## The Elements of Euclid, Viz: 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. the first six books, together with the eleventh and twelfth |

### Inni boken

Resultat 1-5 av 86

Side 13

POST U L A T E S. 1 L I. ET it be granted that a straight line may be drawn from

any one point to any other point . II . That a terminated straight line may be

produced to any length in a flraight line . III . And that a circle may be

from any ...

POST U L A T E S. 1 L I. ET it be granted that a straight line may be drawn from

any one point to any other point . II . That a terminated straight line may be

produced to any length in a flraight line . III . And that a circle may be

**described**from any ...

Side 15

Let AB be the given straight line ; it is required to

upon it . ... AB , d . ift Asis BC are equal to one another ; and the triangle ABC is

there - om . fore equilateral , and it is

Let AB be the given straight line ; it is required to

**describe**an equilateral triangleupon it . ... AB , d . ift Asis BC are equal to one another ; and the triangle ABC is

there - om . fore equilateral , and it is

**described**upon the given straight line AB . Side 44

1 .

of its angles equal to a given rectilineal ... ABC , and it has one of its angles CEF

equal to the given angle D : Wherefore there has been

1 .

**describe**a parallelogram that shall be equal to a given triangle , and have oneof its angles equal to a given rectilineal ... ABC , and it has one of its angles CEF

equal to the given angle D : Wherefore there has been

**described**a paralled 38. Side 47

... rectilineal figure ABCD is equal to the whole parallelogram KFLM ; therefore

the parallelogram KFLM has been

ABCD , having the angle FKM equal to the given angle L. Which was to be done .

... rectilineal figure ABCD is equal to the whole parallelogram KFLM ; therefore

the parallelogram KFLM has been

**described**equal to the given rectilineal figureABCD , having the angle FKM equal to the given angle L. Which was to be done .

Side 48

I. D Let AB be the given straight line ; it is required to

... and it has been demonstrated that it is equilateral ; it is therefore a square , and

it is

I. D Let AB be the given straight line ; it is required to

**describe**a square upon AB .... and it has been demonstrated that it is equilateral ; it is therefore a square , and

it is

**described**upon the given straight line AB : Which was to be done . Cor .### Hva folk mener - Skriv en omtale

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### Andre utgaver - Vis alle

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 |

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 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 magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe magnitude manner meet muſt oppoſite parallel parallelogram perpendicular plane produced prop proportionals propoſition pyramid radius rectangle rectangle contained remaining right angles ſame ſecond ſegment ſhall ſides ſimilar ſolid ſphere ſquare ſquare of AC Take taken theſe third triangle ABC wherefore whole

### Populære avsnitt

Side 32 - 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 165 - D ; wherefore the remaining angle at C is equal to the remaining angle at F ; Therefore the triangle ABC is equiangular to the triangle DEF.

Side 170 - 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 10 - When several angles are at one point B, any ' one of them is expressed by three letters, of which ' the letter that is at the vertex of the angle, that is, at ' the point in which the straight lines that contain the ' angle meet one another, is put between the other two ' letters, and one of these two is...

Side 55 - 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 32 - ... then shall the other sides be equal, each to each; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.

Side 45 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Side 211 - AB shall be at right angles to the plane CK. Let any plane DE pass through AB, and let CE be the common section of the planes DE, CK ; take any point F in CE, from which draw FG in the plane DE at right D angles to CE ; and because AB is , perpendicular to the plane CK, therefore it is also perpendicular to every straight line in that plane meeting it (3.

Side 38 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 304 - Thus, if B be the extremity of the line AB, or the common extremity of the two lines AB, KB, this extremity is called a point, and has no length : For if it have any, this length must either be part of the length of the line AB, or of the line KB.