## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 7

Side 311

in it; the straight line drawn to C, (; F, ' , E which makes a given angle with CB, is

def); let this be the angle at D : at the given A C B point C, in the given straight

line ...

in it; the straight line drawn to C, (; F, ' , E which makes a given angle with CB, is

**given in position**. F. Because the angle is given, one equal to it can be found (1.def); let this be the angle at D : at the given A C B point C, in the given straight

line ...

Side 312

If therefore D be equal to AE, AE is the straight line given in magnitude, drawn D

from the given point A to BC: and it is evident that AE is

), because it is drawn from the given point A to BC, which is

If therefore D be equal to AE, AE is the straight line given in magnitude, drawn D

from the given point A to BC: and it is evident that AE is

**given in position**, (33. dat.), because it is drawn from the given point A to BC, which is

**given in position**, ... Side 314

Let the straight line AD given in magnitude be drawn from the point A to the

straight line BC, given in posi- E A H F tion, in the given angle ADC: the straight

line EAF drawn through A parallel to BC is

given ...

Let the straight line AD given in magnitude be drawn from the point A to the

straight line BC, given in posi- E A H F tion, in the given angle ADC: the straight

line EAF drawn through A parallel to BC is

**given in position**. . In BC take thegiven ...

Side 315

From the given point A, let the straight line AED be drawn to the two parallel

straight lines FG, BC, and let the ratio of the segments AE, AD be given; if one of

the parallels BC be

the ...

From the given point A, let the straight line AED be drawn to the two parallel

straight lines FG, BC, and let the ratio of the segments AE, AD be given; if one of

the parallels BC be

**given in position**, the other FG is also**given in position**. Fromthe ...

Side 341

Let the straight line A be to B, as C to D: as A to the straight line to which B has a

given ratio, so is a straight line to which C has a ... And the ratio of this excess to

the triangle ABC may be found thus: take a straight line EF

Let the straight line A be to B, as C to D: as A to the straight line to which B has a

given ratio, so is a straight line to which C has a ... And the ratio of this excess to

the triangle ABC may be found thus: take a straight line EF

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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.