## The Elements of Euclid |

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Resultat 1-5 av 12

Side 20

PROP. XVII.

angles. - - Let ABC be any triangle; any two of A its angles together are less than

two right A angles. ," Produce BC to D; and because ACD is / the exterior angle ...

PROP. XVII.

**THEOR**. Any two angles of a triangle are together less than two rightangles. - - Let ABC be any triangle; any two of A its angles together are less than

two right A angles. ," Produce BC to D; and because ACD is / the exterior angle ...

Side 32

XXXVI.

parallels, are equal to one another. Let ABCD, EFGH be parallelograms upon

equal bases A F. H BC, FG, and between the same \ 2^ parallels AH, BG; the

paral- ...

XXXVI.

**THEOR**. PARALLELOGRAMs upon equal bases, and between the sameparallels, are equal to one another. Let ABCD, EFGH be parallelograms upon

equal bases A F. H BC, FG, and between the same \ 2^ parallels AH, BG; the

paral- ...

Side 49

acute angles to the opposite side produced, the square of the side subtending

the obtuse angle is greater than the squares of the sides containing the obtuse ...

**THEOR**. In obtuse angled triangles, if a perpendicular be drawn from any of theacute angles to the opposite side produced, the square of the side subtending

the obtuse angle is greater than the squares of the sides containing the obtuse ...

Side 56

W.

Let the two circles ABC, CDG cut one another in the points B, C; they have not the

same centre. For, if it be possible, let E be their centre: join EC, and draw any ...

W.

**THEOR**. If two circles cut one another, they shall not have the same Centre.Let the two circles ABC, CDG cut one another in the points B, C; they have not the

same centre. For, if it be possible, let E be their centre: join EC, and draw any ...

Side 60

their centres being produced shall pass through the point of contact. Let the two

circles ABC, ADE touch each other internally in the point A, and let F be the

centre of ...

**THEOR**. If two circles touch each other internally, the straight line which joinstheir centres being produced shall pass through the point of contact. Let the two

circles ABC, ADE touch each other internally in the point A, and let F be the

centre of ...

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

### 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.