## The Elements of Euclid |

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Resultat 1-5 av 7

Side 180

It is required from AB to describe a

situated to CD. At the point A of the given straight line AB, make (26. 11.) a solid

angle equal to the solid angle at C; and let BAK, KAH, HAB, be the three plane

angles ...

It is required from AB to describe a

**solid parallelopiped**similar and similarlysituated to CD. At the point A of the given straight line AB, make (26. 11.) a solid

angle equal to the solid angle at C; and let BAK, KAH, HAB, be the three plane

angles ...

Side 181

Therefore the solid AL is similar (11. def. 11.) to the solid CD. Wherefore from a

given straight line AB, a

similarly situated to the given one CD. Which was to be done. PROP. XXVIII.

Therefore the solid AL is similar (11. def. 11.) to the solid CD. Wherefore from a

given straight line AB, a

**solid parallelopiped**AL has been described similar andsimilarly situated to the given one CD. Which was to be done. PROP. XXVIII.

Side 184

lelopiped; but the solid CM, of which the base is ACBL, to which FDHM is the

opposite parallelogram, is equal (29. ... Produce OD, HB, and let them meet in Q,

and complete the

LQ ...

lelopiped; but the solid CM, of which the base is ACBL, to which FDHM is the

opposite parallelogram, is equal (29. ... Produce OD, HB, and let them meet in Q,

and complete the

**solid parallelopiped**LR, the base of which is the paralelogramLQ ...

Side 185

the solid AE to the solid LR; for the same reason, because the

planes CP, BR ; as the base CD to the base LQ, so P F R. is the solid CF to the N

TM E solid LR ...

the solid AE to the solid LR; for the same reason, because the

**solid****parallelopiped**CR is cut by the plane LMFD, which is parallel to the oppositeplanes CP, BR ; as the base CD to the base LQ, so P F R. is the solid CF to the N

TM E solid LR ...

Side 186

For the same reason the planes MV, GT are parallel to one another: therefore the

a

...

For the same reason the planes MV, GT are parallel to one another: therefore the

**solid**QE is a**parallelopiped**: in like manner it may be proved, that the**solid**YF isa

**parallelopiped**: but, from what has been demonstrated, the**solid**EQ is 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.