## 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 |

### Inni boken

Side 262

Book XII . greater than the

ereét a prikin of the fame altitude with the cylinder ; this priim is greater than

of the cylinder ; because if a square be defcribed about the circle , and a piiiin

crected ...

Book XII . greater than the

**half**of the circle ABCD + . upon the square ABCDereét a prikin of the fame altitude with the cylinder ; this priim is greater than

**half**of the cylinder ; because if a square be defcribed about the circle , and a piiiin

crected ...

Side 5

IN N a plain triangle , the sum of any two sides is to their difference , as the

tangent of

difference . Let ABC be a plain triangle , the sum of any two fides AB , AC will be

to their ...

IN N a plain triangle , the sum of any two sides is to their difference , as the

tangent of

**half**the sum of the angles at the base , to the tangent of**half**theirdifference . Let ABC be a plain triangle , the sum of any two fides AB , AC will be

to their ...

Side 9

the given fum , AC the greater , and BC the less . Let AD be

and ...

**Half**the given sum added 10**half**the given difference , will be the greater , and**half**the difference subtracted from**half**the sum , will be the lefs . For , let AB bethe given fum , AC the greater , and BC the less . Let AD be

**half**the given fuin ;and ...

Side 34

THE rectangle contained by

lines of two arches , is equal to the rectangle contained by the fines of

fum , and

THE rectangle contained by

**half**of the radius , and ' HE the excess of the versedlines of two arches , is equal to the rectangle contained by the fines of

**half**thefum , and

**half**the difference of the fame arches , Let AB , AC be any two arches ... Side 35

BE or AE therefore is the fine of the arch DB or AD , the

perpendicular to AC , and AF will be the versed fine of the arch BA ; but , because

of the similar triangles CAE , BAF , CA is to AE as AB , that is , twice AE to AF ;

and ...

BE or AE therefore is the fine of the arch DB or AD , the

**half**of AB : let BF beperpendicular to AC , and AF will be the versed fine of the arch BA ; but , because

of the similar triangles CAE , BAF , CA is to AE as AB , that is , twice AE to AF ;

and ...

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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...