## 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 twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 sider |

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Resultat 1-5 av 6

Side 34

For , if it be not parallel , AB and CD being produced shall

D , or towards A , C ; let them be produced and

; therefore GEF a 16. 1. is a triangle , and its exterior angle AEF is greater a ...

For , if it be not parallel , AB and CD being produced shall

**meet**either towards B ,D , or towards A , C ; let them be produced and

**meet**towards B , D , in the point G; therefore GEF a 16. 1. is a triangle , and its exterior angle AEF is greater a ...

Side 209

IF two straight lines meeting one another , be pa- See N. rallel to two straight

lines which

the plane which passes through these is parallel to the plane passing through the

...

IF two straight lines meeting one another , be pa- See N. rallel to two straight

lines which

**meet**one another , but are not in the same plane with the first two ;the plane which passes through these is parallel to the plane passing through the

...

Side 210

For , if it is not , EF , GH shall

first , let them be produced on the side of FH , and

since EFK is in the plane AB , every point in K EFK is in that plane : and K is a ...

For , if it is not , EF , GH shall

**meet**, if produced , either on the side of FH , or EG :first , let them be produced on the side of FH , and

**meet**in the point K ; therefore ,since EFK is in the plane AB , every point in K EFK is in that plane : and K is a ...

Side 348

The words at the end of this , “ for a straight line cannot

more than one point , ” are left out , as an addition by some unskilful hand ; for

this is to be demonstrated , not assumed . Mr. Thomas Simpson , in his notes at

the ...

The words at the end of this , “ for a straight line cannot

**meet**a straight line inmore than one point , ” are left out , as an addition by some unskilful hand ; for

this is to be demonstrated , not assumed . Mr. Thomas Simpson , in his notes at

the ...

Side 349

lines meeting one another ; the thing that should have been de - Book XI .

monstrated is , that two , or three straight lines , that

plane . And as this is not sufficiently done , the enunciation and demonstration

are ...

lines meeting one another ; the thing that should have been de - Book XI .

monstrated is , that two , or three straight lines , that

**meet**one another are in oneplane . And as this is not sufficiently done , the enunciation and demonstration

are ...

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The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2015 |

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

### Vanlige uttrykk og setninger

ABCD added altitude angle ABC angle BAC base Book centre circle circle ABC circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples excess 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 multiple opposite parallel parallelogram pass perpendicular plane prisms produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 30 - Any two sides of a triangle are together greater than the third side.

Side 64 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.

Side 30 - IF, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let...

Side 59 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.

Side 165 - 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 19 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.

Side 191 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.

Side 39 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.

Side 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.