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 23
... perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be produced to any length both ways , and let C be a point without it ; it is re- quired to ...
... perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be produced to any length both ways , and let C be a point without it ; it is re- quired to ...
Page 206
... perpendicular to the plane BH . In the plane draw any straight line BC , and from the point A draw a AD perpendicular to BC . If then AD be also perpendi- cular to the plane BH , the thing required is already done ; but if it be not ...
... perpendicular to the plane BH . In the plane draw any straight line BC , and from the point A draw a AD perpendicular to BC . If then AD be also perpendi- cular to the plane BH , the thing required is already done ; but if it be not ...
Page 207
... perpendicular to DE : therefore AF is perpendicular to each of the straight lines GH , DE . But if a straight line stands at right angles to each of two straight lines in the point of their intersection , it shall also be at right ...
... perpendicular to DE : therefore AF is perpendicular to each of the straight lines GH , DE . But if a straight line stands at right angles to each of two straight lines in the point of their intersection , it shall also be at right ...
Page 209
... perpendicular to BC : since therefore the straight line GB stands at right angles to the two straight lines BA , BC , that cut one another in B , GB is perpendicularf to the plane through BA , BC ; and it is f 4. 11 . perpendicular to ...
... perpendicular to BC : since therefore the straight line GB stands at right angles to the two straight lines BA , BC , that cut one another in B , GB is perpendicularf to the plane through BA , BC ; and it is f 4. 11 . perpendicular to ...
Page 212
... perpendicular to a third plane , their common section shall be perpendicular to the same plane . Let the two planes AB , BC be each of them perpendicular to a third plane , and let BD be the common section of the first two ; BD is ...
... perpendicular to a third plane , their common section shall be perpendicular to the same plane . Let the two planes AB , BC be each of them perpendicular to a third plane , and let BD be the common section of the first two ; BD is ...
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 ratio given straight line gnomon greater join less Let ABC line BC meet multiple opposite parallel parallelogram perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure right angles segment side BC similar sine solid angle solid parallelepipeds square of AC straight line AB straight line AC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Popular passages
Page 26 - Any two sides of a triangle are together greater than the third side.
Page 60 - 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 26 - 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 55 - 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 24 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Page 161 - 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 15 - 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 187 - 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 35 - 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 176 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.