## 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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Side 167

Next , Let it be required to describe upon a

figure similar , and similarly situated to the rectilineal figure CDKEF of ... SIMILA

IMILAR triangles are to one another in the duplicate

fides .

Next , Let it be required to describe upon a

**given**straight line AB , a rectilinealfigure similar , and similarly situated to the rectilineal figure CDKEF of ... SIMILA

IMILAR triangles are to one another in the duplicate

**ratio**of their homologousfides .

Side 369

D BEC Let the excess of the magnitude AB above a given magnitude , have a

a given magnitude , has a

D BEC Let the excess of the magnitude AB above a given magnitude , have a

**given ratio**to the magnitude BC ; the excess of AC , both of them together , abovea given magnitude , has a

**given ratio**to BC . Let AD be the given magnitude the ... Side 370

Ę DBC Let AD be the given magnitude ; and because DB , the excess of AB

above AD , has a

make : he ratio of AD to DE the same with this ratio ; therefore the ratio of AD to

DE is ...

Ę DBC Let AD be the given magnitude ; and because DB , the excess of AB

above AD , has a

**given ratio**to BC ; the ratio of DC to DB is 2. 7. Dat . givena .make : he ratio of AD to DE the same with this ratio ; therefore the ratio of AD to

DE is ...

Side 375

S fore b AG is

the

than AG . and C F D AB , AG are

...

S fore b AG is

**given**; and because the**ratio**of AB to CD is greater b . 2. Dät . thanthe

**ratio**of ( AE to CF , that is , than the**ratio**of ) AG to CD ; A GB AB is greaterthan AG . and C F D AB , AG are

**given**, therefore the remainder BG is**given**. and...

Side 377

Because GD has a

the ratio of CG to HA is given ; and CG is given , wherefore a HA is given . and

because as GD to AB , so is CG a . 2. Dat . to HA , and so is b CD to HB ; the ratio

...

Because GD has a

**given ratio**to AB , as GD to AB , so make CG to HA ; thereforethe ratio of CG to HA is given ; and CG is given , wherefore a HA is given . and

because as GD to AB , so is CG a . 2. Dat . to HA , and so is b CD to HB ; the ratio

...

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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.