## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 20

Side 42

also to GK , and CG to BK ; u

likewise rectangular ; for CG is parallel to BK , and CB meets them ; the angles

KBC , GCB are therefore equal to two right angles ; and KBC is a right angle ;

also to GK , and CG to BK ; u

**wherefore**the figure CGKB is equilateral ; it islikewise rectangular ; for CG is parallel to BK , and CB meets them ; the angles

KBC , GCB are therefore equal to two right angles ; and KBC is a right angle ;

**wherefore**... Side 87

... DAC : but BCD is equal to the angles CDA , DAC ; therefore also BCD is

double of DAC , and BCD is equal to each of the angles BDA , DBA ; each

therefore of the angles BDA , DBA , is double of the angle DAB ;

isosceles ...

... DAC : but BCD is equal to the angles CDA , DAC ; therefore also BCD is

double of DAC , and BCD is equal to each of the angles BDA , DBA ; each

therefore of the angles BDA , DBA , is double of the angle DAB ;

**wherefore**anisosceles ...

Side 89

each to each ;

in the same manner it may be demonstrated H , AK - 7 that FL , FM , FG are each

of them 12 BOOK IV . 89 TAB ELEMENTS OF EUCLID . angle FLC: and ...

each to each ;

**wherefore**the perpendicular FH is equal to the perpendicular FK :in the same manner it may be demonstrated H , AK - 7 that FL , FM , FG are each

of them 12 BOOK IV . 89 TAB ELEMENTS OF EUCLID . angle FLC: and ...

Side 113

but HO is equal to EB , and MH to FD ;

therefore GK be greater than HO , LN is greater than MP ; and if equal , equal ;

and if less ( Ax . 5 . ) , less . But let HO , MP be equimultiples of EB , FD ; and

because ...

but HO is equal to EB , and MH to FD ;

**wherefore**GK is to HO as LN to MP . Iftherefore GK be greater than HO , LN is greater than MP ; and if equal , equal ;

and if less ( Ax . 5 . ) , less . But let HO , MP be equimultiples of EB , FD ; and

because ...

Side 129

BCA ;

32 . 1 . ) , and the triangle ABC is therefore equiangular to the triangle GEF ; and

consequently they have their sides opposite to the в equal angles proportionals ...

BCA ;

**wherefore**the remaining angle BAC is equal to the remaining angle EGF (32 . 1 . ) , and the triangle ABC is therefore equiangular to the triangle GEF ; and

consequently they have their sides opposite to the в equal angles proportionals ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

### Vanlige uttrykk og setninger

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.