## The Elements of Euclid |

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Side 169

... DCB; and the angles CDA, ADB, greater than BDC: wherefore the six angles

CBA, ABD, BCA, ACD, CDA, ADB, are greater than the three an- D

BCD, CDB; but the three angles DBC, BCD, CDB, are equal to two right angles (

32.

... DCB; and the angles CDA, ADB, greater than BDC: wherefore the six angles

CBA, ABD, BCA, ACD, CDA, ADB, are greater than the three an- D

**gles**DBC,BCD, CDB; but the three angles DBC, BCD, CDB, are equal to two right angles (

32.

Side 174

And ABP is equal to the two angles ABC, CBP, that is, to the two angles ABC,

GHK; therefore the M N angle DEF is greater than the two an- -

but it is also less than X these; which is impossible. Therefore AB is not less than

LX, ...

And ABP is equal to the two angles ABC, CBP, that is, to the two angles ABC,

GHK; therefore the M N angle DEF is greater than the two an- -

**gles**ABC, GHK;but it is also less than X these; which is impossible. Therefore AB is not less than

LX, ...

Side 181

F-N

lar to EG. For the same N reason, the parallelogram A B CTE KH is similar to GF,

and HB to FE. Wherefore three parallelograms of the solid AL are similar to ...

F-N

**gles**ECG, BAK are proportionals: therefore the | parallelogram BK is simi- - Glar to EG. For the same N reason, the parallelogram A B CTE KH is similar to GF,

and HB to FE. Wherefore three parallelograms of the solid AL are similar to ...

Side 198

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

equal an- Y

angles are equal; N O therefore the angle N XYD is equal to the T angle OYE,

and ...

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

equal an- Y

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

and ...

Side 322

ko. the ratio of the side FE to EM or EN E N O the same with the ratio of H to K;

and let the angle EMF be greater, and ENF less than a right angle. And because

H ...

**gles**EFM, EEN, each of which has the // ~& angle EFL for one of its angles, andko. the ratio of the side FE to EM or EN E N O the same with the ratio of H to K;

and let the angle EMF be greater, and ENF less than a right angle. And because

H ...

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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1834 |

The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson Ingen forhåndsvisning tilgjengelig - 2017 |

The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson Ingen forhåndsvisning tilgjengelig - 2017 |

### Vanlige uttrykk og setninger

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gles gnomon join less Let ABC meet multiple parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third three plane angles triangle ABC triplicate ratio vertex wherefore

### Populære avsnitt

Side 45 - Ir a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 41 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.

Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.

Side 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.

Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 256 - 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 129 - 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 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...

Side 20 - ANY two angles of a triangle are together less than two right angles.