## 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 |

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Resultat 1-5 av 15

Side 41

41.1 .

double of the triangle FBC , because thicse also are upon the fame

between the fame parallels TB , GC . but the doubles of cquals are equal h to ...

41.1 .

**base**BD , and between the fame parallels BD , AL ; and the square GB isdouble of the triangle FBC , because thicse also are upon the fame

**base**FB , andbetween the fame parallels TB , GC . but the doubles of cquals are equal h to ...

Side 148

Scc N. TRIA TRIANGLES and parallelograms of the same altitude are one to

another as their

K , L , and take any number of straight lines BG , GH , each equal to the

...

Scc N. TRIA TRIANGLES and parallelograms of the same altitude are one to

another as their

**bases**. r Let the triangles ... Produce BD both ways to the pointsK , L , and take any number of straight lines BG , GH , each equal to the

**base**BC...

Side 184

... GK , and that they contain equal angles ; the

and the triangle GBC to the triangle GCK . and because the circumference BC is

equal to the circumference CK , the rčinaining part of the whole circumference of

...

... GK , and that they contain equal angles ; the

**base**BC is equal to the**base**CK ,and the triangle GBC to the triangle GCK . and because the circumference BC is

equal to the circumference CK , the rčinaining part of the whole circumference of

...

Side 209

... each to each ; and the

wherefore the angle ABC is equal to the angle LXMd . for the fame reason the

angle DEF is d . 6. 1 . equal to the angle MXN , and the R. angle GAK to the angle

NXL ...

... each to each ; and the

**base**AC is , by construction , equal to the**base**LM ;wherefore the angle ABC is equal to the angle LXMd . for the fame reason the

angle DEF is d . 6. 1 . equal to the angle MXN , and the R. angle GAK to the angle

NXL ...

Side 211

1 .

than the angle LXN , the angle XLN is greater than the angle BCP . therefore the

whole angle MLN is greater than the whole angle ACP . and because ML , LN

are ...

1 .

**base**. for the same reason , because the R angle GHK , or CBP , is greaterthan the angle LXN , the angle XLN is greater than the angle BCP . therefore the

whole angle MLN is greater than the whole angle ACP . and because ML , LN

are ...

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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.