## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illus., and an Appendix in Five Books |

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Resultat 1-5 av 8

Side 27

has been shown, that it is not

Wherefore, if two triangles, &c. PROP. XXVI. THEOR. If two

be

has been shown, that it is not

**equal**to it: therefore, the**angle**A is greater than D.Wherefore, if two triangles, &c. PROP. XXVI. THEOR. If two

**angles**of one trianglebe

**equal**to two**angles**of another, each to each, and if a side of the one be ... Side 28

to BCA; therefore also the

BHA of the triangle A HC is

straight lines, in the same plane, make the alternate

...

to BCA; therefore also the

**angle**BHA is**equal**to BCA, that is, the exterior**angle**BHA of the triangle A HC is

**equal**to its ... If a straight line falling upon two otherstraight lines, in the same plane, make the alternate

**angles equal**to one another,...

Side 141

CAD ; and because the straight line FAE meets the parallels AD, FC, the angle

CFA is equal to DAE : therefore also ACF, CFA are (I. ax. 1.) equal to one another

, because they are respectively equal to the A L. F.

...

CAD ; and because the straight line FAE meets the parallels AD, FC, the angle

CFA is equal to DAE : therefore also ACF, CFA are (I. ax. 1.) equal to one another

, because they are respectively equal to the A L. F.

**equal angles**DAC, DAE; and...

Side 143

angular, and the

angle ABC equal to DEF, BCA to EFD, and BAC to EDF. At the points E, F, in the

straight line EF, make (I. 23.) the angle FEG equal to B, and EFG equal to C. Then

...

angular, and the

**equal angles**are opposite to the homologous sides, viz., theangle ABC equal to DEF, BCA to EFD, and BAC to EDF. At the points E, F, in the

straight line EF, make (I. 23.) the angle FEG equal to B, and EFG equal to C. Then

...

Side 189

the angle at B by the three FBG, FBH, HBG, which are equal to the other three,

each to each : the planes in which the

inclination to one another. In AC take any point K, and in the plane CAD, from K

draw KD at ...

the angle at B by the three FBG, FBH, HBG, which are equal to the other three,

each to each : the planes in which the

**equal angles**are, have the sameinclination to one another. In AC take any point K, and in the plane CAD, from K

draw KD at ...

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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol segments semicircle sides similar similar triangles solid angles square of AC straight lines drawn tangent THEOR third triangle ABC triplicate ratio vertex vertical angle wherefore

### Populære avsnitt

Side 94 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Side 53 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.

Side 143 - 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 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.

Side 57 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.

Side 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...

Side 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.

Side 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 40 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Side 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...