## 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 - Trigonometry - 518 pages |

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Page 265

... are contained by the same planes ; and that the Pyramid of which the base is

the triangle ABD , and vertex the B. XII . point C , has been

OF EUCLID . 265 therefore, ex æquali c, as the base ABCDE ...

... are contained by the same planes ; and that the Pyramid of which the base is

the triangle ABD , and vertex the B. XII . point C , has been

**demonstrated**to 2 LOF EUCLID . 265 therefore, ex æquali c, as the base ABCDE ...

Page 272

B But it is also less , for it is contained F within the cylinder ; which is impossible .

Therefore the cylinder is not less than the triple of the cone . And it has been

triple ...

B But it is also less , for it is contained F within the cylinder ; which is impossible .

Therefore the cylinder is not less than the triple of the cone . And it has been

**demonstrated**that neither is it greater than the triple . Therefore the cylinder istriple ...

Page 281

axis KL and cylinder PG ; and of the axis KF and cylinder GD , B. XII . any

equimultiples whatever , viz . the axis KM and cylinder GQ : and it has been

greater than the ...

axis KL and cylinder PG ; and of the axis KF and cylinder GD , B. XII . any

equimultiples whatever , viz . the axis KM and cylinder GQ : and it has been

**demonstrated**, if the axis KL be greater than the axis KM , the cylinder PG isgreater than the ...

Page 289

... and therefore the straight line BZ is equal to ZK ; in the like manner it may be

are equal to BZ or ZK : therefore the circle described from the centre Z , and

distance ...

... and therefore the straight line BZ is equal to ZK ; in the like manner it may be

**demonstrated**, that the straight lines drawn from the point Z to the points ( ) , Sare equal to BZ or ZK : therefore the circle described from the centre Z , and

distance ...

Page 290

And that the other planes between the quadrants BX , KX fall without the lesser

sphere , is thus

plane of the quadrilateral SOPT , and join 10 ; and , as was

plane ...

And that the other planes between the quadrants BX , KX fall without the lesser

sphere , is thus

**demonstrated**: from the point A draw AI perpendicular to theplane of the quadrilateral SOPT , and join 10 ; and , as was

**demonstrated**of theplane ...

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The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid No preview available - 2018 |

The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid No preview available - 2015 |

The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson No preview available - 2017 |

### Common terms and phrases

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

### Popular passages

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

Page 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.

Page 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...

Page 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.

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

Page 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.

Page 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.

Page 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.

Page 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.

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