## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 15

Side 36

to two right

: but straight lines which with another straight line ... To describe a o equal to a

to two right

**angles**: wherefore the**angles**BHF, HFE are less than two right**angles**: but straight lines which with another straight line ... To describe a o equal to a

**given**retilineal figure, and having an**angle**equal to a**given**rectilineal**angle**. Side 89

manner, it may be shown that HK is ... Let ABCDE be the

equiangular pentagon: it is required to inscribe a circle in the pentagon ABCDE.

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

**given**equilateral andequiangular pentagon: it is required to inscribe a circle in the pentagon ABCDE.

Side 241

... the

three different cases of the proposition, ...

and modern geometers: it seems not to be properly placed among the axioms, ...

... the

**angle**EDG equal to BAC, because, without D this restriction, there might bethree different cases of the proposition, ...

**given**a great deal to do, both to ancientand modern geometers: it seems not to be properly placed among the axioms, ...

Side 249

... as is necessary, that the two straight lines which bisect the sides of the triangle

at right angles must meet one another; and, ... is made of a

there neither is, nor can be any thing in the proposition relating to a

... as is necessary, that the two straight lines which bisect the sides of the triangle

at right angles must meet one another; and, ... is made of a

**given angle**, thoughthere neither is, nor can be any thing in the proposition relating to a

**given angle**. Side 265

... and composition and permutation, demonstrated, that the sides about the

these superfluous things are now left out, and a more simple demonstration is

... and composition and permutation, demonstrated, that the sides about the

**angle**common to the two parallelograms are ... demonstration is not Euclid's:these superfluous things are now left out, and a more simple demonstration is

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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.