## 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, 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

But indeed this Proposition , which makes the 1 oth Definition of the i Ith Book , is

not true universally , except in the

figures is contained by no more than three plane angles ; for , in other

...

But indeed this Proposition , which makes the 1 oth Definition of the i Ith Book , is

not true universally , except in the

**case**in which each of the folid angles of thefigures is contained by no more than three plane angles ; for , in other

**cases**, two...

Side 167

Join DE , and upon the given straight line AB describe the rectilineal figure ABHG

similar and similarly situated to the quadrilateral figure CDEF , by the former

. and at the points B , H in the straight line BH , make the angle HBL equal to ...

Join DE , and upon the given straight line AB describe the rectilineal figure ABHG

similar and similarly situated to the quadrilateral figure CDEF , by the former

**case**. and at the points B , H in the straight line BH , make the angle HBL equal to ...

Side 211

1 . therefore AB is not equal to LX . nor yet is it lefs ; for then , as has been proved

in the first

GHK greater than the angle LXN . at the point B in the straight line CB make the ...

1 . therefore AB is not equal to LX . nor yet is it lefs ; for then , as has been proved

in the first

**case**, the angle ABC is greater than the angle MXL , and the angleGHK greater than the angle LXN . at the point B in the straight line CB make the ...

Side 292

B. I. There are two

but is as necessary as the other , and ... 5. which is necessary to the

Demonstration of this

else , but ...

B. I. There are two

**cases**of this Proposition , one of which is not ia the Greek text ,but is as necessary as the other , and ... 5. which is necessary to the

Demonstration of this

**case**, can be of no use at all in the Elements , or any whereelse , but ...

Side 303

Propositions are divided into more

than are necessary . Nor can it be supposed that Euclid omitted them because

they are easy ; as he has given the

viz ...

Propositions are divided into more

**cases**, so this 35. is divided into fewer**cases**than are necessary . Nor can it be supposed that Euclid omitted them because

they are easy ; as he has given the

**case**which by far is the easiest of them all ,viz ...

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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 Ago ... Robert Simson Uten tilgangsbegrensning - 1762 |

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

### Vanlige uttrykk og setninger

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

### Populære avsnitt

Side 156 - 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 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 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 92 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square- of the line which meets it, the line which meets shall touch the circle.

Side 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.

Side 52 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.

Side 36 - 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 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.

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 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...