## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 17

Side 25

Let AB be the greater of the two, and make BG equal to DE and

therefore, because BG is equal to DE, and BC to EF, the two sides GB, BC are

eual to the two DE, EF, each to each; and the angle GBC is equal to the angle

DEF; ...

Let AB be the greater of the two, and make BG equal to DE and

**join**GC ;therefore, because BG is equal to DE, and BC to EF, the two sides GB, BC are

eual to the two DE, EF, each to each; and the angle GBC is equal to the angle

DEF; ...

Side 33

parallel to BC, and

because it is upon the same base BC, and between the same parallels BC, A D ...

**Join**AD; AD is parallel to BC: for, if it is not, through the point A draw (31. 1.) AEparallel to BC, and

**join**EC; the triangle ABC is equal (37. 1.) to the triangle EBC,because it is upon the same base BC, and between the same parallels BC, A D ...

Side 36

AH parallel to BG or EF, and

upon the parallels AH, EF, the ahgles AHF, HFE are together equal (29. 1.) to two

right angles: wherefore the angles BHF, HFE are less than two right angles: but ...

AH parallel to BG or EF, and

**join**HB. Then, because the straight line HF fallsupon the parallels AH, EF, the ahgles AHF, HFE are together equal (29. 1.) to two

right angles: wherefore the angles BHF, HFE are less than two right angles: but ...

Side 60

If two circles touch each other internally, the straight line which

being produced shall pass through the ... being produced, - passes through the

point A. For, if not, let it fall otherwise, if possible, as FGDH, and

...

If two circles touch each other internally, the straight line which

**joins**their centresbeing produced shall pass through the ... being produced, - passes through the

point A. For, if not, let it fall otherwise, if possible, as FGDH, and

**join**AF, AG: and...

Side 72

XXIX. THEOR. In equal circles equal circumferences are subtended by equal

straight lines. Let ABC, DEF be equal circles, and let the circumferences BGC,

EHF also be equal; and

line EF.

XXIX. THEOR. In equal circles equal circumferences are subtended by equal

straight lines. Let ABC, DEF be equal circles, and let the circumferences BGC,

EHF also be equal; and

**join**BC, EF: the straight line BC is equal to the straightline EF.

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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.