## The Elements of Euclid |

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Side 319

Let the sides AB, BC about the acute angle ABC of the triangle ABC, which has a

right angle at A, have a given ratio to one another; the triangle ABC is

the ...

Let the sides AB, BC about the acute angle ABC of the triangle ABC, which has a

right angle at A, have a given ratio to one another; the triangle ABC is

**given in****species**. Take a straight line DE given in position and magnitude; and becausethe ...

Side 321

Let the C circle meet EF in the points F, K which are B LS-T given, as was shown

in the preceding case; and ...) DF, DK being joined, the triangles DEF, DEK are

Let the C circle meet EF in the points F, K which are B LS-T given, as was shown

in the preceding case; and ...) DF, DK being joined, the triangles DEF, DEK are

**given in species**, as was there shown. From d the centre A, at the distance AC, ... Side 323

But the ratio of BA and AC together to BC is given, therefore also the ratio of AB to

BD is given. And the angle ABD is given, wheresore (44. dat.) the triangle ABD is

But the ratio of BA and AC together to BC is given, therefore also the ratio of AB to

BD is given. And the angle ABD is given, wheresore (44. dat.) the triangle ABD is

**given in species**: and consequently the angle BAD, and its double the angle ... Side 324

Let the rectilineal figure ABCDE be

triangles

the angle BAE is given (3. def), and the ratio of BA to A AE is given (3. def); ...

Let the rectilineal figure ABCDE be

**given in species**; ABCDE may be divided intotriangles

**given in species**. Join BE, BD; and because ABCDE is**given in species**,the angle BAE is given (3. def), and the ratio of BA to A AE is given (3. def); ...

Side 327

If two straight lines have a given ratio to one another; the rectilineal figures

CD be two straight lines which have a given ratio to one another: the rectilineal ...

If two straight lines have a given ratio to one another; the rectilineal figures

**given****in species**described upon them, shall have to one another a given ratio. Let AB,CD be two straight lines which have a given ratio to one another: the rectilineal ...

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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.