## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 11

Side 21

THEOR. Any two sides of a triangle are together greater than the third side. * Let

ABC be a triangle; any two sides of it together are greater than the third side, viz.

the

...

THEOR. Any two sides of a triangle are together greater than the third side. * Let

ABC be a triangle; any two sides of it together are greater than the third side, viz.

the

**sides BA**, AC greater than the side BC; and AB, BC greater than AC ; and BC,...

Side 38

upon the

the

described upon the

upon the

**side**subtending the right angle, is equal to the squares described uponthe

**sides**which contain the right angle. ... having the right angle BAC; the squaredescribed upon the

**side**BC is equal to the squares described upon**BA**, AC. Side 86

Join AC, BD cutting one another in E; and because DA is equal to AB, and AC

common to the triangles DAC, BAC, the two

, AC ; and the base DC is equal to the base BC; wherefore the angle DAC is

equal ...

Join AC, BD cutting one another in E; and because DA is equal to AB, and AC

common to the triangles DAC, BAC, the two

**sides**DA, AC are equal to the two**BA**, AC ; and the base DC is equal to the base BC; wherefore the angle DAC is

equal ...

Side 150

Therefore the figure described on BC is equal (A. 5.) to the similar and similarly

described figures on

PROP. XXXII. THEOR. v If two triangles which have two

proportional ...

Therefore the figure described on BC is equal (A. 5.) to the similar and similarly

described figures on

**BA**, AC. Wherefore, in right angled triangles, &c. Q. E. D.PROP. XXXII. THEOR. v If two triangles which have two

**sides**of the oneproportional ...

Side 154

to the ... THE rectangle contained by the diagonals of a quadrilateral inscribed in

a circle, is equal to both the rectangles contained by its opposite

**BA**to AD, so is EA to AC; and consequently the rectangle**BA**, AC is equal (16. 6.)to the ... THE rectangle contained by the diagonals of a quadrilateral inscribed in

a circle, is equal to both the rectangles contained by its opposite

**sides**.### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

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.