## 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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**wherefore**AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC .**Wherefore**from the given point A a straight line AL has been drawn equal ... Página 17

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**wherefore**also the point C shall coincide with the point F , because the straight line AC is equal to DF : but the point B coincides with the point E ;**wherefore**the base BC shall coincide with the base EF , because the point B ... Página 21

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**wherefore**, likewise , the angle BAC coincides with the angle EDF , and is equal to it . Therefore , if two triangles , b 8. Ax . & c . Q. E. D. PROP . IX . PROB . TO bisect a given rectilineal angle , that is , to di- vide it into two ... Página 25

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**Wherefore**, if at a point , & c . Q. E. D. PROP . XV . THEOR . IF two straight lines cut one another , the vertical , or opposite , angles shall be equal . Let the two straight lines AB , CD cut one another in the point E ; the angle ... Página 33

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**wherefore**also the angle BCG is equal to the angle BCA , the less to the greater , which is im- possible ; therefore ...**wherefore**BC is not unequal to EF , that is , it is b 16. 1 . equal to it ; and AB is equal to DE ; therefore the ...### Otras ediciones - Ver todas

### 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 perpendicular point F polygon prisms proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure right angles segment sides BA similar sine 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 30 - Any two sides of a triangle are together greater than the third side.

Página 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.

Página 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...

Página 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.

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

Página 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.

Página 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.

Página 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.

Página 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.

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