## 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 6-10 av 14

Side 184

3. rence EN , the angle BGL is also equal a to the angle EHN ; and if the

circumference BL be

EHN ; and if lefs , less . there being then four magnitudes , the two

circumferences BC , EF ...

3. rence EN , the angle BGL is also equal a to the angle EHN ; and if the

circumference BL be

**greater**than EN , likewise the angle BGL is**greater**thanEHN ; and if lefs , less . there being then four magnitudes , the two

circumferences BC , EF ...

Side 209

... and about the triangle LMN describe a circle , and find its center X , which will

either be within c . s .. the triangle , or in one of its fides , or without it . First , Let

the center X be within the triangle , and join LX , MX , NX . AB is

if ...

... and about the triangle LMN describe a circle , and find its center X , which will

either be within c . s .. the triangle , or in one of its fides , or without it . First , Let

the center X be within the triangle , and join LX , MX , NX . AB is

**greater**than LX .if ...

Side 211

MN , the angle MXN is equal to the angle DEF . and it has been Book XI . proved

that it is

yet is it less ; for then , as has been proved d . 8 . in the first case , the angle ABC

...

MN , the angle MXN is equal to the angle DEF . and it has been Book XI . proved

that it is

**greater**than DEF , which is abfurd . therefore AB is not equal to LX . noryet is it less ; for then , as has been proved d . 8 . in the first case , the angle ABC

...

Side 265

12 . ramid ; therefore the pyramid of which the base is the square EFGH , and its

vertex the same with that of the cone , is

circumferences EF , FG , GH , HE , each into two equal parts in the points O , P ...

12 . ramid ; therefore the pyramid of which the base is the square EFGH , and its

vertex the same with that of the cone , is

**greater**than half of the cone , divide thecircumferences EF , FG , GH , HE , each into two equal parts in the points O , P ...

Side 327

To apply a rectangle which shall be equal to a given square , to a given straight

line , deficient by a square . but the given square must not be

upon the half of the given line . Let AB be the given straight line , and let the

square ...

To apply a rectangle which shall be equal to a given square , to a given straight

line , deficient by a square . but the given square must not be

**greater**than thatupon the half of the given line . Let AB be the given straight line , and let the

square ...

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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.