## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 23

Side 25

o to

also the third angle of the one to the third angle of the other. Let ABC, DEF be two

triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.

o to

**equal angles**in each; then shall the other sides be equal, each to each; andalso the third angle of the one to the third angle of the other. Let ABC, DEF be two

triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.

Side 36

to two right

: but straight lines which with another ... to BF; but BF is

wherefore LB is

to two right

**angles**: wherefore the**angles**BHF, HFE are less than two right**angles**: but straight lines which with another ... to BF; but BF is

**equal**to the triangle C :wherefore LB is

**equal**to the triangle C : and because the**angle**GBE is**equal**(15. Side 86

Join AC, BD cutting one another in E; and because DA is

common to the triangles DAC, BAC, the two sides DA, AC are

, AC ; and the base DC is

Join AC, BD cutting one another in E; and because DA is

**equal**to AB, and ACcommon to the triangles DAC, BAC, the two sides DA, AC are

**equal**to the two BA, AC ; and the base DC is

**equal**to the base BC; wherefore the**angle**DAC is**equal**... Side 89

manner, it may be shown that HK is ... that each of the

...

**angle**FLC: and because KC is**equal**to CL, KL is double of KC: in the samemanner, it may be shown that HK is ... that each of the

**angles**KHG, HGM, GML is**equal**to the**angle**HKL or KLM : therefore the five**angles**GHK, HKL, KLM, LMG,...

Side 126

If the angle of a triangle be divided into two

also cuts the base; the segments of the base shall have the same ratio which the

other sides of the triangle have to one another: and if the segments of the base ...

If the angle of a triangle be divided into two

**equal angles**, by a straight line whichalso cuts the base; the segments of the base shall have the same ratio which the

other sides of the triangle have to one another: and if the segments of the base ...

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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.