## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 5

Side 13

FBC is equal to the angle GCB , and the angle BCF to the angle CBG ; and ,

since it has been demonstrated , that the whole angle ABG is equal to the whole

ACF ...

**gles**, each to each , to which the equal sides , are opposite ; therefore the angleFBC is equal to the angle GCB , and the angle BCF to the angle CBG ; and ,

since it has been demonstrated , that the whole angle ABG is equal to the whole

ACF ...

Side 198

to one another : and because DX is equal D K to OE , and XY to YO , and contain

equal anY

angles are equal ; therefore the angle XYD is equal to the angle OYE , and DYE

is a ...

to one another : and because DX is equal D K to OE , and XY to YO , and contain

equal anY

**gles**, the base DY is equal ( 4 . 1 . ) to the base YE , and the otherangles are equal ; therefore the angle XYD is equal to the angle OYE , and DYE

is a ...

Side 244

the angle AGF is equal to CHF , and AFG to the angle CFH : to these last add the

common angles AFH ; therefore the two an - -

two angles CFH , HFA , which two last are equal together to two right angles ( 13 .

the angle AGF is equal to CHF , and AFG to the angle CFH : to these last add the

common angles AFH ; therefore the two an - -

**gles**AFG , AFH are equal to thetwo angles CFH , HFA , which two last are equal together to two right angles ( 13 .

Side 371

4 , is thus ; “ Points , lines , spaces , and an .

which have always the same situation ; " but this is imperfect and useless ,

because there are in . numerable cases in which things may be given according

to this ...

4 , is thus ; “ Points , lines , spaces , and an .

**gles**are said to be given in positionwhich have always the same situation ; " but this is imperfect and useless ,

because there are in . numerable cases in which things may be given according

to this ...

Side 394

This sides and an angle oppo -

site to one of them . may be greater or less than a quadrant . ( Cor . to def . 4 . )

AB + AC : AB - AC : : T , C + B : 3 AB , AC , and A , two The ansides and the

included ...

This sides and an angle oppo -

**gles**A and case admits of two solutions ; for Csite to one of them . may be greater or less than a quadrant . ( Cor . to def . 4 . )

AB + AC : AB - AC : : T , C + B : 3 AB , AC , and A , two The ansides and the

included ...

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added altitude angle ABC angle BAC base BC is given centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid sphere square square of BC taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 36 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.

Side 145 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.

Side 65 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.

Side 248 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Side 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.

Side 121 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 21 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 14 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.

Side 80 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Side 133 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.