 20. A

scalene triangle is that which has three unequal sides . 21. A right angled triangle

is ...

Of three sided figures , an

**equilateral**triangle is that which has three equal sides .19. An isosceles triangle is that which has only two sides equal . AAA 20. A

scalene triangle is that which has three unequal sides . 21. A right angled triangle

is ...

Side 7

An

polygon , one which has all its angles equal . 32. Two polygons are mutually

same ...

An

**equilateral**polygon , is one which has all its sides equal ; an equiangularpolygon , one which has all its angles equal . 32. Two polygons are mutually

**equilateral**, when they have their sides equal to each other , and placed in thesame ...

Side 10

Every

triangles ADC , BDC , proves also that AD is equal to BD , and the angle ADC

equal to the angle BDC ; hence , these two are right angles : hence , the line ...

Every

**equilateral**triangle is also equiangular . SCHOLIUM . The equality of thetriangles ADC , BDC , proves also that AD is equal to BD , and the angle ADC

equal to the angle BDC ; hence , these two are right angles : hence , the line ...

Side 11

ACB , the less to the greater ; which is absurd . B Therefore , AB is not unequal to

AC , that is , it is equal to it . Cor . Hence every equiangular triangle is also

the one ...

ACB , the less to the greater ; which is absurd . B Therefore , AB is not unequal to

AC , that is , it is equal to it . Cor . Hence every equiangular triangle is also

**equilateral**. PROP . Y. THEOR . When two triangles have all the three sides inthe one ...

Side 23

Since every

angles will be equal to the third part of two right angles ; so that if the right angle

is expressed by unity , the angle of an

one ...

Since every

**equilateral**triangle ( Cor . 3. 1. ) is also equiangular , each of itsangles will be equal to the third part of two right angles ; so that if the right angle

is expressed by unity , the angle of an

**equilateral**triangle will be expressed by ofone ...

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### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circumference coincide common consequently construction cosine cylinder definition demonstrated described diameter difference distance divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremities fall fore four fourth given given straight line greater half Hence inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism Prob produced PROP proportional proposition proved radius ratio reason rectangle contained rectilineal figure remaining right angles segment shewn sides similar sine solid square straight line taken tangent THEOR third touch triangle ABC wherefore whole