## 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 páginas |

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Página 270

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**cylinder**; this prism is greater than half of the**cylinder**; because if a square be described about the circle , and a prism erected upon the square , of the same altitude with the**cylinder**, the inscribed square is half of that ... Página 271

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**cylinder**, that B. XII . is , the prism of which the base is the polygon AEBFCGDH , and of which the altitude is the same with that of the**cylinder**, is greater than the triple of the cone : but this prism is tripled of d 1. Cor . the ... Página 272

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**cylinder**. But this pyramid is the third part of the prism upon the same base AEBFCGDH , and of the same altitude with the**cylinder**. Therefore this prism is greater than the**cylinder**of which the base is the circle ABCD . But it is ... Página 271

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**cylinder**, that B. XII . is , the prism of which the base is the polygon AEBFCGDH , and of which the altitude is the same with that of the**cylinder**, is greater than the triple of the cone : but this prism is triple d of d 1. Cor . the ... Página 275

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**cylinder**to the**cylinder**, because b'15 . 5 . the**cylinders**are triple of the cone , each to each . Therefore , c 10. 12 . as the circle ABCD to the circle EFGH , so are the**cylinders**up- on them of the same altitude . Wherefore , cones ...### Términos y frases comunes

altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gnomon greater join less Let ABC meet multiple opposite parallel parallelogram parallelogram AC perpendicular point F polygon prism proposition pyramid Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelepipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore

### Pasajes populares

Página 28 - Any two sides of a triangle are together greater than the third side.

Página 62 - 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.

Página 28 - 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...

Página 57 - 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.

Página 26 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.

Página 163 - 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.

Página 17 - 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.

Página 189 - 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.

Página 37 - 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.

Página 178 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.