## The Elements of Euclid |

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Side 19

to two right an- >~ gles; and CEA, AED have been de- D monstrated to be equal

to two right angles; wherefore the angles CEA, AED are equal to the angles AED,

DEB. Take away the common angle AED, and the

to two right an- >~ gles; and CEA, AED have been de- D monstrated to be equal

to two right angles; wherefore the angles CEA, AED are equal to the angles AED,

DEB. Take away the common angle AED, and the

**remaining angle**CEA is ... Side 82

HAC is equal to the angle DEF, therefore also the angle ABC is equal to DEF; for

the same reason, the angle ACB is equal to the angle DFE; therefore the

...

HAC is equal to the angle DEF, therefore also the angle ABC is equal to DEF; for

the same reason, the angle ACB is equal to the angle DFE; therefore the

**remaining angle**BAC is equal (32. 1.) to the**remaining angle**EDF: wherefore the...

Side 129

BCA; wherefore the remaining A D angle BAC is equal to the

EGF (32. 1.), and the triangle ABC is therefore equiangular to the triangle E F

GEF; and consequently they J have their sides opposite to the B C equal angles ...

BCA; wherefore the remaining A D angle BAC is equal to the

**remaining angle**EGF (32. 1.), and the triangle ABC is therefore equiangular to the triangle E F

GEF; and consequently they J have their sides opposite to the B C equal angles ...

Side 130

and the triangle EDF to the triangle GDF, and the

therefore the angle DFG is equal to the angle DFE, and the angle at G to the

angle at E.: but ...

and the triangle EDF to the triangle GDF, and the

**remaining angles**to the**remaining angles**, each to each, which are subtended by the equal sides;therefore the angle DFG is equal to the angle DFE, and the angle at G to the

angle at E.: but ...

Side 169

... the other DC is greater than the E E C

equal to EA, and AC common, but the base DC greater than the base EC:

therefore the

construction, ...

... the other DC is greater than the E E C

**remaining**part E.C. And because DA isequal to EA, and AC common, but the base DC greater than the base EC:

therefore the

**angle**DAC is greater (25. 1.) than the**angle**EAC: and, by theconstruction, ...

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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.