## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, to this Second Edition is Added the Book of Euclid's Data. In Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |

### Inni boken

Resultat 1-5 av 5

Side 222

11. opposite planes ALGF , CBHD , AH is cut into two equal parts by the plane

AGHC . therefore the D K folid AH is double of the

the triN angles ALG , CBH . for the fame reason , because the folid C B AK is cut

by ...

11. opposite planes ALGF , CBHD , AH is cut into two equal parts by the plane

AGHC . therefore the D K folid AH is double of the

**prism**which is contained bythe triN angles ALG , CBH . for the fame reason , because the folid C B AK is cut

by ...

Side 243

F there be two triangular

a parallelogram , and the base of the ... for its base ; if the parallelogram AF be

double of the triangle GHK , the

F there be two triangular

**prisms**of the same altitude , the base of one of which isa parallelogram , and the base of the ... for its base ; if the parallelogram AF be

double of the triangle GHK , the

**prism**ABCDEF is equal to the**prism**GHKLMN . Side 251

angle that is half of the parallelogram , these

another ; therefore the

straight line KH opposite to it , is equal to the 1.40.11 .

angle that is half of the parallelogram , these

**prisms**are equal to Book XII . oneanother ; therefore the

**prism**having the parallelogram EBFG for its base , and thestraight line KH opposite to it , is equal to the 1.40.11 .

**prism**having the triangle ... Side 253

RVF , and the opposite triangle STY . and because the two

ABCG are equal to one another , and also the two

equal to one another , as the

RVF , and the opposite triangle STY . and because the two

**prisms**in the pyramidABCG are equal to one another , and also the two

**prisms**in the pyramid DEFHequal to one another , as the

**prism**of which the base is the parallelogram KBXL ... Side 262

Book XII greater than the half of the circle ABCD + . upon the square ABCD erect

a

cylinder ; because if a square be described about the circle , and a

Book XII greater than the half of the circle ABCD + . upon the square ABCD erect

a

**prism**of the same altitude with the cylinder ; this**prism**is greater than half of thecylinder ; because if a square be described about the circle , and a

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### Andre utgaver - Vis alle

The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... Robert Simson Uten tilgangsbegrensning - 1775 |

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... Robert Simson Uten tilgangsbegrensning - 1827 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1781 |

### Vanlige uttrykk og setninger

added alſo altitude angle ABC angle BAC baſe BC is given becauſe Book Book XI caſe circle circle ABCD circumference common cone cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides firſt folid fore four fourth given angle given in poſition given in ſpecies given magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe magnitude manner meet muſt oppoſite parallel parallelogram perpendicular plane priſm produced PROP proportionals Propoſition pyramid reaſon rectangle remaining right angles ſame ſecond ſegment ſhall ſhewn ſides ſimilar ſolid ſquare ſquare of AC taken THEOR theſe third thro triangle ABC wherefore whole

### Populære avsnitt

Side 5 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 163 - 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 48 - 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 in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.

Side 73 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle; and no straight line can be drawn from the extremity between that straight line and the circumference, so as not to cut the circle...

Side 105 - 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. either the sides adjacent to the equal...

Side 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Side 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.

Side 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.

Side 47 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Side 37 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.