## The Elements of Euclid |

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Resultat 1-5 av 17

Side 16

To

the same. Let AB be a given straight line, and C a point given in it: it is required to

To

**draw**a straight line at right angles to a given straight line, from a given point inthe same. Let AB be a given straight line, and C a point given in it: it is required to

**draw**a straight line from the point C at right angles to AB." Take any point D in ... Side 33

Produce AD both ways to the points G, H, and through B

to CA, and through F

GBCA, DEFHis a parallelo- o - —- gram; and they are equal \ N | B C E F (36. 1.) ...

Produce AD both ways to the points G, H, and through B

**draw**BG parallel (31. 1.)to CA, and through F

**draw**FH parallel to ED: then each of the figures G A * D HGBCA, DEFHis a parallelo- o - —- gram; and they are equal \ N | B C E F (36. 1.) ...

Side 36

through A

straight line HF falls 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 ...

through A

**draw**(31. 1.) AH parallel to BG or EF, and join HB. Then, because thestraight line HF falls 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 ...

Side 43

DHG parallel to CE or BF; and through H

through A

equal (43. 1.) to the complement HF, to each of these add DM; therefore the

whole ...

DHG parallel to CE or BF; and through H

**draw**KLM parallel to CB or EF; and alsothrough A

**draw**AK parallel to CL or BM; and because the complement CH isequal (43. 1.) to the complement HF, to each of these add DM; therefore the

whole ...

Side 89

the angles BCD, CDE by the straight lines CF, DF, and from the point F, in which

they meet,

and CF common to the triangles BCF, DCF, the two sides BC, CF, are equal to ...

the angles BCD, CDE by the straight lines CF, DF, and from the point F, in which

they meet,

**draw**the straight lines FB, FA, FE; therefore, since BC is equal to CD,and CF common to the triangles BCF, DCF, the two sides BC, CF, are equal to ...

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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.