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 pages |
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Page 71
... circle two straight lines cut one another which do not both pass through the centre , they do not bisect each other . Let ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do not both ...
... circle two straight lines cut one another which do not both pass through the centre , they do not bisect each other . Let ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do not both ...
Page 73
... ABCD be a circle , and AD its diameter , in which let any point F be taken which is not the centre ; let the centre be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA is the greatest ...
... ABCD be a circle , and AD its diameter , in which let any point F be taken which is not the centre ; let the centre be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA is the greatest ...
Page 80
... circle ; and , of all others , that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less . Let ABCD be a circle , of which the diameter is AD , and the centre E ...
... circle ; and , of all others , that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less . Let ABCD be a circle , of which the diameter is AD , and the centre E ...
Page 85
... ABC be a circle , and BEC an angle at the centre , and Book III . BAC an angle at the circumference , which have the same cir- cumference BC for their base ; the angle BEC is double of the angle BAC . A First , let E the centre of the ...
... ABC be a circle , and BEC an angle at the centre , and Book III . BAC an angle at the circumference , which have the same cir- cumference BC for their base ; the angle BEC is double of the angle BAC . A First , let E the centre of the ...
Page 86
... circle are together equal to two right angles . Let ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles are together equal to two right angles . Join AC , BD ; and because the three angles of every tri- a ...
... circle are together equal to two right angles . Let ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles are together equal to two right angles . Join AC , BD ; and because the three angles of every tri- a ...
Common terms and phrases
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
Popular passages
Page 28 - Any two sides of a triangle are together greater than the third side.
Page 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.
Page 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...
Page 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.
Page 26 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Page 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.
Page 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.
Page 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.
Page 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.
Page 178 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.